Locally optimized variational evolution for quantum many-body systems
Abstract
Quantum many-body dynamics is difficult to simulate because the global wavefunction develops extensive complexity, whereas local observables may retain only an intrinsic, system-size-independent complexity. This distinction is especially relevant in thermalizing systems, where local subsystems lose microscopic information and relax towards equilibrium. We introduce a variational time-evolution principle that exploits this separation by replacing global-state fidelity with a cost function defined on local reduced density matrices. The resulting locally optimized matrix-product-state (LOMPS) algorithm retains coherent short-time dynamics while using the simplification generated by thermalization at later times, and admits closed-form equations of motion analogous to the time-dependent variational principle. The same principle yields a quantum-classical algorithm in which a quantum processor evaluates the local cost and a noise-robust classical procedure performs the optimization. Proof-of-principle implementations on Quantinuum H2 and IBM Heron processors recover the characteristic local dynamics.
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BibTeX
@misc{wille2026locally,
title = {{Locally optimized variational evolution for quantum many-body systems}},
author = {Carolin Wille and Maximilian Marvell and Lauren Stewart and Maximillian Murphy and Vinul Wimalaweera and Lesley Gover and Andrew G. Green},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.20802},
eprint = {2609.20802},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20802},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Locally optimized variational evolution for quantum many-body systems
AU - Carolin Wille
AU - Maximilian Marvell
AU - Lauren Stewart
AU - Maximillian Murphy
AU - Vinul Wimalaweera
AU - Lesley Gover
AU - Andrew G. Green
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2609.20802
UR - https://arxiv.org/abs/2609.20802
AB - Quantum many-body dynamics is difficult to simulate because the global wavefunction develops extensive complexity, whereas local observables may retain only an intrinsic, system-size-independent complexity. This distinction is especially relevant in thermalizing systems, where local subsystems lose microscopic information and relax towards equilibrium. We introduce a variational time-evolution principle that exploits this separation by replacing global-state fidelity with a cost function defined on local reduced density matrices. The resulting locally optimized matrix-product-state (LOMPS) algorithm retains coherent short-time dynamics while using the simplification generated by thermalization at later times, and admits closed-form equations of motion analogous to the time-dependent variational principle. The same principle yields a quantum-classical algorithm in which a quantum processor evaluates the local cost and a noise-robust classical procedure performs the optimization. Proof-of-principle implementations on Quantinuum H2 and IBM Heron processors recover the characteristic local dynamics.
ER -