Read the breakthroughs in order, with the mechanism, evidence and limits beside each event. The worked examples explain gate order, error checks and how to read a research result.
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The full chronology
217 events. Dates distinguish proposals, preprints, publications, experiments and other milestones.
1801–1964 / Discover the rules
What makes the quantum world different?
Begin with waves, discrete energy and the probabilities of measurement. These are clues about nature, long before they become ingredients for a computer.
· Presentation
Young explains how light waves can cancel
Light added to light can make a dark band. Thomas Young explained how two waves reinforce each other where their peaks line up and cancel where a peak meets a trough.
Why it mattered. Quantum algorithms also rely on reinforcement and cancellation. What combines in a quantum circuit is an amplitude, a quantity used to calculate the chance of a particular result.
Interference. The reinforcement or cancellation that happens when wave contributions combine.
Still to solve. Young was describing ordinary light waves in his 1801 lecture. The paper appeared in 1802, about a century before the development of quantum mechanics.
Where does a dark fringe come from?
At one point on a screen, equal light waves arriving half a cycle apart have opposite electric fields. Their fields add to zero there. Elsewhere they can add together. Young’s example concerns light waves; a quantum circuit instead adds amplitudes for a particular measurement outcome.
Young reads his Bakerian lecture on light and colours to the Royal Society. This is the lecture date, not the invention of quantum mechanics. The Philosophical Transactions paper followed in 1802.
The next question. A wave can reinforce or cancel another wave. Much later, physicists would discover that nature needed more than this classical picture.
· Historical context
Kirchhoff frames the black-body problem
Hot objects emit characteristic spectra.
Why it mattered. Black-body radiation later motivates quantization.
Still to solve. Classical precursor, not quantum computing.
Historical record and sources
Kirchhoff defines an ideal radiation absorber and emitter. Classical precursor, not quantum computing.
Planck connects the size of an energy step to frequency
Why does a hot object emit more light at some frequencies than at others? Max Planck calculated its spectrum by counting energy in steps. The higher the frequency of an oscillator, the larger each energy step.
Why it mattered. Doubling the frequency doubled the energy in each step. It gave physicists a way to connect a measurable spectrum to a microscopic model.
Quantum. A discrete amount; “quanta” is the plural. Planck connected its energy to frequency.
Still to solve. Planck was explaining heat radiation. His original proposal was not yet the modern picture of light particles or quantum computers.
Are all energy steps the same height?
Planck’s energy element is h times the oscillator’s frequency, where h is Planck’s constant. Double the frequency and the element doubles. This was a way to calculate the spectrum of hot objects. Einstein later asked whether light itself could transfer energy in packets.
Planck derives the radiation law using discrete energy elements. This dates the 14 December presentation. The expanded paper followed in 1901; the model was not yet modern photon theory.
The next question. Discrete energy exchange was one clue. The next challenge was finding rules that could predict the results of experiments.
· Publication
Einstein proposes light quanta
Brighter light and higher-frequency light change different aspects of emission.
Why it mattered. Extends quantization to the interaction of light and matter.
Still to solve. His 1921 Nobel Prize was awarded in 1922.
Why can brighter light still fail to release electrons?
In the simple one-photon picture, one electron absorbs energy from one photon. The photon’s energy depends on frequency. Increasing the number of low-energy photons does not make each photon energetic enough to eject an electron.
Einstein explains the photoelectric effect using energy packets tied to light frequency. His 1921 Nobel Prize was awarded in 1922.
Albert Einstein: Facts · Nobel Prize · Undated institutional profile; its associated Nobel year is not a webpage publication date.
· Experiment
Helium is liquefied
Very cold environments reveal otherwise hidden material behavior.
Why it mattered. Opens access to temperatures important for later quantum hardware.
Still to solve. Cryogenic capability is an enabling technology.
Historical record and sources
Kamerlingh Onnes produces liquid helium. Cryogenic capability is an enabling technology.
Heike Kamerlingh Onnes: Facts · Nobel Prize · Kamerlingh Onnes liquefied helium in 1908 and observed superconductivity in 1911. He received the Nobel Prize in 1913.
· Experiment
Superconductivity is discovered
Electrical current can flow through a superconducting material without resistance.
Why it mattered. Begins the material lineage of superconducting quantum circuits.
Still to solve. Superconductivity alone does not constitute a quantum processor.
How far is a superconductor from a qubit?
Cold mercury carried current without electrical resistance. To make a qubit, engineers also need two states that they can select, manipulate and distinguish in a measurement. The Josephson junction later supplied a crucial circuit element.
Mercury loses its measured electrical resistance at very low temperature. Superconductivity alone does not constitute a quantum processor.
Heike Kamerlingh Onnes: Facts · Nobel Prize · Kamerlingh Onnes liquefied helium in 1908 and observed superconductivity in 1911. He received the Nobel Prize in 1913.
· Publication
Rutherford publishes the nuclear atom
Most atomic volume is not occupied by the nucleus.
Why it mattered. Sets up the atomic-structure problem addressed by quantum models.
Still to solve. The scattering experiments preceded the 1911 interpretation.
Historical record and sources
Rutherford explains scattering results through a small, dense atomic nucleus. The scattering experiments preceded the 1911 interpretation.
Atoms exchange specific amounts of energy when their state changes.
Why it mattered. Connects atomic spectra with discrete quantum states.
Still to solve. Orbit pictures are historical models, not literal modern electron trajectories.
Why does hydrogen emit particular colors?
In Bohr’s historical model, an atom can occupy only certain energies. Moving between them exchanges energy equal to the difference, giving light of a particular frequency. Modern quantum states describe these energies without requiring an electron to follow a miniature planetary orbit.
Bohr models hydrogen using allowed electron energies and transitions between them. Orbit pictures are historical models, not literal modern electron trajectories.
Niels Bohr: Facts · Nobel Prize · Undated institutional profile; its associated Nobel year is not a webpage publication date.
· Experiment
Franck and Hertz probe atomic excitation
Atoms absorb particular energy increments instead of every possible amount.
Why it mattered. Provides experimental evidence for quantized atomic energy changes.
Still to solve. Evidence for discrete excitation energies does not validate every detail of Bohr's atomic model.
Historical record and sources
Electron collisions reveal discrete excitation energies in mercury atoms. Evidence for discrete excitation energies does not validate every detail of Bohr's atomic model.
A quantum measurement can give separated outcomes rather than a continuous spread.
Why it mattered. Makes quantized measurement outcomes visible.
Still to solve. Electron spin was not the original interpretation; exact-day accounts differ.
What did the detector actually record?
A magnetic-field gradient sent a beam of silver atoms into two separated groups. The apparatus registered positions on a detector. The later spin description explains the two possible projections along the chosen axis; it does not depict a little sphere turning in space.
A silver-atom beam separates into discrete components in a magnetic-field gradient. Electron spin was not the original interpretation; exact-day accounts differ.
Identical quantum particles are counted differently from distinguishable objects.
Why it mattered. Introduces a quantum way of counting indistinguishable particles.
Still to solve. Bose worked in Dhaka, then part of British India and today the capital of Bangladesh.
Historical record and sources
Bose derives the Planck distribution statistically and sends his paper to Einstein. Bose worked in Dhaka, then part of British India and today the capital of Bangladesh.
Particles can produce interference patterns under suitable conditions.
Why it mattered. Expands wave-particle reasoning beyond light.
Still to solve. The proposal preceded the later electron-diffraction experiments.
What could test a wave description of matter?
De Broglie associated momentum with wavelength: greater momentum corresponds to shorter wavelength. A crystal can act as a regularly spaced scatterer. Later electron diffraction tested the prediction by recording a pattern of arrivals across many electrons.
Why it mattered. A mathematical framework for quantum predictions.
Still to solve. Heisenberg proposed the new rules. Max Born and Pascual Jordan recognized and developed their matrix form.
Can changing the order change the answer?
In the matrix formulation developed by Heisenberg, Born and Jordan, multiplying two quantities in one order can give a different result from multiplying them in reverse. Quantum gates provide a modern example: swapping two successive operations can change a circuit’s final state.
Heisenberg's framework becomes matrix mechanics through work with Born and Jordan. Heisenberg proposed the new rules. Max Born and Pascual Jordan recognized and developed their matrix form.
Certain particles cannot occupy the same complete quantum state.
Why it mattered. Explains essential structure in atoms and materials.
Still to solve. This rule applies to identical fermions, not to all particles.
Historical record and sources
Pauli states that electrons in an atom cannot share identical sets of quantum numbers. This rule applies to identical fermions, not to all particles.
Wolfgang Pauli: Facts · Nobel Prize · Undated institutional profile; its associated Nobel year is not a webpage publication date.
· Publication
Born connects the wave equation to a detector reading
In a collision experiment, an electron can scatter in several directions. Max Born interpreted the wave calculation as a prediction of how likely each direction was. Repeating the experiment could test that prediction.
Why it mattered. A qubit follows the same rule. To predict how often a particular answer will appear, take the squared magnitude of the amplitude for that answer.
Measurement. An interaction that produces a recorded outcome, such as reading a qubit as 0 or 1.
Still to solve. Probabilistic results do not let us read every possible answer at once. Measurement returns an outcome, not the whole mathematical description.
What do repeated measurements estimate?
For an ideal qubit measured in the 0/1 basis, each outcome’s probability is the squared magnitude of its amplitude. To estimate those probabilities, prepare the qubit the same way for each trial. Measuring the same qubit again immediately is a different experiment.
The next question. A rule for measurement also raises a question: what happens when two systems must be described together?
· Publication
Schrodinger develops wave mechanics
His equation predicts a state's changes.
Why it mattered. Enables calculations of quantum-state evolution.
Still to solve. Wavefunctions are not simply visible material waves.
What evolves before a measurement?
Given a starting state and a Hamiltonian describing an isolated system’s dynamics, Schrödinger’s equation determines how that state evolves. The Born rule then turns the state into probabilities for the chosen measurement. Knowing that evolution need not determine which individual result you will see.
Einstein, Podolsky and Rosen challenge completeness
Two separated systems can have linked measurement predictions.
Why it mattered. Makes distant quantum correlations a central scientific problem.
Still to solve. The paper argues a conceptual position; it does not demonstrate faster-than-light messaging.
What belongs to the pair?
An entangled pair can have a definite joint relationship even when each individual outcome is uncertain. EPR asked what that implies for the completeness of quantum mechanics. Bell later turned a related question into a test of correlations between measurements.
EPR use correlated systems to question whether quantum mechanics gives a complete account of reality. The paper argues a conceptual position; it does not demonstrate faster-than-light messaging.
Knowing a joint state is different from knowing two independent states.
Why it mattered. Helps establish entanglement as a distinctive quantum feature.
Still to solve. The journal published the paper in 1935. The 2008 date on its website marks its online appearance.
Historical record and sources
Schrodinger examines probability relations for separated systems described by a shared state. The journal published the paper in 1935. The 2008 date on its website marks its online appearance.
An abstract machine makes precise what an algorithm can do.
Why it mattered. Supplies a classical benchmark for later quantum computation theory.
Still to solve. Submission is in 1936; this publisher lists the journal publication in 1937.
What does it mean to program a machine?
Turing described an ideal machine that reads a symbol, follows a rule and moves on a tape. A universal machine can read an encoded description of another machine and simulate it. The idea separates the instructions for a calculation from the material used to build a device.
Turing submits the paper defining a machine-based approach to computability. Submission is in 1936; this publisher lists the journal publication in 1937.
An oscillating field can drive a quantum system between states.
Why it mattered. Builds theoretical tools for resonant quantum control.
Still to solve. A theoretical publication, separate from the subsequent beam experiment.
Historical record and sources
Rabi calculates transitions of angular-momentum systems in a rotating magnetic field. A theoretical publication, separate from the subsequent beam experiment.
Matching a drive frequency to a transition changes the detected beam.
Why it mattered. Demonstrates controlled transitions for precision measurement.
Still to solve. The experiment dates to 1938; the detailed paper followed in 1939.
Historical record and sources
Rabi and colleagues perform a successful molecular-beam magnetic-resonance experiment. The experiment dates to 1938; the detailed paper followed in 1939.
A population of spins can create a measurable radio-frequency signal.
Why it mattered. Connects spin dynamics with electrical readout.
Still to solve. Felix Bloch and his collaborators at Stanford pursued this approach independently of Edward Purcell’s group at Harvard.
Historical record and sources
Bloch describes how driven nuclear polarization produces observable induction signals. Felix Bloch and his collaborators at Stanford pursued this approach independently of Edward Purcell’s group at Harvard.
Shannon publishes a mathematical theory of communication
Information can be measured and communication limits calculated.
Why it mattered. Provides the classical reference point for quantum information theory.
Still to solve. This work concerns classical information.
How can information have a unit?
For two equally likely outcomes, seeing which occurred resolves one bit of uncertainty. When one outcome is much more likely, the average uncertainty is smaller. Shannon’s quantity depends on the probabilities of the alternatives, independent of what their messages mean.
The same experimental predictions can be discussed through different conceptual accounts.
Why it mattered. Clarifies that mathematical predictions and interpretations are distinct.
Still to solve. This is an interpretation of quantum theory, not a separately verified physical mechanism.
Historical record and sources
Bohm presents an alternative interpretation reproducing standard quantum predictions in its domain. This is an interpretation of quantum theory, not a separately verified physical mechanism.
Stimulated emission can create coordinated electromagnetic radiation.
Why it mattered. Enables coherent-radiation technology.
Still to solve. The device amplified microwaves. A laser uses the same principle at much shorter wavelengths.
Historical record and sources
Townes and colleagues obtain microwave amplification and generation by stimulated emission. The device amplified microwaves. A laser uses the same principle at much shorter wavelengths.
Charles H. Townes: Biographical · Nobel Prize · Undated institutional profile; its associated Nobel year is not a webpage publication date.
· Publication
Everett publishes the relative-state formulation
A description of a subsystem can depend on its relation to the rest.
Why it mattered. Adds an influential interpretation of measurement.
Still to solve. The formulation is not experimental proof of parallel universes.
Historical record and sources
Everett publishes a relative-state approach to quantum mechanics. The formulation is not experimental proof of parallel universes.
BCS theory explains conventional superconductivity
Collective behavior of paired electrons differs from independent electrons.
Why it mattered. Explains a material foundation of superconducting circuits.
Still to solve. BCS theory describes conventional superconductivity; it does not explain every superconducting material.
Historical record and sources
BCS theory describes a superconducting state involving paired electrons. BCS theory describes conventional superconductivity; it does not explain every superconducting material.
The same amplification principle can extend to visible light.
Why it mattered. Provides a blueprint for laser development.
Still to solve. Proposal and working laser demonstration have separate dates.
Historical record and sources
Schawlow and Townes publish a route from masers to optical and infrared operation. Proposal and working laser demonstration have separate dates.
Charles H. Townes: Biographical · Nobel Prize · Undated institutional profile; its associated Nobel year is not a webpage publication date.
· Publication
Aharonov and Bohm highlight quantum phase
Paths can acquire different phases and change interference outcomes.
Why it mattered. Shows why phase is physically consequential.
Still to solve. A proposal is not the same record as a later experimental verification.
Historical record and sources
Aharonov and Bohm predict effects of electromagnetic potentials on quantum interference. A proposal is not the same record as a later experimental verification.
Why it mattered. Establishes that information processing has physical consequences.
Still to solve. The familiar erasure bound requires stated thermodynamic assumptions.
Why does resetting a bit have a cost?
Resetting either 0 or 1 to the same value discards which input you had. For an initially unbiased bit in the ideal thermal setting, the minimum heat released to a reservoir at absolute temperature T is kT ln 2, where k is Boltzmann’s constant. Actual devices can dissipate much more.
Quantum behavior can link two superconductors through a thin barrier.
Why it mattered. Establishes a component used in later superconducting qubits.
Still to solve. The cited event is the prediction, not experimental confirmation.
How can a thin barrier become a circuit element?
Josephson predicted that a supercurrent can tunnel between superconductors separated by a thin barrier. In later qubit circuits the junction provides nonlinearity, making it possible to drive one energy transition selectively. The original proposal described a junction, decades before those devices.
Bell gives experimenters a way to test entanglement
Could two distant particles simply carry a shared set of instructions for how to respond? John Bell showed that such local explanations obey a limit on how often the answers can agree across different measurement settings. For certain entangled states, quantum theory predicts correlations beyond that limit.
Why it mattered. Seeing two matching results is easy to explain with ordinary shared information. Comparing results at different settings lets experimenters test a stronger prediction.
Entanglement. A shared quantum state that cannot be described as independent states of its parts, even allowing ordinary randomness.
Still to solve. Bell supplied the theoretical test; experiments followed. Violating a Bell inequality does not create a faster-than-light communication method.
How can correlations test an explanation?
Two experimenters choose settings and later compare their records. Local hidden-variable models impose bounds on how their outcomes can correlate under the test’s assumptions. Quantum predictions can exceed those bounds. Each observer still needs the other’s records to see the relationship.
Bell publishes an inequality separating local hidden-variable predictions from some quantum predictions. The bound depends on local hidden-variable assumptions. Its violation does not enable faster-than-light communication.
The next question. The rules were becoming testable. A different question would follow: could people use those rules to process information?
What changed. Nature follows quantum rules. Interference, measurement and entanglement will eventually become tools for processing information.
Still open. Could the behavior of light and atoms be controlled well enough to carry out instructions?
1965–1993 / Imagine a computer
Could nature become a new kind of computer?
The question changes from explaining the physical world to using it. A proposal for simulation grows into a model of programmable quantum computation.
· Publication
CHSH formulate an experimentally useful Bell test
Choose measurement settings and compare their correlations against a bound.
Why it mattered. Bridges foundational theory and measurement.
Still to solve. The authors proposed a test in 1969. Their paper includes a correction published in 1970.
Historical record and sources
CHSH generalize Bell's result into a proposal for realizable photon-correlation experiments. The authors proposed a test in 1969. Their paper includes a correction published in 1970.
A calculation can be organized so earlier steps can be reconstructed.
Why it mattered. Connects useful computing with reduced logical erasure.
Still to solve. Logical reversibility alone does not eliminate all practical energy costs.
How can a calculation clean up after itself?
A reversible step keeps enough information to reconstruct its input. Bennett’s construction keeps intermediate results, preserves the requested output, then runs the intermediate steps backward to clear the work space. This links the logic of a program to what it needs to erase.
Bennett constructs reversible computation that removes intermediate history while preserving input and output. Logical reversibility alone does not eliminate all practical energy costs.
Light can slow moving atoms when absorption is velocity-selective.
Why it mattered. Creates a path to motion control needed for precision quantum experiments.
Still to solve. The teams proposed how laser light could slow particles. A trapped-ion cooling experiment followed in 1978.
Historical record and sources
Independent proposals describe radiation-pressure cooling of neutral atoms and trapped ions. The teams proposed how laser light could slow particles. A trapped-ion cooling experiment followed in 1978.
Benioff gives a quantum-mechanical model of a computer
A computer can be treated as a physical quantum system.
Why it mattered. Shows that computation can be described within quantum mechanics.
Still to solve. This is not a demonstration of computational speedup.
Could a familiar computer obey quantum rules?
Benioff proposed a Hamiltonian whose evolution represents successive steps of a Turing-machine calculation. The advance was a physical model for performing the computation. It did not depend on building a faster device or finding a new algorithm.
The Physics of Computation conference connects fields
A quantum device may naturally model another quantum system.
Why it mattered. Feynman's simulation argument becomes a major historical anchor.
Still to solve. The meeting connected important strands of work; it was not the sole origin of quantum computing.
Historical record and sources
The MIT and IBM meeting brings together work on physics and computation. The meeting connected important strands of work; it was not the sole origin of quantum computing.
Zurek analyzes environment-selected measurement records
Interactions with surroundings favor some durable records over others.
Why it mattered. Develops a key part of the decoherence account.
Still to solve. Decoherence analysis does not by itself settle every interpretation of measurement.
Historical record and sources
Zurek relates stable pointer states to the apparatus-environment interaction. Decoherence analysis does not by itself settle every interpretation of measurement.
Dieks independently analyzes the no-cloning limitation
Quantum correlations cannot be amplified into faster-than-light messages.
Why it mattered. Provides an independent no-cloning-era contribution.
Still to solve. The argument concerns a device that would copy any unknown quantum state perfectly. Some known sets of states can be copied.
Historical record and sources
Dieks rules out a proposed superluminal communication scheme using quantum linearity. The argument concerns a device that would copy any unknown quantum state perfectly. Some known sets of states can be copied.
A logic operation can preserve enough information to run backward.
Why it mattered. Connects circuit theory with physical resource limits.
Still to solve. An idealized classical model, not an experimentally lossless quantum computer.
Historical record and sources
A computation model combines reversibility with conservation constraints. An idealized classical model, not an experimentally lossless quantum computer.
Feynman proposes using one quantum system to study another
Richard Feynman argued that simulating quantum systems can be difficult for ordinary computers, and that controlled quantum systems offer a natural alternative. His influential paper followed a talk given in 1981.
Why it mattered. Studying molecules and materials became a major motivation: use a quantum machine to model another system governed by quantum rules.
Simulation. Using one system or a mathematical model to study how another system behaves.
Still to solve. This was a proposal about simulation, not proof that a quantum computer would accelerate every kind of calculation.
Why use one quantum system to study another?
A general state of n qubits has 2ⁿ amplitudes. Writing them all down on a conventional computer quickly becomes impractical. A controlled quantum system can instead evolve under chosen interactions, then yield measurements of a target property. Some structured systems still permit efficient classical methods.
The next question. A machine that imitates nature is one possibility. Could a quantum machine also follow different programs?
· Publication
Wootters and Zurek publish a no-cloning result
An unknown qubit cannot be copied like an ordinary digital file.
Why it mattered. Explains a basic constraint on quantum communication and error correction.
Still to solve. Dennis Dieks independently published a related argument in 1982. James Park had explored the limits of copying quantum states in 1970.
Why can we copy a bit, but not an arbitrary qubit?
A gate can copy the labels 0 and 1 into a blank target. Applied to their superposition, the same gate generally entangles the two qubits instead of producing independent copies. This follows from linearity: an operation must act consistently on both the components and their sum.
Quantum linearity forbids a universal machine that perfectly copies arbitrary unknown quantum states. Dennis Dieks independently published a related argument in 1982. James Park had explored the limits of copying quantum states in 1970.
Change the measurement choices while the experiment is running.
Why it mattered. Strengthens experimental tests of nonclassical correlations.
Still to solve. This influential experiment still had loopholes; it was not a loophole-free Bell test.
Historical record and sources
A Bell test with time-varying analyzers reports correlations agreeing with quantum predictions. This influential experiment still had loopholes; it was not a loophole-free Bell test.
Why it mattered. Foundational quantum cryptography.
Still to solve. Written circa 1970; published in 1983.
Historical record and sources
Wiesner's conjugate coding describes quantum money and incompatible encodings. Written circa 1970; published in 1983.
Bibliography of Quantum Cryptography · Claude Crepeau / McGill University · A researcher-maintained historical bibliography distinguishes manuscript, protocol and prototype dates. Webpage publication year is not established; historical event dates come from its described records.
· Publication
Berry describes geometric quantum phase
The path taken through parameters can matter even after returning to the start.
Why it mattered. Adds a geometric route to understanding phase and control.
Still to solve. The result assumes adiabatic evolution: the parameters change slowly enough for the system to follow the relevant state.
Historical record and sources
Berry derives a phase acquired when quantum parameters trace a slow closed circuit. The result assumes adiabatic evolution: the parameters change slowly enough for the system to follow the relevant state.
Interception can introduce detectable disturbance.
Why it mattered. A quantum protocol for distributing secret keys.
Still to solve. 1984 origin, not 2014 republication; authenticated classical communication required.
How can an intercepted key leave evidence?
In BB84, states are prepared and measured in two possible bases. The users compare bases over an authenticated classical channel and test a sample of their retained bits. An unexpectedly high error rate can make them discard the key. Security depends on the protocol and the devices.
Bennett and Brassard present BB84 in Bangalore. 1984 origin, not 2014 republication; authenticated classical communication required.
Bibliography of Quantum Cryptography · Claude Crepeau / McGill University · A researcher-maintained historical bibliography distinguishes manuscript, protocol and prototype dates. Webpage publication year is not established; historical event dates come from its described records.
· Publication
Deutsch describes a programmable quantum computer
David Deutsch developed a model of a universal quantum computer: a machine that could perform different quantum computations through suitable instructions. The aim expanded from specialized simulations to a general framework for quantum information processing.
Why it mattered. Researchers could now design algorithms, or step-by-step methods, for a quantum computer and identify the operations needed to perform them.
Qubit. A quantum unit of information. Reading it in the usual computational basis gives 0 or 1.
Still to solve. “Universal” describes what the model can represent. It does not mean that every problem becomes easy or faster to solve.
What makes a quantum computer programmable?
A single model can execute different computations when given different instructions. That is what “universal” describes. The time, memory and precision needed still depend on the particular problem. A useful algorithm must therefore do more than show its instructions can be written.
Deutsch formulates a quantum generalization of computing machines and a universal quantum computer. Quantum computing does not make noncomputable functions computable.
The next question. A programmable model gives researchers a place to begin. Next comes the search for a calculation worth building it for.
· Publication
Hong, Ou and Mandel demonstrate two-photon interference
When two matching photons arrive together at opposite inputs of a balanced beam splitter, they tend to leave through the same output. The two detectors then click together less often.
Why it mattered. Supplies a core phenomenon for later photonic quantum experiments.
Still to solve. If the photons differ in arrival time or another detectable property, coincidences can reappear.
Historical record and sources
Two-photon interference enables measurement of very short relative arrival intervals. If the photons differ in arrival time or another detectable property, coincidences can reappear.
A quantum-cryptography prototype is reported working
Sender and receiver exchange key material.
Why it mattered. Brings protocol proposals into the laboratory.
Still to solve. 1989 prototype report; fuller journal article in 1992.
Historical record and sources
A report announces a working quantum-cryptography prototype. 1989 prototype report; fuller journal article in 1992.
Bibliography of Quantum Cryptography · Claude Crepeau / McGill University · A researcher-maintained historical bibliography distinguishes manuscript, protocol and prototype dates. Webpage publication year is not established; historical event dates come from its described records.
· Publication
Ekert proposes entanglement-based key distribution
Shared quantum correlations can support tests for interception.
Why it mattered. Offers a distinct quantum-cryptographic approach.
Still to solve. Theoretical protocol security and deployed-device security are different questions.
Historical record and sources
Ekert connects key distribution with entangled pairs and a Bell test. Theoretical protocol security and deployed-device security are different questions.
A carefully designed question can be answered with fewer oracle calls.
Why it mattered. Shows how interference can change query requirements.
Still to solve. The comparison is with deterministic classical queries under a promise.
What makes this an unusual search problem?
There is a promise about the hidden function: its outputs are either all the same or evenly split. Interference can distinguish those possibilities. Any comparison of query counts must say whether the classical competitor must be exactly right or may occasionally make an error.
A shared quantum resource changes what a later transmission can communicate.
Why it mattered. Demonstrates an operational use of entanglement.
Still to solve. The sender and receiver must first share an entangled pair. The sender then transmits one qubit so the receiver can recover two classical bits.
Historical record and sources
Shared entanglement and transmission of one quantum system enable a two-bit communication protocol. The sender and receiver must first share an entangled pair. The sender then transmits one qubit so the receiver can recover two classical bits.
A receiver reconstructs a state after receiving ordinary measurement information.
Why it mattered. Provides a building block for quantum networks.
Still to solve. Transfers a state, not a person or usable information faster than light.
Why must a teleported state wait for a message?
The sender uses a shared entangled pair and a joint measurement. The measurement outcome supplies two ordinary bits telling the receiver which correction to make. Until those bits arrive, the receiver cannot recover the transmitted state. The protocol consumes the shared entanglement.
A protocol transfers an unknown quantum state using shared entanglement and classical communication. Transfers a state, not a person or usable information faster than light.
Bernstein and Vazirani advance quantum complexity theory
Ask which problems quantum rules make more efficient.
Why it mattered. Places quantum computation within formal complexity analysis.
Still to solve. Oracle-based separations concern specified access models, not a general claim of practical speedup.
Historical record and sources
Bernstein and Vazirani publish a quantum-complexity framework at STOC. Oracle-based separations concern specified access models, not a general claim of practical speedup.
What changed. A quantum computer is now a model researchers can reason about. A model, an algorithm and a built machine are three different achievements.
Still open. Researchers still needed a problem worth solving and hardware capable of running the instructions.
1994–2005 / Find a purpose
What could it do, and how could it work?
Algorithms reveal specific reasons to build quantum computers. Error correction offers protection, while experiments begin turning instructions into controllable hardware.
· Publication
Simon gives an exponential oracle separation
Interference can expose a hidden pattern in function values.
Why it mattered. Provides an important stepping stone toward period-finding algorithms.
Still to solve. The result concerns an oracle problem and its stated distribution.
Historical record and sources
Simon presents a quantum approach to finding a hidden period with an exponential oracle advantage. The result concerns an oracle problem and its stated distribution.
Test of Time 1994 Award: Simon and Shor · IEEE Computer Society · Webpage publication year is not established; historical event dates come from its described records.
· Publication
Shor shows how a quantum computer could factor large numbers
Multiplying 7 by 11 gives 77. Factoring asks the reverse question. For the huge numbers used by RSA, that reversal is difficult with known classical methods. Peter Shor showed how a quantum computer could factor efficiently and solve a related problem called the discrete logarithm.
Why it mattered. RSA relies on the difficulty of recovering the factors of a large public number. Shor’s result gave security researchers a specific reason to design replacements before a machine capable of running the attack exists.
Public-key cryptography. Methods using related public and private keys to protect information or verify signatures.
Still to solve. Attacking real cryptographic keys requires a sufficiently large, reliable quantum computer. The algorithm’s discovery did not immediately break deployed encryption.
Where do the factors come from?
The quantum part finds clues to a repeating pattern in modular arithmetic. A classical calculation uses the period to try to recover factors. This is an efficient algorithm on a sufficiently capable quantum computer. The 1994 paper demonstrated the mathematics, not a machine breaking an encryption key.
Shor gives polynomial-time quantum algorithms for factoring and discrete logarithms. November 1994 dates the FOCS proceedings, not the expanded 1995 preprint. No exponential separation from every possible classical factoring algorithm has been proved.
The next question. A powerful algorithm is only useful if its delicate quantum information survives long enough to run.
· Publication
Schumacher establishes quantum compression
Quantum signals have information limits governing faithful representation.
Why it mattered. Defines a quantitative role for quantum information compression and qubits.
Still to solve. Quantum source compression is distinct from compressing arbitrary classical files.
Historical record and sources
Schumacher proves a quantum analogue of noiseless information coding. Quantum source compression is distinct from compressing arbitrary classical files.
Shared motion can connect the internal states of different ions.
Why it mattered. Provides a concrete physical computing scheme.
Still to solve. This proposal is separate from later gate demonstrations.
How could separated ions share an operation?
In the Cirac–Zoller proposal, internal states carry the qubits, while collective motion can mediate an operation between ions. Lasers couple the internal states to that motion. The proposal set out an architecture whose operations still needed to be demonstrated in the laboratory.
JILA produces a dilute-gas Bose-Einstein condensate
A large population of atoms occupies a shared quantum state.
Why it mattered. Enables new study of collective quantum matter.
Still to solve. The experiment took place in 1995; the Nobel recognition came in 2001.
Historical record and sources
The JILA experiment produces Bose-Einstein condensation in an ultracold rubidium gas. The experiment took place in 1995; the Nobel recognition came in 2001.
Shor’s code spreads the state of one logical qubit across nine physical qubits. If one of the nine suffers an error, checks on the group reveal enough to correct it while keeping the stored quantum information hidden from those checks.
Why it mattered. Making nine copies of an unknown qubit is impossible. Encoding it across a group provides something a copy could not: a way to diagnose damage without reading out the answer.
Logical qubit. A unit of quantum information encoded with redundancy so that errors can be detected or corrected.
Still to solve. This was a theoretical code, not a finished reliable computer. Protection needs extra physical resources and sufficiently accurate operations.
How can a check find an error without reading the message?
Shor’s nine-qubit code stores one logical qubit in relationships among nine physical qubits. Checks designed for the code distinguish patterns of errors without revealing the 0/1 value of the logical qubit. The code can correct an arbitrary error confined to one physical qubit.
Shor proposes protecting quantum-memory information through an error-correcting encoding. A theoretical code is not a demonstrated fault-tolerant computer.
The next question. A protective method is a plan. Carrying it out still requires physical operations that researchers can control.
· Publication
Elementary gate universality is established
A few kinds of building blocks can express many quantum computations.
Why it mattered. Supports circuit construction from a small toolbox.
Still to solve. Universality does not mean an arbitrary unitary is efficient to implement.
Historical record and sources
Single-qubit operations with a two-qubit exclusive-OR gate generate arbitrary quantum unitary operations. Universality does not mean an arbitrary unitary is efficient to implement.
The response to one optical field can depend on another quantum interaction.
Why it mattered. Explores a photonic route toward interactions between quantum signals.
Still to solve. The paper considers a gate proposal based on measured shifts.
Historical record and sources
A strongly coupled atom-cavity system produces conditional phase shifts relevant to quantum logic. The paper considers a gate proposal based on measured shifts.
A NIST team used two properties of a single trapped ion as qubits. One described its vibration and the other an internal state. Laser pulses made a flip of the internal state depend on the vibrational state. The operation is called a controlled-NOT gate.
Why it mattered. A theoretical computer needs physical instructions. Demonstrating a conditional operation was a step toward turning quantum algorithms into laboratory experiments.
Quantum gate. An instruction that transforms the state of one or more qubits. Some gates make one qubit’s operation depend on another’s state.
Still to solve. The two information carriers were properties of one ion, not two separate ions. One operation does not make a complete computer.
Where were the two qubits in this gate?
One was encoded in an ion’s internal energy levels, the other in its quantized motion. A controlled operation couples those degrees of freedom so its action depends on the control state. Both were properties of the same trapped ion.
The next question. While experiments tested the building blocks, algorithms continued to reveal different kinds of possible advantage.
· Publication
Entanglement purification is developed
Trade the quantity of shared pairs for better quality.
Why it mattered. Provides a resource-management tool for communication.
Still to solve. The protocol applies under specified assumptions; the paper also has a published erratum.
Historical record and sources
Local operations can extract fewer high-quality pairs from suitable noisy shared entanglement. The protocol applies under specified assumptions; the paper also has a published erratum.
Shor posts fault-tolerant computation construction
Operations must be designed so error correction itself does not spread failures uncontrollably.
Why it mattered. Extends protection from storage to calculation.
Still to solve. This date records the preprint; its error bound differs from later constant-threshold results.
Historical record and sources
Shor describes encoded computation that tolerates certain accumulating operational errors. This date records the preprint; its error bound differs from later constant-threshold results.
Suppose one item among a million passes a yes-or-no test, and there is no shortcut for finding it. Ordinary search can take hundreds of thousands of checks. In Grover’s ideal quantum algorithm, the number of checks is on the order of a thousand.
Why it mattered. Each round changes the amplitudes so the marked item becomes more likely to appear. Increasing the size of the search by a factor of 100 increases the number of quantum checks by roughly a factor of ten.
Algorithm. A step-by-step method for solving a specified problem, including how to recognize a useful result.
Still to solve. The comparison counts calls to a test that can run inside a quantum circuit. Preparing the data, implementing that test and reading the answer all take work.
What exactly does the square root count?
Suppose exactly one of N candidates passes a test. Grover’s algorithm repeatedly changes the marked candidate’s phase and amplifies its amplitude. It needs on the order of √N calls to that test. A real runtime also includes building the test, preparing the state and reading the answer.
Grover presents an algorithm using order-square-root-of-N oracle queries for unstructured search. The speedup counts calls to a test for a marked answer. The cost of implementing that test and loading data also matters in an application.
The next question. An algorithm describes operations. The hardware question remains: what physical object should carry each qubit?
· Publication
A five-qubit error-correcting code is published
Five physical qubits can preserve one logical state against a specified class of errors.
Why it mattered. Demonstrates compact quantum error protection.
Still to solve. Minimality refers to this error-correction task, not every protection problem.
Historical record and sources
A code encodes one qubit into five to correct arbitrary single-qubit errors. Minimality refers to this error-correction task, not every protection problem.
Classical coding ideas can help protect quantum information when adapted carefully.
Why it mattered. Establishes an influential coding approach.
Still to solve. This is independent work alongside the Calderbank-Shor construction.
Why does a majority vote cover only part of the problem?
A quantum error can change a bit value or a relative phase, and a code needs checks for both. Steane drew on classical codes to protect quantum information against both kinds. Calderbank and Shor independently developed related constructions.
Steane develops quantum error correction using relationships with classical linear codes. This is independent work alongside the Calderbank-Shor construction.
Calderbank and Shor establish families of quantum codes
Larger code families can protect many logical states.
Why it mattered. Shows protection can extend beyond isolated small examples.
Still to solve. Andrew Steane independently developed the related code construction. The name CSS credits Calderbank, Shor and Steane.
Historical record and sources
Calderbank and Shor prove the existence of quantum codes with useful asymptotic rates. Andrew Steane independently developed the related code construction. The name CSS credits Calderbank, Shor and Steane.
Break complex dynamics into implementable local operations.
Why it mattered. Turns a simulation vision into a constructive theoretical result.
Still to solve. The simulation cost depends on locality, the requested accuracy and the physical evolution being represented.
Historical record and sources
Lloyd shows how quantum computers can simulate local quantum systems. The simulation cost depends on locality, the requested accuracy and the physical evolution being represented.
DiVincenzo and Shor develop fault-tolerant correction networks
A repair process must remain reliable when its own components can fail.
Why it mattered. Addresses a central implementation obstacle.
Still to solve. The result is conditional on the modeled errors and circuit construction.
Historical record and sources
They provide procedures that can correct errors even when correction operations themselves are imperfect. The result is conditional on the modeled errors and circuit construction.
Knill, Laflamme and Zurek post a threshold analysis
Below appropriate error conditions, additional protection can improve reliability.
Why it mattered. Supports the possibility of scalable protected computation.
Still to solve. No threshold number is universal across noise models or architectures.
Is there one error threshold for all machines?
A threshold result applies to a specified error model and fault-tolerant construction. Below the relevant threshold, extra encoding can improve reliability even when the operations used for correction are imperfect. Another code, noise process or available set of gates can change the threshold.
A concatenated fault-tolerance analysis describes reaching desired computational accuracy under suitable gate errors. No threshold number is universal across noise models or architectures.
Aharonov and Ben-Or post a constant-threshold result
Reliable long calculations can be possible if elementary errors are sufficiently controlled.
Why it mattered. Strengthens theoretical grounds for scaling quantum computers.
Still to solve. Preprint date differs from conference and later journal publications.
Historical record and sources
Aharonov and Ben-Or describe fault-tolerant computation below a constant error threshold. Preprint date differs from conference and later journal publications.
Gottesman organizes quantum codes through stabilizers
Describe valid encoded states through measurements that leave them unchanged.
Why it mattered. Creates a powerful language for organizing error correction.
Still to solve. Stabilizer methods do not make every quantum circuit efficiently classically simulable.
What does a stabilizer check tell us?
A stabilizer code defines allowed states through checks that can be measured together. An error may reverse the sign of a check. Several such signs make a syndrome that helps identify a correction while preserving the encoded information.
Gottesman's thesis develops the stabilizer framework for quantum codes and fault tolerance. Stabilizer methods do not make every quantum circuit efficiently classically simulable.
Gershenfeld and Chuang propose bulk NMR computation
Many molecules can perform similar controlled spin operations together.
Why it mattered. Uses existing magnetic-resonance techniques for quantum-information experiments.
Still to solve. An ensemble demonstration does not establish a scalable pure-state quantum computer.
Historical record and sources
Bulk spin-resonance methods are described as a route to experimental quantum computation. An ensemble demonstration does not establish a scalable pure-state quantum computer.
Knill and Laflamme formalize error-correction conditions
A code succeeds only when errors can be diagnosed without revealing the protected state.
Why it mattered. Provides a general test for whether a code can correct a noise process.
Still to solve. Conditions apply to the defined code space and error set.
Historical record and sources
They derive necessary and sufficient conditions for perfect recovery of encoded states under specified interactions. Conditions apply to the defined code space and error set.
Cory, Fahmy and Havel publish ensemble NMR computing
Signals from many similar systems are combined in the readout.
Why it mattered. Expands laboratory approaches to early quantum-information processing.
Still to solve. The signal was an average over many molecules. An individual run on a single molecule was not read out.
Historical record and sources
An ensemble-computing model uses magnetic-resonance control and expectation-value readout. The signal was an average over many molecules. An individual run on a single molecule was not read out.
Information can be represented through the collective properties of excitations and their exchanges.
Why it mattered. Establishes a major topological-computing direction.
Still to solve. A theoretical proposal; the journal publication followed in 2003.
Historical record and sources
Kitaev proposes computation through moving and fusing anyonic excitations in two dimensions. A theoretical proposal; the journal publication followed in 2003.
A quantum state can be reconstructed in a different physical carrier.
Why it mattered. Moves quantum teleportation from protocol to experiment.
Still to solve. The team identified successful transfers from detector coincidences. The output photon carried the input polarization only in the selected trials.
Historical record and sources
A photon-polarization state is transferred using entanglement and a joint measurement. The team identified successful transfers from detector coincidences. The output photon carried the input polarization only in the selected trials.
Experimental quantum teleportation · Nature · Page metadata says published December 1; journal issue is December 11. Month precision avoids conflation.
· Publication
Loss and DiVincenzo propose spin qubits in quantum dots
An electron's spin can store information while controlled coupling supplies gates.
Why it mattered. Establishes an influential semiconductor architecture.
Still to solve. The publication is a proposal, not a built processor.
Historical record and sources
Coupled electron spins in quantum dots are proposed for universal quantum gates. The publication is a proposal, not a built processor.
The function has two possible inputs. The experiment asks whether they give the same output or different outputs.
Why it mattered. Shows experimental control of a full computation sequence.
Still to solve. An exact classical answer for this two-input problem needs both function values. The ideal quantum circuit needs one call. This comparison counts calls, rather than laboratory runtime.
Historical record and sources
Nuclear spins implement a small algorithm using fewer oracle calls than its classical comparison. An exact classical answer for this two-input problem needs both function values. The ideal quantum circuit needs one call. This comparison counts calls, rather than laboratory runtime.
Kane proposes donor nuclear-spin qubits in silicon
Atoms placed inside silicon can supply quantum information registers.
Why it mattered. Connects quantum-information hardware with semiconductor engineering.
Still to solve. The architecture depends on fabrication and control advances beyond the proposal.
Historical record and sources
A silicon architecture encodes information in donor nuclear spins with electrically controlled operations. The architecture depends on fabrication and control advances beyond the proposal.
Jones, Mosca and Hansen demonstrate NMR quantum search
Different laboratories can independently turn an abstract circuit into a controlled experiment.
Why it mattered. Provides another early experimental algorithm demonstration.
Still to solve. Chuang, Gershenfeld and Kubinec reported another four-state NMR search experiment the previous month.
Historical record and sources
An NMR quantum computer implements a version of Grover's search algorithm. Chuang, Gershenfeld and Kubinec reported another four-state NMR search experiment the previous month.
Build a longer reliable link from shorter entangled segments.
Why it mattered. Provides a strategy beyond direct transmission over a lossy channel.
Still to solve. This is a protocol proposal, not a deployed long-distance network.
Historical record and sources
A nested entanglement-purification scheme addresses long-distance quantum communication with imperfect operations. This is a protocol proposal, not a deployed long-distance network.
Molmer and Sorensen propose robust ion entanglement
Internal ion states can become entangled while motion acts as an intermediary.
Why it mattered. Introduces an influential trapped-ion interaction scheme.
Still to solve. Hot is relative to specified motional assumptions, not ordinary room-temperature operation.
Historical record and sources
A proposed entangling method uses collective motion without requiring complete motional ground-state control. Hot is relative to specified motional assumptions, not ordinary room-temperature operation.
Researchers control a qubit on a tiny electrical circuit
Yasunobu Nakamura, Yuri Pashkin and Jaw-Shen Tsai used short voltage pulses to control quantum behavior in a tiny superconducting circuit. Its two charge states formed a qubit: an engineered object whose quantum state could be deliberately changed.
Why it mattered. Qubits could be built from manufactured circuits as well as natural systems such as atoms, opening another route to quantum hardware.
Superconducting qubit. A quantum bit made from an electrical circuit operated at very low temperature.
Still to solve. This controlled one qubit. It did not yet demonstrate a large processor, reliable computation or a practical speed advantage.
What was being controlled inside the circuit?
Two charge states of a tiny superconducting island differed by one Cooper pair. After a voltage pulse, the measured charge signal oscillated with pulse duration. These oscillations provided evidence for coherent control of the circuit’s quantum states.
Voltage pulses control coherent oscillations between charge states of a Cooper-pair box. A single controlled qubit is not a scalable error-corrected computer.
The next question. Building a controllable qubit is a start. Keeping unwanted disturbances from spoiling it becomes the next engineering problem.
· Publication
A persistent-current superconducting qubit is designed
Two circulating-current configurations can define quantum states of a circuit.
Why it mattered. Develops a superconducting flux-qubit architecture.
Still to solve. This was a design proposal. Later demonstrations of coherent control are separate milestones.
Historical record and sources
A Josephson-junction loop is designed with opposite persistent-current states for a qubit. This was a design proposal. Later demonstrations of coherent control are separate milestones.
Change the problem landscape slowly enough that the quantum state can follow it.
Why it mattered. It established another way to organize quantum computation.
Still to solve. The proposal did not establish efficient solutions for every satisfiability problem.
Historical record and sources
Farhi and collaborators posted an algorithm based on slowly changing a quantum Hamiltonian. The proposal did not establish efficient solutions for every satisfiability problem.
A carefully traced path can determine the effect of a quantum operation.
Why it mattered. Control can use geometric properties of an evolution, expanding the gate-design toolbox.
Still to solve. A small NMR experiment does not establish a scalable computer.
Historical record and sources
Jones and collaborators reported geometric quantum computation using nuclear magnetic resonance. A small NMR experiment does not establish a scalable computer.
A quantum computer needs preparation, control, memory and readout to work together.
Why it mattered. The criteria provide a common vocabulary for comparing proposed platforms.
Still to solve. These are engineering requirements, not a certification that a platform has met them.
What does good hardware have to do together?
DiVincenzo’s computation criteria ask for scalable qubits, a known starting state, coherence long enough to apply gates, a universal set of gates and qubit-specific measurement. Additional criteria address moving quantum information between locations. Meeting one criterion alone cannot qualify an entire architecture.
DiVincenzo described five requirements for quantum computation and two additional requirements for quantum communication. These are engineering requirements, not a certification that a platform has met them.
Microtrap arrays offer a scalable ion architecture
Many small traps can become coordinated parts of one machine.
Why it mattered. The design addressed organization of a larger trapped-ion computer.
Still to solve. An architecture proposal is distinct from a fabricated processor.
Historical record and sources
Cirac and Zoller proposed quantum computing with ions arranged in an array of microtraps. An architecture proposal is distinct from a fabricated processor.
Exchange interactions alone can implement universal computation
A simpler type of physical interaction can do more when information is encoded differently.
Why it mattered. Encoding can trade additional qubits for simpler physical controls.
Still to solve. The construction has overhead and was a theoretical scheme.
Historical record and sources
DiVincenzo and collaborators showed how encoded qubits can support universal computation using exchange interactions alone. The construction has overhead and was a theoretical scheme.
Linear optics gains a route to scalable quantum logic
Light can process quantum information when interference and measurement are combined carefully.
Why it mattered. The KLM proposal made photonic quantum computation a concrete architecture.
Still to solve. Linear optical components alone without the required resources do not provide deterministic universal logic.
How could photons take part in a logic gate?
The KLM scheme combines linear optical elements with prepared photons, measurements and choices conditioned on those measurements. Detection can herald a successful operation. The proposal relies on this combination of resources; passive optical components by themselves are only part of the design.
Knill, Laflamme and Milburn proposed efficient quantum computation using linear optics, measurements and additional resources. Linear optical components alone without the required resources do not provide deterministic universal logic.
Prepare a connected quantum state, then calculate by measuring selected parts.
Why it mattered. The work introduced the one-way measurement-based model.
Still to solve. A cluster state must first be prepared; measurements alone do not create the computational resource.
How can measuring qubits carry out a program?
Start with a prepared entangled state called a cluster state. The chosen measurement bases determine the computation, and earlier results can affect later measurement choices. The resource is consumed as the computation proceeds. Independent measurements on unconnected qubits would lack that resource.
Raussendorf and Briegel described computation by single-qubit measurements on entangled cluster states. A cluster state must first be prepared; measurements alone do not create the computational resource.
Atomic ensembles and light support a repeater proposal
Intermediate quantum memories can help distribute links over longer distances.
Why it mattered. The DLCZ scheme connected memories, photons and heralding in a repeater design.
Still to solve. This was a communication architecture proposal, not a completed global network.
Historical record and sources
Duan, Lukin, Cirac and Zoller proposed long-distance quantum communication using atomic ensembles and linear optics. This was a communication architecture proposal, not a completed global network.
NMR demonstrates a small instance of Shor factoring
A famous algorithm moved from a mathematical proposal to a small physical experiment.
Why it mattered. The experiment brought a landmark quantum algorithm into a laboratory demonstration.
Still to solve. A compiled small-number example does not demonstrate scalable factoring or cryptographic code-breaking.
What did factoring 15 demonstrate?
In this nuclear magnetic resonance experiment, seven nuclear spins carried the qubits for a small instance of Shor’s algorithm. The circuit was tailored to that instance. It demonstrated control of a sequence of operations; larger inputs require resources and error control that this experiment did not establish.
Vandersypen and collaborators reported an NMR realization of Shor's factoring algorithm. A compiled small-number example does not demonstrate scalable factoring or cryptographic code-breaking.
Josephson arrays are proposed for protected qubits
Some designs try to make information harder for local disturbances to damage.
Why it mattered. The work explored hardware structures that could protect quantum information.
Still to solve. Protection was proposed theoretically; this was not a demonstrated topological computer.
Historical record and sources
Ioffe and collaborators proposed topologically protected quantum bits using Josephson-junction arrays. Protection was proposed theoretically; this was not a demonstrated topological computer.
Quantronium improves control of an electrical-circuit qubit
An electrical circuit can behave like a controllable two-level quantum system.
Why it mattered. The experiment strengthened the case for artificial atoms built from circuits.
Still to solve. One controlled circuit is distinct from a complete scalable processor.
Historical record and sources
Vion and collaborators demonstrated programmable state manipulation and readout in a superconducting circuit called quantronium. One controlled circuit is distinct from a complete scalable processor.
Surface-code quantum memory receives a detailed analysis
Many local checks can protect a quantum state spread across a surface.
Why it mattered. The work connected local error checks with scalable protection in two dimensions.
Still to solve. The threshold depends on the noise and decoding assumptions.
Historical record and sources
Dennis, Kitaev, Landahl and Preskill analyzed surface-code memory and recovery thresholds. The threshold depends on the noise and decoding assumptions.
Two superconducting charge qubits exhibit coupled oscillations
Two circuit-based quantum bits were made to interact coherently.
Why it mattered. Interacting circuit qubits were an essential step beyond isolated-device control.
Still to solve. Coupling and oscillations alone do not establish universal computation.
Historical record and sources
Pashkin and collaborators reported quantum oscillations in two coupled charge qubits. Coupling and oscillations alone do not establish universal computation.
Shared ion motion can help one quantum bit control another.
Why it mattered. The experiment realized a gate in a foundational ion-computing proposal.
Still to solve. A two-qubit gate is a component milestone, not a large computer.
Historical record and sources
Schmidt-Kaler and collaborators demonstrated the Cirac-Zoller controlled-NOT gate with trapped ions. A two-qubit gate is a component milestone, not a large computer.
Conditional logic is demonstrated in charge qubits
The state of one circuit qubit can influence an operation on another.
Why it mattered. Circuit technology progressed from coherent qubits toward conditional logic.
Still to solve. The team demonstrated the expected changes in state amplitudes. How the phases evolved during the operation remained open.
Historical record and sources
Yamamoto and collaborators demonstrated a conditional gate operation with superconducting charge qubits. The team demonstrated the expected changes in state amplitudes. How the phases evolved during the operation remained open.
A state is reconstructed elsewhere using entanglement, measurement and a classical message.
Why it mattered. Teleportation became an experimentally controlled operation between matter qubits.
Still to solve. Quantum teleportation transfers a state and requires classical communication; it does not transport matter instantly.
Historical record and sources
Riebe and collaborators reported deterministic quantum teleportation with atoms. Quantum teleportation transfers a state and requires classical communication; it does not transport matter instantly.
A microwave resonator can exchange quantum information with a circuit qubit.
Why it mattered. The work established an important control and readout architecture for circuit qubits.
Still to solve. Strong coupling is a building block, not evidence of quantum computational advantage.
Historical record and sources
Wallraff and collaborators coupled a superconducting qubit strongly to a single microwave photon. Strong coupling is a building block, not evidence of quantum computational advantage.
Fault tolerance is studied for realistically noisy devices
Protective coding can make noisy components more useful when the full design is considered.
Why it mattered. The paper explored how error-correcting constructions could tolerate substantial component noise.
Still to solve. Numerical thresholds are conditional on the stated model and overhead.
Historical record and sources
Knill presented an approach to quantum computation with realistically noisy devices. Numerical thresholds are conditional on the stated model and overhead.
Photonic cluster states demonstrate one-way computing
Measuring a prepared web of entangled photons can implement quantum operations.
Why it mattered. A new computational model gained a laboratory proof of principle.
Still to solve. The experiment was small and did not establish scalable photonic advantage.
Historical record and sources
Walther and collaborators experimentally demonstrated one-way quantum computation using a photonic cluster state. The experiment was small and did not establish scalable photonic advantage.
Tiny semiconductor structures can hold and control interacting electron spins.
Why it mattered. Electrical control of coupled spins strengthened a route to semiconductor quantum information processing.
Still to solve. The September 1 date is online publication; the journal issue is September 30.
Historical record and sources
Petta and collaborators controlled two-electron spin states in semiconductor quantum dots. The September 1 date is online publication; the journal issue is September 30.
Quantum algorithms were tested on models of molecules before suitable hardware existed.
Why it mattered. The work helped make chemistry a concrete target for quantum computation.
Still to solve. The reported calculations used a quantum-computer simulator, not a large quantum device.
Historical record and sources
Aspuru-Guzik and collaborators simulated quantum algorithms for molecular ground-state energies. The reported calculations used a quantum-computer simulator, not a large quantum device.
Entanglement scales to larger trapped-ion registers
More ions were controlled as one connected quantum state.
Why it mattered. Larger entangled registers tested control beyond two-particle examples.
Still to solve. Entanglement size alone does not quantify computational usefulness.
Historical record and sources
Haffner and collaborators reported scalable multiparticle entanglement of trapped ions. Entanglement size alone does not quantify computational usefulness.
What changed. The field has promising methods, a way to protect information and experimental building blocks. None alone is a complete useful computer.
Still open. A laboratory operation had to work reliably alongside many others in a larger calculation.
2006–2018 / Open the field
How does a research idea become an industry?
Better component designs, remote hardware access and coordinated public programs widen participation. An industry needs people and institutions as well as processors.
· Publication
Topological protection is integrated with one-way computation
A structured entangled resource can support both computation and protection from errors.
Why it mattered. Theoretical links between cluster states and surface codes joined computation and error protection.
Still to solve. Threshold values depend on the stated error model and are not measured hardware records.
Historical record and sources
Raussendorf, Harrington and Goyal described fault-tolerant one-way computing using three-dimensional cluster states. Threshold values depend on the stated error model and are not measured hardware records.
A single electron spin is coherently driven in a quantum dot
An oscillating control field rotated one trapped electron's quantum spin state.
Why it mattered. The result advanced single-qubit control in semiconductor-spin architectures.
Still to solve. Single-spin control and a scalable multiqubit processor remain different achievements.
Historical record and sources
Koppens and collaborators demonstrated driven coherent rotations of a single electron spin in a quantum dot. Single-spin control and a scalable multiqubit processor remain different achievements.
A resonator transfers states between superconducting qubits
A resonator acts as a temporary quantum-information link between qubits.
Why it mattered. A quantum bus could connect separated circuit qubits.
Still to solve. State storage and transfer are not, by themselves, fault-tolerant computation.
Historical record and sources
Sillanpaa, Park and Simmonds demonstrated storage and transfer of quantum states through a resonant cavity. State storage and transfer are not, by themselves, fault-tolerant computation.
The transmon design makes charge fluctuations less disruptive
Jens Koch and collaborators proposed the transmon, a redesigned superconducting qubit. Their analysis showed how changing the circuit could sharply reduce its sensitivity to fluctuating electric charge while retaining the ability to control its quantum states.
Why it mattered. Progress could come from making each component less vulnerable to disturbance, rather than only increasing the number of components.
Noise. Unwanted disturbances that change a quantum system or interfere with its control and measurement.
Still to solve. This paper proposed and analyzed a design. Reducing sensitivity to charge noise does not remove every source of error.
Which trade-off makes a transmon work?
Increasing the ratio of Josephson energy to charging energy makes a qubit’s transition frequency much less sensitive to small charge fluctuations. It also makes adjacent transition frequencies more alike. The design keeps enough separation to target the qubit transition with a control pulse.
Koch and collaborators introduced the transmon, a superconducting qubit design with reduced charge sensitivity. Reduced charge noise does not eliminate all error sources.
The next question. Improved components are one part of the story. Wider access would let more people learn to program real hardware.
· Publication
Quantum random-access memory is proposed
A memory request can itself be in a quantum superposition.
Why it mattered. Quantum algorithms need careful accounts of how information is loaded and queried.
Still to solve. A qRAM architecture is not freely available memory or a demonstrated large device.
Historical record and sources
Giovannetti, Lloyd and Maccone proposed an architecture for coherent quantum memory addressing. A qRAM architecture is not freely available memory or a demonstrated large device.
One quantum device can imitate the behavior of a different quantum system.
Why it mattered. A controlled quantum system was used to study another quantum system.
Still to solve. The demonstrated model was small and classically tractable.
Historical record and sources
Friedenauer and collaborators simulated a two-spin quantum magnetic transition using trapped ions. The demonstrated model was small and classically tractable.
A superconducting processor runs two-qubit algorithms
A circuit-based machine executed complete small quantum programs.
Why it mattered. Integrated circuit hardware combined preparation, gates and readout in algorithm demonstrations.
Still to solve. Tiny algorithm examples are demonstrations of control, not useful computational speedups.
Historical record and sources
DiCarlo and collaborators demonstrated Grover and Deutsch-Jozsa algorithms on a two-qubit superconducting processor. Tiny algorithm examples are demonstrations of control, not useful computational speedups.
Quantum information is teleported between distant matter qubits
Light can help transfer a state between separated stationary quantum memories.
Why it mattered. Photon-mediated connections linked matter qubits at separate locations.
Still to solve. The protocol required heralded entanglement and classical communication.
Historical record and sources
Olmschenk and collaborators teleported an atomic quantum state between trapped-ion memories separated by about one meter. The protocol required heralded entanglement and classical communication.
The algorithm extracts certain information about a solution without listing the entire vector.
Why it mattered. The work opened a route to quantum linear-algebra subroutines.
Still to solve. Input access, conditioning and quantum-state output constrain the speedup; it does not print every solution entry efficiently.
Historical record and sources
Harrow, Hassidim and Lloyd introduced a quantum algorithm for selected properties of linear-system solutions. Input access, conditioning and quantum-state output constrain the speedup; it does not print every solution entry efficiently.
A neutral-atom controlled-NOT gate uses Rydberg blockade
Exciting one atom can prevent a neighboring atom from being excited.
Why it mattered. Strong Rydberg interactions enabled conditional logic in neutral-atom traps.
Still to solve. Gate truth-table fidelity and postselected entanglement are different quantities.
Historical record and sources
Isenhower and collaborators demonstrated a controlled-NOT gate between individually addressed neutral atoms using Rydberg blockade. Gate truth-table fidelity and postselected entanglement are different quantities.
A laboratory quantum processor was used to explore a simple chemistry calculation.
Why it mattered. Molecular-energy algorithms were connected with controlled photonic hardware.
Still to solve. Small demonstrations do not establish a chemistry advantage over classical computation.
Historical record and sources
The Towards quantum chemistry on a quantum computer study reported an experimental quantum-chemistry demonstration. Small demonstrations do not establish a chemistry advantage over classical computation.
Boson sampling receives a complexity-theory foundation
Even a specialized photon experiment may produce distributions that are difficult to imitate classically.
Why it mattered. The proposal motivated restricted quantum devices as benchmark experiments.
Still to solve. Hardness arguments depend on complexity assumptions; boson sampling is not universal quantum computation.
Historical record and sources
Aaronson and Arkhipov studied the classical difficulty of sampling outputs from linear-optical networks. Hardness arguments depend on complexity assumptions; boson sampling is not universal quantum computation.
A network of controllable spins searches for low-energy configurations.
Why it mattered. The experiment tested quantum annealing in manufactured hardware.
Still to solve. An annealing demonstration does not establish a speedup or a universal gate-based computer.
Historical record and sources
Johnson and collaborators reported quantum annealing in an eight-spin programmable superconducting network. An annealing demonstration does not establish a speedup or a universal gate-based computer.
The device checked and repaired a chosen kind of error more than once.
Why it mattered. Repeated cycles are necessary for protecting information over time.
Still to solve. Protection of one error type is narrower than arbitrary fault-tolerant computation.
Historical record and sources
Schindler and collaborators implemented repeated correction of phase-flip errors on encoded trapped-ion qubits. Protection of one error type is narrower than arbitrary fault-tolerant computation.
Engineers placed a single useful atom inside a working silicon device.
Why it mattered. Atomic precision advanced a manufacturing route relevant to donor-based qubits.
Still to solve. A transistor is not itself a universal quantum computer.
Historical record and sources
Fuechsle and collaborators fabricated a transistor with an individually positioned phosphorus atom in silicon. A transistor is not itself a universal quantum computer.
The blueprint explains how a large grid could protect and process logical qubits.
Why it mattered. The paper connected logical operations, layout and resource estimates.
Still to solve. Resource estimates depend on error rates and architectural assumptions.
Historical record and sources
Fowler and collaborators analyzed a surface-code route to large-scale quantum computation. Resource estimates depend on error rates and architectural assumptions.
A donor electron becomes a controllable silicon qubit
A single donor-bound electron can store a controllable quantum bit.
Why it mattered. Readout and coherent control advanced the silicon-donor approach.
Still to solve. The paper demonstrated control and readout of one electron spin. A processor also needs operations linking different qubits.
Historical record and sources
Pla and collaborators demonstrated an electron-spin qubit bound to a single phosphorus donor in silicon. The paper demonstrated control and readout of one electron spin. A processor also needs operations linking different qubits.
Nobel Prize recognizes control of individual quantum systems
Researchers learned to observe and control fragile quantum systems individually.
Why it mattered. The award recognized experimental foundations of quantum information technology.
Still to solve. This is the award announcement date, not the date their experiments began.
Historical record and sources
The Physics Nobel Prize was awarded to Serge Haroche and David Wineland for methods of measuring and manipulating individual quantum systems. This is the award announcement date, not the date their experiments began.
A photonic chip performs small boson-sampling experiments
A photonic chip produced the output patterns of interfering photons.
Why it mattered. The benchmark model gained a chip-based proof of principle.
Still to solve. The small experiment did not establish computational advantage.
Historical record and sources
Spring and collaborators demonstrated boson sampling in an integrated photonic circuit. The small experiment did not establish computational advantage.
UK announces a national quantum-technology investment
Public investment helped organize a national quantum-technology effort.
Why it mattered. A coordinated national program supported research and translation beyond isolated projects.
Still to solve. Funding announcements describe commitments, not completed quantum hardware.
Historical record and sources
The United Kingdom announced a 270-million-pound quantum-technologies investment in its 2013 Autumn Statement. Funding announcements describe commitments, not completed quantum hardware.
A superconducting circuit teleports states with feedforward
A circuit used a measured result to decide how to reconstruct another qubit's state.
Why it mattered. Integrated measurement and control made teleportation a reusable circuit operation.
Still to solve. The millimeter-scale chip experiment is not long-distance teleportation or faster-than-light signaling.
Historical record and sources
Steffen and collaborators demonstrated deterministic quantum teleportation with real-time feedforward in a superconducting circuit. The millimeter-scale chip experiment is not long-distance teleportation or faster-than-light signaling.
Better individual operations reduced one barrier to error correction.
Why it mattered. Gate quality approached requirements relevant to surface-code error correction.
Still to solve. A gate-fidelity threshold result is not a working fault-tolerant processor.
Historical record and sources
Barends and collaborators reported high-fidelity one- and two-qubit gates on a five-qubit superconducting processor. A gate-fidelity threshold result is not a working fault-tolerant processor.
VQE couples a quantum processor with classical optimization
A classical computer adjusts a quantum experiment to improve an energy estimate.
Why it mattered. Hybrid optimization became a major approach for near-term algorithms.
Still to solve. The demonstration does not guarantee speedup or easy optimization for large problems.
Which part of a variational calculation is quantum?
The quantum processor prepares a trial state and measures terms needed to estimate its energy. A classical optimizer adjusts the preparation and asks for another estimate. Total cost depends on the family of trial states, how many measurements are needed and how the optimization behaves.
Peruzzo and collaborators demonstrated a variational eigenvalue solver using a photonic processor and a classical computer. The demonstration does not guarantee speedup or easy optimization for large problems.
QAOA introduces alternating layers for optimization
Alternate two kinds of quantum operations and tune them to improve candidate answers.
Why it mattered. The proposal gave hybrid optimization a structured circuit family.
Still to solve. Increasing depth and proving useful advantage are separate challenges.
Historical record and sources
Farhi, Goldstone and Gutmann proposed the quantum approximate optimization algorithm. Increasing depth and proving useful advantage are separate challenges.
Repeated error detection protects classical states in a qubit array
Additional checks helped preserve selected information despite repeated disturbances.
Why it mattered. Repeated parity checks demonstrated useful error suppression with more qubits.
Still to solve. A repetition code protecting one error type is not a complete surface-code logical qubit.
Historical record and sources
Kelly and collaborators suppressed environmental bit-flip errors by scaling a superconducting repetition-code experiment. A repetition code protecting one error type is not a complete surface-code logical qubit.
Two silicon spin qubits performed a conditional operation together.
Why it mattered. The result joined controlled interactions with a semiconductor platform.
Still to solve. Two-qubit logic alone does not establish scalable manufacturing or fault tolerance.
Historical record and sources
Veldhorst and collaborators demonstrated a two-qubit gate using electron spins in enriched silicon. Two-qubit logic alone does not establish scalable manufacturing or fault tolerance.
Distant measurement results violated the limit allowed by the tested local-realist models.
Why it mattered. The experiment strengthened empirical tests underlying quantum-information protocols.
Still to solve. It does not enable faster-than-light communication or settle every philosophical interpretation.
What makes a Bell-test loophole important?
If many outcomes go undetected, the observed subset could misrepresent the full set. If settings or outcomes can reach the other detector in time, local communication could explain a correlation. Hensen and colleagues addressed these two issues together. Their finite data still required a statistical test.
Hensen and collaborators reported a loophole-free Bell test with electron spins separated by 1.3 kilometers. It does not enable faster-than-light communication or settle every philosophical interpretation.
IBM made a five-qubit quantum processor accessible through the internet. People outside the laboratory could submit quantum circuits, run experiments on real hardware and inspect the results through a cloud service.
Why it mattered. Hands-on learning and experimentation reached a much wider audience, helping researchers, students and developers explore quantum programming together.
Quantum circuit. An ordered set of operations and measurements that describes a quantum computation.
Still to solve. Access to real quantum hardware does not guarantee a useful speedup. Small processors remain limited by size, errors and available operations.
What travels over the internet?
A visitor submits a classical description of a circuit. IBM’s five-qubit processor performs the quantum operations at the laboratory. Measurement results return as ordinary data. A user could therefore experiment with real qubits without transporting their quantum states through the public internet.
IBM announced public cloud access to its quantum processor through Quantum Experience. Access is not evidence that the processor outperforms classical computers.
The next question. Access brings more people into the field. Research also needs institutions that can support years of development.
· Publication
A bosonic logical qubit reaches memory break-even
A protected quantum memory lasted longer than the relevant unprotected components.
Why it mattered. The experiment showed a memory could benefit from an error-correcting encoding.
Still to solve. Memory break-even is narrower than universal fault-tolerant computation.
Historical record and sources
Ofek and collaborators extended an encoded qubit lifetime using real-time error correction in superconducting circuits. Memory break-even is narrower than universal fault-tolerant computation.
NIST formally calls for post-quantum cryptography proposals
New mathematical locks were sought before large cryptographic quantum computers existed.
Why it mattered. An international evaluation process began turning cryptographic research into future standards.
Still to solve. Post-quantum cryptography runs on classical computers and is distinct from quantum key distribution.
Historical record and sources
NIST opened nominations for public-key algorithms intended to resist future quantum attacks. Post-quantum cryptography runs on classical computers and is distinct from quantum key distribution.
Quantum signal processing improves Hamiltonian simulation
Precisely chosen rotations help simulate a quantum system efficiently.
Why it mattered. Single-qubit rotations became a powerful language for constructing quantum algorithms.
Still to solve. Optimality concerns the stated query model, not every end-to-end implementation cost.
Historical record and sources
Low and Chuang presented an optimal Hamiltonian-simulation method based on quantum signal processing. Optimality concerns the stated query model, not every end-to-end implementation cost.
Micius distributes entanglement over continental distances
Two widely separated ground stations received linked quantum particles from space.
Why it mattered. The experiment extended entanglement distribution using satellite downlinks.
Still to solve. This was entanglement distribution, not the transmission of matter or a universal quantum internet.
Historical record and sources
Yin and collaborators distributed entangled photon pairs to ground locations separated by approximately 1,203 kilometers. This was entanglement distribution, not the transmission of matter or a universal quantum internet.
Satellite-to-ground quantum key distribution is demonstrated
Quantum signals helped establish shared keys over a space-to-ground link.
Why it mattered. Space links offered another route to long-distance key establishment.
Still to solve. Security depends on protocol and device assumptions; this does not make every communication system unhackable.
Historical record and sources
Liao and collaborators demonstrated decoy-state quantum key distribution between a satellite and ground stations. Security depends on protocol and device assumptions; this does not make every communication system unhackable.
A 51-atom programmable simulator explores many-body dynamics
Dozens of trapped atoms imitated interacting quantum matter.
Why it mattered. Arrays of optical tweezers became a strong platform for many-body simulation.
Still to solve. An analog simulation experiment is not interchangeable with universal digital computation.
Historical record and sources
Bernien and collaborators used reconfigurable neutral-atom arrays to investigate a programmable quantum spin model with up to 51 qubits. An analog simulation experiment is not interchangeable with universal digital computation.
QSVT unifies important quantum-algorithm constructions
A common circuit technique can transform mathematical information in several useful ways.
Why it mattered. The framework brought several algorithmic speedups into a shared mathematical construction.
Still to solve. Input encoding and measurement costs still matter; not every matrix task obtains an end-to-end speedup.
Historical record and sources
Gilyen and collaborators posted a framework for quantum singular-value transformation. Input encoding and measurement costs still matter; not every matrix task obtains an end-to-end speedup.
Useful exploration may begin before quantum machines can run very long protected programs.
Why it mattered. The term helped distinguish exploratory devices from fully fault-tolerant systems.
Still to solve. NISQ is a descriptive era, not a guarantee of commercial advantage.
Why does circuit depth matter on a noisy processor?
More sequential operations create more opportunities for error before the answer is measured. Preskill used NISQ to describe a period in which processors could manipulate many qubits but noise limited the computations they could reliably perform. Qubit count alone leaves out this constraint.
Preskill described the opportunities and limits of noisy intermediate-scale quantum technology. NISQ is a descriptive era, not a guarantee of commercial advantage.
European institutions organized a broad quantum research and technology program.
Why it mattered. The initiative coordinated long-term work across several quantum-technology areas.
Still to solve. Program budgets and goals are commitments, not measured hardware capabilities.
Historical record and sources
The European Quantum Flagship launched in Vienna with its initial research projects. Program budgets and goals are commitments, not measured hardware capabilities.
Some circuit choices make the training signal too flat to follow.
Why it mattered. The result exposed a scaling challenge for variational algorithms.
Still to solve. It does not prove all quantum machine learning or all variational methods fail.
Historical record and sources
McClean and collaborators showed that broad classes of parametrized quantum circuits can have exponentially small optimization gradients. It does not prove all quantum machine learning or all variational methods fail.
A U.S. law coordinates quantum research across agencies
The United States enacted the National Quantum Initiative Act. It established a coordinated federal program for quantum research and development, bringing multiple agencies into a shared effort. A laboratory field was also becoming a long-term institutional priority.
Why it mattered. Research depends on people, facilities and sustained support. Coordination can help those pieces develop alongside the processors themselves.
Quantum industry. The researchers, companies, suppliers, software tools and institutions working to develop and use quantum technologies.
Still to solve. A law organizes an effort. Authorized funding and actual spending are different, and neither demonstrates a computer’s performance.
What can a research law change?
The US National Quantum Initiative Act established a framework for coordinating federal quantum information science work. Sharing facilities, training researchers and supporting research centers address different obstacles from lowering the error of a laboratory gate. The date records the enactment of a law.
The next question. A wider effort needs a way to judge results. What does it mean when a quantum machine claims to beat a classical one?
What changed. More people can experiment and more institutions can contribute. Wider access and investment are different from better computational performance.
Still open. Remote access made a machine easier to reach. Measuring what it could do required fair comparisons.
2019–Aug 2024 / Test the progress
What do the breakthroughs really prove?
Benchmarks test difficult tasks. Encoded experiments test reliability. Security standards prepare conventional systems for possible future quantum attacks.
· Announcement
IBM challenges the Sycamore classical-runtime estimate
A quantum speedup claim can change when classical algorithms improve.
Why it mattered. The debate showed why benchmark claims need explicit classical baselines.
Still to solve. IBM's proposed runtime was an estimate, not the same as a completed run.
Historical record and sources
IBM argued that a different classical simulation strategy could substantially reduce the estimated cost of the Sycamore task. IBM's proposed runtime was an estimate, not the same as a completed run.
Google’s Sycamore tests the limits of classical simulation
Google’s Sycamore processor used 53 qubits to sample results from specially constructed random circuits. The team reported a large speed advantage over its estimate of the classical computing effort needed to reproduce the task.
Why it mattered. Quantum processors could challenge classical simulation on a carefully chosen task, making the quality of the comparison especially important.
Benchmark. A specified test task used to compare performance under stated conditions.
Still to solve. This was not a useful general application. The classical runtime estimate was contested, and classical simulation methods subsequently improved.
What counts as a fair comparison?
The task was to sample bit strings from specified random circuits. The quantum run was measured, while the headline classical runtime was an estimate. Later classical methods narrowed the gap. To compare the approaches, match the circuits, the target sampling quality and the computing resources.
Google reported a 53-qubit random-circuit sampling experiment and a large advantage over its estimated classical baseline. The task was specialized; classical methods improved and the headline runtime comparison was contested.
The next question. A difficult benchmark is one test. Another is whether the machine can keep information reliable as its protective encoding grows.
· Launch
Amazon Braket opens general access across hardware types
Developers could try different quantum machines through one service.
Why it mattered. A common service lowered the coordination barrier to comparing platforms.
Still to solve. Cloud access and diverse hardware do not establish a useful computational advantage.
Historical record and sources
AWS announced general availability of Amazon Braket with simulators and access to multiple quantum-hardware technologies. Cloud access and diverse hardware do not establish a useful computational advantage.
Interfering light produced a difficult sampling distribution on a specialized photonic machine.
Why it mattered. Photonic hardware supplied a different route to sampling-based advantage experiments.
Still to solve. Photon clicks and optical modes are not directly comparable with gate-model qubit counts.
Historical record and sources
Zhong and collaborators reported Gaussian boson sampling on the Jiuzhang photonic device. Photon clicks and optical modes are not directly comparable with gate-model qubit counts.
Hundreds of trapped atoms became an adjustable laboratory for quantum matter.
Why it mattered. Larger reconfigurable arrays expanded accessible many-body experiments.
Still to solve. The atom count is a physical-system size, not a count of error-corrected logical qubits.
Historical record and sources
Ebadi and collaborators studied programmable spin models in two-dimensional arrays containing up to 256 neutral atoms. The atom count is a physical-system size, not a count of error-corrected logical qubits.
More well-controlled qubits improved protection against a chosen error type.
Why it mattered. Stable repeated checks moved error-suppression experiments toward larger systems.
Still to solve. Separate repetition-code experiments do not simultaneously protect arbitrary quantum errors as a full surface code does.
Historical record and sources
Google demonstrated exponential suppression of bit-flip or phase-flip errors as repetition-code size increased. Separate repetition-code experiments do not simultaneously protect arbitrary quantum errors as a full surface code does.
Fault-tolerant primitives operate on an encoded ion qubit
Protecting how an operation is performed can prevent one fault from spreading.
Why it mattered. Circuit design reduced error propagation during logical operations.
Still to solve. The team analyzed error information after the experiments. A scalable processor must also handle errors during an ongoing calculation.
Historical record and sources
Egan and collaborators demonstrated fault-tolerant preparation, measurement and operations on a Bacon-Shor logical qubit using trapped ions. The team analyzed error information after the experiments. A scalable processor must also handle errors during an ongoing calculation.
A larger circuit experiment tested how difficult its output distribution was to reproduce classically.
Why it mattered. The experiment extended the scale of superconducting sampling comparisons.
Still to solve. The stated speedup depends on the benchmark and dated classical simulation estimates.
Historical record and sources
Wu and collaborators reported random-circuit sampling on the Zuchongzhi superconducting processor. The stated speedup depends on the benchmark and dated classical simulation estimates.
A classical attack breaks SIDH-based SIKE assumptions
A proposed quantum-resistant lock was broken without a quantum computer.
Why it mattered. The result illustrated the need for sustained cryptanalysis of post-quantum candidates.
Still to solve. This was a classical attack on a specific construction, not proof that all post-quantum cryptography fails.
Historical record and sources
Castryck and Decru presented an efficient classical key-recovery attack on SIDH, with consequences for SIKE. This was a classical attack on a specific construction, not proof that all post-quantum cryptography fails.
A small two-dimensional code repeatedly checked the information it protected.
Why it mattered. Both bit- and phase-error information entered repeated surface-code cycles.
Still to solve. Reported performance depends on leakage rejection and post-processing conditions.
Historical record and sources
Krinner and collaborators repeatedly corrected errors in a distance-three surface-code experiment using 17 physical qubits. Reported performance depends on leakage rejection and post-processing conditions.
A configurable photonic system produced complex patterns of detected light.
Why it mattered. Programmable optical processing broadened photonic benchmark capabilities.
Still to solve. A specialized sampling advantage is distinct from a universal useful-application advantage.
Historical record and sources
Madsen and collaborators reported a programmable photonic Gaussian boson-sampling experiment using time-multiplexed modes. A specialized sampling advantage is distinct from a universal useful-application advantage.
NIST selects its first four post-quantum algorithms
Four candidate mathematical protections advanced toward official standards.
Why it mattered. The selection narrowed candidate algorithms for future migration.
Still to solve. Selection was not final publication of the standards; final names and status differ.
Historical record and sources
NIST selected Kyber, Dilithium, Falcon and SPHINCS+ for standardization. Selection was not final publication of the standards; final names and status differ.
Classical sampling methods narrow the Sycamore gap
The classical benchmark improved after the original quantum experiment.
Why it mattered. Classical algorithm advances changed the comparison underlying earlier benchmark headlines.
Still to solve. The measured GPU-cluster runtime is distinct from the paper's projected supercomputer runtime.
Historical record and sources
Pan, Chen and Zhang reported a tensor-network method generating samples for the Sycamore benchmark on a GPU cluster. The measured GPU-cluster runtime is distinct from the paper's projected supercomputer runtime.
Decades of tests of entanglement received a shared Nobel recognition.
Why it mattered. The award highlighted experiments central to modern quantum information.
Still to solve. The award year is separate from the dates of the recognized experiments.
Historical record and sources
Alain Aspect, John Clauser and Anton Zeilinger received the Physics Nobel Prize for entanglement experiments and quantum-information foundations. The award year is separate from the dates of the recognized experiments.
Canada set a national plan for developing quantum technologies.
Why it mattered. The strategy coordinated research, talent and commercialization priorities.
Still to solve. Projected jobs and economic impacts are forecasts, not observed outcomes.
Historical record and sources
Canada launched a National Quantum Strategy backed by previously committed federal investment. Projected jobs and economic impacts are forecasts, not observed outcomes.
A larger quantum memory makes slightly fewer errors
Google stored one logical qubit in two sizes of error-correcting code. The larger code averaged about 2.91% logical errors per correction cycle, compared with about 3.03% for the smaller codes. Adding more hardware had produced a small but measurable improvement.
Why it mattered. Every extra qubit can introduce a fault. This comparison tested whether the extra information from a larger group could outweigh those new chances for failure.
Error correction. Encoding information and checking for faults so mistakes can be detected and, when possible, corrected.
Still to solve. The improvement was modest and concerned memory. It did not establish reliable, arbitrary computations or practical advantage.
When does adding physical qubits start to help?
Researchers compared a distance-five surface-code memory with an ensemble of smaller distance-three memories. The larger code showed a modest average improvement in logical error per correction cycle. Extra checks help only if they identify errors more effectively than they introduce new ones.
Google reported that a distance-five logical surface-code qubit modestly outperformed average distance-three counterparts. The improvement was modest and did not demonstrate arbitrary fault-tolerant computation.
The next question. Protecting memory is only part of the job. Researchers also need operations on the information they have encoded.
· Launch
Japan opens access to a domestically built superconducting system
Researchers gained remote access to a quantum processor developed in Japan.
Why it mattered. The launch broadened national access to experimental quantum hardware.
Still to solve. The March 27 service launch differs from the March 24 announcement and later repost dates.
Historical record and sources
A Japanese research consortium began cloud service for its domestically developed superconducting quantum computer. The March 27 service launch differs from the March 24 announcement and later repost dates.
IBM reports error-mitigated calculations beyond brute-force simulation
Repeated noisy experiments can be combined to estimate selected ideal results.
Why it mattered. The work tested whether noisy processors could yield useful scientific information.
Still to solve. The paper did not prove general practical advantage; later classical approximations changed comparisons.
Historical record and sources
Kim and collaborators reported accurate observables from noisy 127-qubit experiments using error mitigation. The paper did not prove general practical advantage; later classical approximations changed comparisons.
A classical response simulates the IBM utility benchmark
A new classical method reproduced important parts of a prominent quantum test.
Why it mattered. The response demonstrated the importance of evolving classical baselines.
Still to solve. This result concerns the selected benchmark circuits, not all quantum computations.
Historical record and sources
Begusic and Chan posted a sparse-Pauli method for efficiently simulating circuits studied in IBM's utility experiment. This result concerns the selected benchmark circuits, not all quantum computations.
Quantum hardware development included both better chips and the systems that operate them.
Why it mattered. The announcement emphasized modular infrastructure and improved circuit quality.
Still to solve. Co-located processors do not automatically form one entangled large processor.
Historical record and sources
IBM introduced the Heron processor and announced operation of Quantum System Two with three Heron processors. Co-located processors do not automatically form one entangled large processor.
Trapped atoms run sampling circuits with up to 48 logical qubits
Researchers held atoms in laser light, then grouped them to encode quantum information. Some circuits used up to 48 logical qubits to generate samples. The team could detect certain errors and exclude the affected runs when analyzing the results.
Why it mattered. The experiment tested whether groups of encoded qubits could work together on a circuit. Keeping track of how many runs survive the error checks matters when comparing its performance.
Still to solve. Detecting errors and rejecting affected runs helped the results. This was not 48 fully error-corrected qubits running arbitrary long calculations.
What does it mean to operate on an encoded qubit?
A group of atoms represents a logical qubit. Reconfiguring atom arrays lets the processor perform operations between such groups. In some experiments, detecting errors and discarding affected runs improved the accepted results. That differs from correcting errors while retaining every run.
Bluvstein and collaborators demonstrated a programmable neutral-atom logical processor with experiments reaching 48 logical qubits. Error-detected and postselected sampling is not equivalent to arbitrary fully corrected computation.
The next question. Hardware experiments continue. Meanwhile, the possibility of stronger machines already calls for changes to ordinary security systems.
· Publication
Low-overhead quantum LDPC memory designs advance
Different code structures may protect information using fewer physical resources.
Why it mattered. The work explored lower physical-qubit overhead than comparable surface-code examples.
Still to solve. Reported memory performance was calculated under specified noise models, not demonstrated on the proposed hardware.
Historical record and sources
Bravyi and collaborators presented a high-threshold fault-tolerant memory protocol using low-density parity-check codes. Reported memory performance was calculated under specified noise models, not demonstrated on the proposed hardware.
A carefully encoded circuit can fail less often than its physical counterpart.
Why it mattered. Encoding and repeated correction became measurable improvements in selected circuits.
Still to solve. Improvement factors depend on circuit choice and postselection; there is no single universal multiplier.
Historical record and sources
Paetznick and collaborators posted experiments showing lower logical error rates than corresponding physical circuits on a trapped-ion QCCD processor. Improvement factors depend on circuit choice and postselection; there is no single universal multiplier.
NIST publishes standards for shared keys and digital signatures
Two computers may need a shared secret to protect a connection. They may also need to verify who signed a message or software update. NIST finalized one post-quantum standard for establishing a shared key and two for digital signatures.
Why it mattered. Software and hardware makers could start implementing the same published specifications. These methods run on ordinary computers and are designed to withstand known quantum attacks.
Post-quantum cryptography. Mathematical security methods designed to resist classical and quantum attacks, without requiring quantum hardware.
Still to solve. These methods run on ordinary computers. Publishing the standards did not mean that quantum computers could already break deployed encryption.
Which security jobs do the three standards cover?
ML-KEM helps two parties establish a shared secret. ML-DSA and SLH-DSA let a recipient verify a digital signature. All three run on ordinary computers. Selecting which one to deploy starts with identifying the job the current cryptography performs.
NIST finalized FIPS 203, 204 and 205 for ML-KEM, ML-DSA and SLH-DSA. These are classical cryptographic standards; finalization does not mean quantum computers can already break deployed RSA.
The next question. Security can prepare before a large quantum computer arrives. Back in the lab, reliability still has to be demonstrated.
What changed. Every result has a task, a comparison and a boundary. A benchmark, protected memory and a security standard answer different questions.
Still open. Could researchers protect information while operating on it, over the full length of a useful calculation?
Sep 2024–2026 / Build reliability
Can all the pieces work reliably together?
Stronger memory results and increasingly integrated experiments tackle the engineering ahead. Meanwhile, organizations prepare their ordinary systems for future change.
· Announcement
Microsoft and Quantinuum report 12 entangled logical qubits
More encoded qubits were demonstrated, alongside a limited hybrid chemistry example.
Why it mattered. The announcement extended logical-state demonstrations and connected them with a small application workflow.
Still to solve. The chemistry demonstration was not claimed as scientific advantage over the best classical methods.
Historical record and sources
Microsoft and Quantinuum reported 12 logical qubits and a hybrid chemistry demonstration using two logical qubits. The chemistry demonstration was not claimed as scientific advantage over the best classical methods.
On Willow, larger codes roughly halve memory errors at each step
Google tested three sizes of surface code, a layout that uses neighboring qubits to check for errors. Each step up in size reduced the logical error rate per correction cycle by about a factor of two. All three sizes stored a single logical qubit.
Why it mattered. In 2023 the improvement from a larger code had been small. Willow showed a much steeper drop in errors across the sizes tested, bringing longer-lived quantum memory closer.
Below threshold. Errors are low enough that increasing the error-correcting code’s size improves protection.
Still to solve. The result protected quantum memory. It did not demonstrate a large computer performing arbitrary useful calculations with full error correction.
How is “below threshold” visible in a memory?
Researchers increased the surface code’s distance and measured fewer logical errors per cycle. Larger encodings protected one stored qubit more effectively over the distances tested. A working computation would also require reliable logical gates and coordination between protected qubits.
Google reported surface-code memories on Willow whose logical errors decreased as code distance increased. This was a quantum-memory result, not arbitrary fault-tolerant computation. A 28 April 2026 correction fixes the repetition-code axis and legend labels in Figure 3a.
A photonic prototype brought many required functions into one connected system.
Why it mattered. A complete modular architecture could be exercised at prototype scale.
Still to solve. The paper explicitly describes a sub-performant scale model; billions of temporal modes are not billions of usable qubits.
What did connecting the modules establish?
Aurora linked the preparation, processing and measurement of light in a modular photonic system. Its authors described it as a scale model. Counting optical modes used over time measures one aspect of the apparatus; it does not count useful logical qubits operating simultaneously.
Xanadu's Aurora experiment integrated photonic chips, networking, feedforward and error-decoding functions in a scale-model system. The paper explicitly describes a sub-performant scale model; billions of temporal modes are not billions of usable qubits.
Separated ion modules execute a distributed quantum algorithm
Two quantum modules worked together through a light-based connection.
Why it mattered. Gate teleportation connected modular hardware to algorithm execution.
Still to solve. The small distributed demonstration is not a large fault-tolerant network.
Historical record and sources
Main and collaborators distributed computations between photonically linked trapped-ion modules separated by about two meters. The small distributed demonstration is not a large fault-tolerant network.
Microsoft reports parity measurement in hybrid devices
A device measured a property needed by one proposed route to protected qubits.
Why it mattered. Parity readout is relevant to proposed topological quantum-computing architectures.
Still to solve. This paper alone does not establish a working topological qubit or the broader Majorana 1 claims. A later published critique disputes the topological interpretation.
Historical record and sources
Microsoft researchers reported interferometric single-shot parity measurement in InAs-Al hybrid devices. This paper alone does not establish a working topological qubit or the broader Majorana 1 claims. A later published critique disputes the topological interpretation.
One protective layer suppresses certain faults while another checks the remaining dominant type.
Why it mattered. Intrinsic error bias was combined with active correction to reduce resource overhead.
Still to solve. Suppression of biased errors does not establish a universal asymptotic threshold for the repetition code.
Historical record and sources
AWS researchers demonstrated a logical memory combining bosonic cat qubits with an outer repetition code. Suppression of biased errors does not establish a universal asymptotic threshold for the repetition code.
Zuchongzhi-3 reports a larger superconducting sampling experiment
A larger chip ran a specialized circuit-sampling benchmark.
Why it mattered. The result extended a superconducting sampling benchmark family.
Still to solve. The speedup is task-specific and estimate-dependent; 105 physical qubits are not 105 logical qubits.
Historical record and sources
USTC reported a 105-qubit processor and an 83-qubit random-circuit sampling benchmark with estimated classical difficulty. The speedup is task-specific and estimate-dependent; 105 physical qubits are not 105 logical qubits.
A backup approach was chosen to avoid relying on only one mathematical family.
Why it mattered. A different mathematical family provided a diversification option.
Still to solve. Selection is not final standard publication and does not replace ML-KEM.
Historical record and sources
NIST selected HQC as an additional key-establishment algorithm for standardization. Selection is not final standard publication and does not replace ML-KEM.
IBM announces the Starling fault-tolerance roadmap
A company published a plan for a larger protected machine.
Why it mattered. The roadmap tied error-correction design, modularity and planned hardware milestones together.
Still to solve. Starling's 200 logical qubits by 2029 are a roadmap target, not a delivered capability.
Historical record and sources
IBM announced a roadmap targeting a 200-logical-qubit Starling system by 2029. Starling's 200 logical qubits by 2029 are a roadmap target, not a delivered capability.
Nobel Prize honors macroscopic quantum effects in circuits
Quantum effects were demonstrated in electrical circuits large enough to engineer directly.
Why it mattered. The award highlighted experimental roots of superconducting quantum technology.
Still to solve. The recognized experiments occurred in the 1980s; 2025 is the award date.
Historical record and sources
The Physics Nobel Prize recognized John Clarke, Michel Devoret and John Martinis for tunneling and energy quantization in electrical circuits. The recognized experiments occurred in the 1980s; 2025 is the award date.
A carefully reversed quantum evolution made selected chaotic-system signals measurable and comparable.
Why it mattered. The work emphasized outputs that can be checked across quantum systems.
Still to solve. The separate molecular demonstration remained within classical reach; it is distinct from the benchmark advantage claim.
Historical record and sources
Google reported a Quantum Echoes experiment measuring out-of-time-order correlators and a claimed advantage over tested classical methods. The separate molecular demonstration remained within classical reach; it is distinct from the benchmark advantage claim.
DARPA advances teams in its quantum benchmarking program
Technical plans were advanced to a more detailed government evaluation stage.
Why it mattered. The program organized independent evaluation of plans for utility-scale quantum computing.
Still to solve. Selection is an evaluation step, not certification of useful quantum advantage.
Historical record and sources
DARPA reported selecting 11 companies for Stage B of its Quantum Benchmarking Initiative. Selection is an evaluation step, not certification of useful quantum advantage.
An atom processor combines correction, logic and qubit reuse
A neutral-atom processor demonstrated several ingredients needed for reliable quantum computation, including repeated error correction, logical operations and reusing atoms during a computation. The work connected capabilities that must eventually function together in a larger machine.
Why it mattered. A useful computer needs an integrated design for storing, processing and refreshing protected information, not just a large qubit count.
Fault tolerance. Designing operations so that faults remain manageable by error correction, rather than spreading uncontrollably.
Still to solve. These were demonstrations of building blocks and architecture. They did not establish a fully scaled machine solving practical problems beyond classical reach.
Why is reusing an atom during a circuit significant?
An atom can be measured, reset and put to work again while other encoded information remains in the processor. The neutral-atom architecture combined such reuse with logical operations and repeated correction. Scaling these ingredients into long computations remains a separate test.
Bluvstein and collaborators reported a neutral-atom architecture for universal fault-tolerant processing. An architecture and demonstrated components are not a completed large-scale fault-tolerant computer.
The next question. Different hardware approaches tackle these problems differently. One newer approach protects memory with fewer active control steps.
Error-checking patterns can change over time to fit a machine more effectively.
Why it mattered. Changing the correction circuit can address constraints imposed by hardware and leakage.
Still to solve. 13 January 2026 dates the research-team explanation. The underlying Nature Physics paper was published on 17 October 2025.
Historical record and sources
Google described experiments with dynamic surface-code circuits using altered connectivity, moving roles and alternative entangling gates. 13 January 2026 dates the research-team explanation. The underlying Nature Physics paper was published on 17 October 2025.
Error checks can teach the controller how to keep the hardware tuned.
Why it mattered. Calibration and correction could cooperate without the traditional complete stop-and-recalibrate cycle.
Still to solve. The demonstrated drift tests and numerical scaling studies have different evidentiary status.
Historical record and sources
Sivak and collaborators used quantum-error detections to train control adjustments during operation of a Willow quantum memory. The demonstrated drift tests and numerical scaling studies have different evidentiary status.
IBM and Chicago announce encoded-circuit benchmark results
An error check let the team discard suspect runs and estimate how closely the remaining results matched the intended quantum state.
Why it mattered. For a hard sampling task, even checking the answer can strain a classical computer. The experiment used the structure of the circuit itself to estimate its accuracy.
Still to solve. The July announcement described 70 encoded qubits. The September revision reports a 64-qubit circuit encoded using 76 physical qubits. Its estimate of fidelity depends on the device and on selecting runs that pass error checks.
Historical record and sources
IBM and the University of Chicago announced a verifiable sampling result using 70 encoded logical qubits. The July announcement described 70 encoded qubits. The September revision reports a 64-qubit circuit encoded using 76 physical qubits. Its estimate of fidelity depends on the device and on selecting runs that pass error checks.
A silicon array maintains high-quality parallel single-qubit control
Several silicon qubits were controlled together while limiting interference between their controls.
Why it mattered. The work addressed calibration and crosstalk challenges in parallel control.
Still to solve. Single-qubit fidelity is not full-circuit fidelity and does not certify a fault-tolerant computer.
Historical record and sources
Wu and collaborators demonstrated high-fidelity simultaneous single-qubit gates in a five-qubit silicon-spin array. Single-qubit fidelity is not full-circuit fidelity and does not certify a fault-tolerant computer.
Surface-code states undergo teleportation on a processor
Quantum information encoded across many qubits can participate in teleportation protocols.
Why it mattered. The experiment linked encoded states, entanglement and teleportation transitions.
Still to solve. The experiment transferred encoded states within a processor. Connecting separate processors reliably is a further step.
Historical record and sources
Zou and collaborators demonstrated teleportation of surface-code states with code distances up to seven on a superconducting processor. The experiment transferred encoded states within a processor. Connecting separate processors reliably is a further step.
A trapped ion protects a memory without a measurement loop
Researchers stored one logical qubit in several internal states of a trapped ion. Engineered interactions and cooling with a second ion removed errors without repeated measurement and feedback, extending memory lifetime beyond the unprotected comparison.
Why it mattered. Reliable quantum hardware is being pursued through different approaches. Some can reduce the extra controls normally needed for error correction.
Break-even. A memory benchmark. The protected and comparison memories are equally long-lived at break-even. Beyond it, the protected memory lasts longer.
Still to solve. This protected quantum memory under specified noise conditions. It did not demonstrate universal computation or remove the need for further engineering.
How can a memory shed an error without measuring it?
The logical qubit occupies several internal states of one ion. Engineered interactions transfer error information into motion, and a second ion helps cool that motion. The resulting memory outlasted the unprotected comparison under the tested noise conditions without a repeated measurement-and-feedback loop.
Li and collaborators reported autonomous quantum error correction using internal ion states and engineered dissipation, extending memory lifetime beyond break-even. The result is a quantum-memory demonstration under specified noise conditions, not universal computation.
The next question. Progress in memory remains distinct from a complete machine. Organizations can still prepare for the possibilities ahead.
· Publication
NIST maps how to replace vulnerable cryptography
In 2024, NIST published standards for new cryptographic tools. Its 2026 transition report connects the old tools to their replacements. An organization can use the report to identify which of its key-establishment and signature methods need to change.
Why it mattered. Replacing a cryptographic method can mean changing many products that must still communicate with one another. The report helps organizations plan that work while quantum hardware continues to develop.
Post-quantum cryptography. Security methods designed to resist attacks from both classical and future quantum computers.
Still to solve. Post-quantum cryptography runs on ordinary computers. A migration roadmap does not predict when a quantum computer will break deployed encryption.
What is an organization actually migrating?
A service may use one public-key mechanism to establish secrets and another to sign messages. NIST’s transition report connects vulnerable mechanisms with standardized replacements. The decision concerns which services and keys need to change, independently of when a quantum computer could attack them.
NIST released the final IR 8547 roadmap for transition from quantum-vulnerable algorithms to post-quantum standards. A migration timetable is not a prediction of the date a quantum computer will break deployed cryptography.
The next question. The story has no finish line yet. Read each new claim by asking what was tested, against which comparison and with what limits.
What changed. Real quantum processors exist. Making large, dependable computations useful remains a challenge, and security preparation can proceed while hardware develops.
Still open. The cost of a complete calculation still depends on its duration, the hardware and the accuracy the task requires.
WORKED EXAMPLES
Three ideas on paper
1. The same gates. A different order.
A quantum gate is an instruction that changes a qubit. Both sequences below start in |0⟩ and measure only at the end. H combines or recombines the two basis states. Z reverses the sign of the amplitude of |1⟩.
H → Z → H
The first H combines the basis states. Z changes their relative sign. The final H recombines them into |1⟩, so the ideal final reading is 1.
Z → H → H
The initial Z leaves |0⟩ unchanged. The two H operations undo each other, so the ideal final reading is 0.
A circuit specifies both its operations and their order. These are ideal single-qubit examples, not hardware measurements.
2. Find a flipped bit.
Encode an ordinary 0 as 000. Compare the first two bits and the last two bits. Each check is 1 when the pair differs. A decoder that assumes at most one flip can locate it.
Classical repetition analogy, starting from 000
Flips
Bits
Checks
After decoder
Original recovered?
None
000
00
000
Yes
A
100
10
000
Yes
B
010
11
000
Yes
C
001
01
000
Yes
A and B
110
01
111
No
Two flips can produce the same check values as one flip elsewhere. The decoder can then choose the wrong correction. This classical example does not encode an unknown quantum state.
3. Read a breakthrough.
Compare what the investigators actually showed. An algorithm and a memory experiment answer different questions, so a single performance ranking would be misleading.
An efficient factoring algorithm
Theoretical result · 1994 conference presentation · August 30, 1995 expanded preprint
Task
Find the factors of an integer or compute a discrete logarithm.
Resources
An ideal quantum computer. Cost is counted in steps as the number of input digits grows.
Result
Shor showed a quantum algorithm with polynomial growth in the number of steps.
Boundary
The paper gives no hardware runtime for breaking a deployed encryption key.