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Cited by 51Quantum Computing Algorithms and ArchitectureQuantum many-body systemsQuantum Mechanics and Applications

Unbiasing time-dependent Variational Monte Carlo by projected quantum evolution

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Sinibaldi, Alessandro, Giuliani, Clemens, Carleo, Giuseppe, Vicentini, Filippo·2023·Quantum
DOI 10.22331/q-2023-10-10-1131
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Abstract

We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate the dynamics of many-body quantum systems classically. By systematically studying the relevant stochastic estimators, we are able to: (i) prove that the most used scheme, the time-dependent Variational Monte Carlo (tVMC), is affected by a systematic statistical bias or exponential sample complexity when the wave function contains some (possibly approximate) zeros, an important case for fermionic systems and quantum information protocols; (ii) show that a different scheme based on the solution of an optimization problem at each time step is free from such problems; (iii) improve the sample complexity of this latter approach by several orders of magnitude with respect to previous proofs of concept. Finally, we apply our advancements to study the high-entanglement phase in a protocol of non-Clifford unitary dynamics with local random measurements in 2D, first benchmarking on small spin lattices and then extending to large systems.

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  • Since e^{iτH} is not a local operator that we can easily evaluate on our variational wave function, in practice we have to approximate the full unitary propagator.

    “Since e iτ H is not a local operator that we can easily evaluate on our variational wave function, in practice we have to approximate the full unitary propagator, which can be done in several ways 57,137,138 .”

    From Beyond-classical computation in quantum simulation (2025) · cites this paper as [138]

  • In order to efficiently estimate the infidelity, the authors of Ref. 138 propose a control-variate method to reduce the variance of the estimator similar to Ref. 123.

    “In order to efficiently estimate the infidelity, the authors of Ref. 138 propose a control-variate method to reduce the variance of the estimator similar to Ref. 123.”

    From Beyond-classical computation in quantum simulation (2025) · cites this paper as [138]

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Cited by

Sorted by citations

Authors
Sinibaldi, A., Giuliani, C., Carleo, G., & Vicentini, F.
Affiliations
  • École Polytechnique Fédérale de Lausanne (CH)
  • Centre National de la Recherche Scientifique (FR)
ORCID
Venue
Quantum
Publisher
Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
Published
2023-10-10
Volume
7
Pages
1131
ISSN
2521-327X (ISSN-L)
DOI
10.22331/q-2023-10-10-1131
OpenAlex
W4378447137
Cited by
51
References
13
Citations by year
2026: 15 · 2025: 21 · 2024: 12 · 2023: 3
FWCI
4.60
Type
journal article
Language
en
Open access
Licence
Locations
  • Quantum (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion, cc-by)
  • HAL (submittedVersion, cc-by)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
  • arXiv (Cornell University) (cc-by)
Funders
  • SEFRI (MB22.00051)
  • Swiss National Science Foundation (200021_200336)
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
statistical bias, sample complexity, fermionic systems, quantum simulation, spin lattices

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