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Connects quantum many-body physics, computational complexity and machine learning with the design of quantum-computing architectures and applications that could outperform classical approaches.
arXiv / Physical Review LettersarXiv / ScienceTroyer’s research helps define both the difficulty of simulating quantum matter and the tools available to approach it. His work on the fermionic sign problem identifies a fundamental obstacle to a generic classical simulation method, while neural-network quantum states offer a different representation for selected many-body systems. At Microsoft he works on quantum architecture and applications. The thread across these activities is concrete computational cost: understanding what makes a problem hard and what an alternative method would need to improve.
Microsoft ResearcharXiv / Physical Review LettersarXiv / ScienceThe work behind the recognition
Work, in context- 2005
Complexity of the fermionic sign problem
Troyer and Uwe-Jens Wiese showed that the generic fermionic sign problem in quantum Monte Carlo is NP-hard. This explains why a universally efficient cure is unlikely under standard complexity assumptions, while leaving room for useful solutions in special cases.
Co-author of the complexity result with Uwe-Jens Wiese.
Source-supported recordarXiv / Physical Review Letters - 2017
Neural-network representations of quantum states
With Giuseppe Carleo, Troyer introduced an artificial-neural-network representation of many-body wavefunctions and demonstrated it on interacting spin systems. The work explored a compact computational approach to ground states and quantum dynamics.
Co-author of the neural-network quantum-state work with Giuseppe Carleo.
Source-supported recordarXiv / Science
Keep in perspective
The complexity result concerns the generic sign problem; neural-network demonstrations do not solve every many-body system. A current personal work-base country was not established.
The evidence map
Both views link each contribution to its sources. Choose a contribution on the map or read them all in the list.
Complexity of the fermionic sign problem
Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
Supports: Co-authorship and NP-hardness of the generic sign problem; journal publication 2005.
Published 2004 · Checked 19 Sept 2026Credit & limits: Co-author of the complexity result with Uwe-Jens Wiese.
Read the full contribution| Contribution | Evidence & what it supports | Credit & limits |
|---|---|---|
| Complexity of the fermionic sign problem2005 | Primary paperComputational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations Co-authorship and NP-hardness of the generic sign problem; journal publication 2005. Published 2004 · Checked 19 Sept 2026 | Co-author of the complexity result with Uwe-Jens Wiese. |
| Neural-network representations of quantum states2017 | Primary paperSolving the Quantum Many-Body Problem with Artificial Neural Networks Co-authorship and neural-network quantum-state representation demonstrated on selected many-body systems; journal publication 2017. Published 2016 · Checked 19 Sept 2026 | Co-author of the neural-network quantum-state work with Giuseppe Carleo. |
Follow the evidence
3 sourcesPrimary papers, institutional records and attributed announcements. Each source supports the claims linked above.
- Microsoft ResearchInstitutional record
Matthias Troyer
Current Technical Fellow and corporate vice-president role; quantum architecture and application remit.
Checked 19 Sept 2026 - arXiv / Physical Review LettersPrimary paper
Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
Co-authorship and NP-hardness of the generic sign problem; journal publication 2005.
Published 2004 · Checked 19 Sept 2026 - arXiv / SciencePrimary paper
Solving the Quantum Many-Body Problem with Artificial Neural Networks
Co-authorship and neural-network quantum-state representation demonstrated on selected many-body systems; journal publication 2017.
Published 2016 · Checked 19 Sept 2026