Quantum Metropolis sampling
Open accessAbstract
The original motivation to build a quantum computer came from Feynman, who imagined a machine capable of simulating generic quantum mechanical systems--a task that is believed to be intractable for classical computers. Such a machine could have far-reaching applications in the simulation of many-body quantum physics in condensed-matter, chemical and high-energy systems. Part of Feynman's challenge was met by Lloyd, who showed how to approximately decompose the time evolution operator of interacting quantum particles into a short sequence of elementary gates, suitable for operation on a quantum computer. However, this left open the problem of how to simulate the equilibrium and static properties of quantum systems. This requires the preparation of ground and Gibbs states on a quantum computer. For classical systems, this problem is solved by the ubiquitous Metropolis algorithm, a method that has basically acquired a monopoly on the simulation of interacting particles. Here we demonstrate how to implement a quantum version of the Metropolis algorithm. This algorithm permits sampling directly from the eigenstates of the Hamiltonian, and thus evades the sign problem present in classical simulations. A small-scale implementation of this algorithm should be achievable with today's technology.
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For a fixed precision, the number of resources required grows weakly with system size.
“On the other hand, for a fixed precision, the number of resources required grows weakly with system size.”
From Can one trust quantum simulators? (2012) · cites this paper as [120]
If the error probability per gate can be reduced well below threshold to achieve the desired precision without many layers of concatenated error-correction encoding, then digital quantum simulation will scale favorably with the number of particles.
“So, if the error probability per gate can be reduced well below threshold to achieve the desired precision without many layers of concatenated error-correction encoding, then digital quantum simulation will scale favorably with the number of particles.”
From Can one trust quantum simulators? (2012) · cites this paper as [120]
Clark et al. found that for 100 spins, achieving at least 10 bits of precision requires at least two levels of concatenated error correction and at least 100 days of run time, while achieving at least 18 bits requires three levels and at least 7.5×10^3 years, assuming a gate time of 10 microseconds.
“They found that for 100 spins, in order to achieve b ≥ 10 bits of precision, at least two levels of concatenated error correction are necessary, requiring at least 100 days of run time on the ion-trap quantum computer; for b ≥ 18 , three levels are necessary, requiring at least 7 . 5 × 10 3 years! These results assume a gate time of 10 µ s .”
From Can one trust quantum simulators? (2012) · cites this paper as [120]
A fault-tolerant implementation of the standard Trotter-expansion approach to digital quantum simulation has an overhead in the number of gates and time required that grows exponentially with the degree of precision required.
“Indeed, as discussed above, a fault-tolerant implementation of the standard approach based on the Trotter expansion [98] comes at the cost of an overhead in the number of gates and time required that grows exponentially with the degree of precision required [64, 120].”
From Can one trust quantum simulators? (2012) · cites this paper as [120]
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- Authors
- Temme, K., Osborne, T. J., Vollbrecht, K. G., Poulin, D., & Verstraete, F.
- Affiliations
- University of Vienna (AT)
- Leibniz University Hannover (DE)
- Max Planck Society (DE)
- Université de Sherbrooke (CA)
- Corresponding author
- Verstraete, F.
- Venue
- Nature
- Published
- 2011-03
- Volume
- 471
- Issue
- 7336
- Pages
- 87-90
- ISSN
- 0028-0836 (ISSN-L)
- 1476-4687
- OpenAlex
- W2046481556
- Cited by
- 305
- References
- 55
- Citations by year
- 2026: 20 · 2025: 37 · 2024: 36 · 2023: 31 · 2022: 23 · 2021: 31 · 2020: 23 · 2019: 15 · 2018: 14 · 2017: 15 · 2016: 8 · 2015: 11 · 2014: 13 · 2013: 8 · 2012: 7
- FWCI
- 10.88
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Nature (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Ghent University Academic Bibliography (Ghent University) (submittedVersion, other-oa)
- RePEc: Research Papers in Economics (submittedVersion)
- Max Planck Institute for Plasma Physics (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Kempe Foundation
- Deutsche Forschungsgemeinschaft
- Austrian Science Fund
- Fonds Québécois de la Recherche sur la Nature et les Technologies
- Mitacs
- Natural Sciences and Engineering Research Council of Canada
- Engineering and Physical Sciences Research Council (EP/G045771/1)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- quantum simulation, quantum Monte Carlo, sign problem, ground state preparation, Hamiltonian eigenstates, quantum computing, quantum many-body systems
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