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Rigorous error bounds for dissipative thermal state preparation from weak system-bath coupling

Christopher Ong, S. A. Parameswaran, Benedikt Placke, and Dominik Hahn

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Phys. Rev. A 114, 042445 – Published 21 October, 2026

DOI: https://doi.org/10.1103/25wc-17zy

Abstract

Thermal state preparation is a central challenge in the simulation of quantum many-body systems. Yet provably efficient algorithms for this task were only introduced recently [Chen et al., Nature (London) 646, 561 (2025)]. These algorithms are based on dissipative Lindbladian evolution which exactly fixes the thermal state. Controlled and efficient digital simulation of this evolution, although possible in principle, remains out of reach for present-day quantum hardware. Subsequent work has therefore focused on analog approximations of the proposed Lindbladians via “collision models” with relatively modest requirements—a resettable bath of ancilla qubits whose couplings to the system can be tuned in time-dependent fashion—while still admitting rigorous fixed-point error bounds. Existing rigorous approaches, however, do not exploit the fact that these constructions generically implement not only the desired Lindblad dynamics but also an additional unitary evolution generated by the system Hamiltonian which may aid convergence to the thermal state [Lloyd and Abanin, Phys. Rev. X 16, 031053 (2026)]. Here we show that this unitary contribution does indeed tighten the fixed-point error bound and demonstrate that it is rigorously controlled by the system-bath coupling strength J, scaling as J2. This demonstrates that the effect of the spurious “Lamb shift” term generated by the system-bath interaction can be controlled by tuning J. We clarify the role, previously observed, of a randomized implementation in suppressing possible resonances of the drive with the many-body spectrum and bound the additional variance that this randomization imposes on observables. Finally, we numerically study aspects of the protocol which are relevant for its practical realization, such as the mixing time.

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Phys. Rev. A 114, 042445– Published 21 October, 2026
  • Received 21 May 2026
  • Accepted 5 October 2026
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