Efficient thermalization of one-dimensional noncommuting Hamiltonians via system-bath interactions with Θ(n) ancilla qubits
Abstract
We prove rapid convergence of a system-bath interaction algorithm for preparing Gibbs states of one-dimensional noncommuting Hamiltonians at every fixed positive temperature. For a chain of n qudits of local dimension 2q with bounded nearest-neighbor interactions, the algorithm prepares the Gibbs state from any initial state to trace-norm error 0<ε≤1/2 in expected total Hamiltonian evolution time Õ(n/ε). This improves the previously proved Õ(n6/ε) bound for single-ancilla system-bath Gibbs samplers, up to logarithmic factors. The proposed algorithm couples 4q−1 resettable bath qubits to each site in parallel and randomizes the interaction time. Our analysis bounds both the one-round approximation error and the stationarity defect of an approximate stationary state in Gibbs-weighted L2 norms, with only linear dependence on the system size. It also uses the dephasing induced by randomized evolution to control the extensive Lamb shift without treating it as a small perturbation of the dissipative dynamics.
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BibTeX
@misc{ding2026efficient,
title = {{Efficient thermalization of one-dimensional noncommuting Hamiltonians via system-bath interactions with $Θ(n)$ ancilla qubits}},
author = {Zhiyan Ding and Bowen Li and Ruizhe Zhang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03422},
eprint = {2611.03422},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03422},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Efficient thermalization of one-dimensional noncommuting Hamiltonians via system-bath interactions with Θ(n) ancilla qubits
AU - Zhiyan Ding
AU - Bowen Li
AU - Ruizhe Zhang
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03422
UR - https://arxiv.org/abs/2611.03422
AB - We prove rapid convergence of a system-bath interaction algorithm for preparing Gibbs states of one-dimensional noncommuting Hamiltonians at every fixed positive temperature. For a chain of n qudits of local dimension 2^q with bounded nearest-neighbor interactions, the algorithm prepares the Gibbs state from any initial state to trace-norm error 0<ε≤1/2 in expected total Hamiltonian evolution time Õ(n/ε). This improves the previously proved Õ(n^6/ε) bound for single-ancilla system-bath Gibbs samplers, up to logarithmic factors. The proposed algorithm couples 4^q−1 resettable bath qubits to each site in parallel and randomizes the interaction time. Our analysis bounds both the one-round approximation error and the stationarity defect of an approximate stationary state in Gibbs-weighted L^2 norms, with only linear dependence on the system size. It also uses the dephasing induced by randomized evolution to control the extensive Lamb shift without treating it as a small perturbation of the dissipative dynamics.
ER -