Polylog-depth Quantum Thermal Simulation via Local Recovery Channels
Abstract
We establish sufficient conditions for preparing quantum thermal states of noncommuting local Hamiltonians with polylogarithmic circuit depth in arbitrary fixed spatial dimension. Our conditions combine locality and stability bounds on the effective interactions of reduced density matrices of a Gibbs state with a quantitative high-temperature condition and access to coarse classical reference Hamiltonians. When these references can be generated locally, the classical preprocessing cost is N1+o(1) for N sites at inverse-polynomial global accuracy. We construct the preparation circuit from spatially localized Petz recovery maps. Quantum corrections derived from the microscopic Hamiltonian enable accurate recovery while the classical references remain coarse. After preprocessing, the resulting circuit prepares the canonical purification using Npolylog(N/ε) gates and qubits, where ε is the preparation error. These results link two fundamental questions: how correlations are organized in thermal equilibrium, and how efficiently the corresponding states can be realized through operations allowed by quantum mechanics. By translating static equilibrium structure into explicit preparation circuits, they give equilibrium locality a constructive computational interpretation and a physically grounded role in quantum algorithm design.
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BibTeX
@misc{hakoshima2026polylogdepth,
title = {{Polylog-depth Quantum Thermal Simulation via Local Recovery Channels}},
author = {Hideaki Hakoshima and Atsushi Iwaki and Nobuyuki Yoshioka},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39674},
eprint = {2609.39674},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39674},
}
RIS
TY - UNPB
TI - Polylog-depth Quantum Thermal Simulation via Local Recovery Channels
AU - Hideaki Hakoshima
AU - Atsushi Iwaki
AU - Nobuyuki Yoshioka
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39674
UR - https://arxiv.org/abs/2609.39674
AB - We establish sufficient conditions for preparing quantum thermal states of noncommuting local Hamiltonians with polylogarithmic circuit depth in arbitrary fixed spatial dimension. Our conditions combine locality and stability bounds on the effective interactions of reduced density matrices of a Gibbs state with a quantitative high-temperature condition and access to coarse classical reference Hamiltonians. When these references can be generated locally, the classical preprocessing cost is N^1+o(1) for N sites at inverse-polynomial global accuracy. We construct the preparation circuit from spatially localized Petz recovery maps. Quantum corrections derived from the microscopic Hamiltonian enable accurate recovery while the classical references remain coarse. After preprocessing, the resulting circuit prepares the canonical purification using Npolylog(N/ε) gates and qubits, where ε is the preparation error. These results link two fundamental questions: how correlations are organized in thermal equilibrium, and how efficiently the corresponding states can be realized through operations allowed by quantum mechanics. By translating static equilibrium structure into explicit preparation circuits, they give equilibrium locality a constructive computational interpretation and a physically grounded role in quantum algorithm design.
ER -