Real time evolution with neural-network quantum states
Open accessAbstract
A promising application of neural-network quantum states is to describe the time dynamics of many-body quantum systems. To realize this idea, we employ neural-network quantum states to approximate the implicit midpoint rule method, which preserves the symplectic form of Hamiltonian dynamics. We ensure that our complex-valued neural networks are holomorphic functions, and exploit this property to efficiently compute gradients. Application to the transverse-field Ising model on a one- and two-dimensional lattice exhibits an accuracy comparable to the stochastic configuration method proposed in [Carleo and Troyer, Science 355, 602-606 (2017)], but does not require computing the (pseudo-)inverse of a matrix.
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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 [137]
Section 2, “Time evolution method” (page not specified), describes approximating a Schrödinger-equation time step with an implicit midpoint method. It does not say that the exponential propagator is nonlocal or difficult to evaluate on a variational wave function, and it also describes stochastic reconfiguration as another approach; thus it does not support the claim that one has to approximate the full unitary propagator. (LLM, conf=0.82)
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Variational Methods for Solving High-Dimensional Quantum Systems
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Adaptive quantum dynamics with the time-dependent variational Monte Carlo method
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Non-Equilibrium Dynamics of Quantum Many-Body Systems for Image Processing
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Quantum machine learning for complex systems: paradigms, applications, and challenges
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Data for "Adaptive quantum dynamics with the time-dependent variational Monte Carlo method"
Salioni, R., Martinazzo, R., Galli, D. E., & Apostoli, C. (2025) · Zenodo (CERN European Organization for Nuclear Research) · doi:10.5281/zenodo.15736911
- Authors
- Gutiérrez, I. L., & Mendl, C. B.
- Affiliations
- Technical University of Munich (DE)
- Venue
- Quantum
- Published
- 2022-01-20
- Volume
- 6
- Pages
- 627
- ISSN
- 2521-327X (ISSN-L)
- OpenAlex
- W2994906999
- Cited by
- 20
- References
- 41
- Citations by year
- 2023: 1 · 2022: 4 · 2021: 8 · 2020: 7
- FWCI
- 0.51
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Quantum (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- mediaTUM – the media and publications repository of the Technical University Munich (Technical University Munich) (submittedVersion, other-oa)
- arXiv (Cornell University) (cc-by)
- Bulletin of the American Physical Society
- Funders
- Munich Center for Quantum Science and Technology
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Mathematics › Numerical Analysis › Numerical methods for differential equations
- Keywords
- neural quantum states, time evolution, quantum many-body systems, implicit midpoint rule, symplectic integration, complex-valued neural networks, analytic functions, gradient computation, transverse-field Ising model
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