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 guided chronology
22 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.
· Presentation
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
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
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
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
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.
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
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
Shor shows how nine qubits can protect one
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
Two properties of one ion carry out a logic gate
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.
· Preprint submission
Grover shows how to search with fewer checks
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
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.
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
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.
· Launch
IBM opens a five-qubit processor to the public
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.
· Enactment
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.
· Publication
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.
· Publication
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.
· Publication
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.
· Standard
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.
· Publication
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.
The next question. A stronger memory result raises the next challenge: can storage, operations and error correction work together?
· Publication
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.
· Publication
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.