Beyond Lindblad Approximation: Rigorous Guarantees for Thermal and Ground State Preservation under System-Bath Interactions

arXiv:2512.03457 · quant-ph · Submitted 2025-12-03 · Read on arXiv

quant-ph

Submitted: 2025-12-03

Updated: 2026-09-19

Code: https://github.com/kewang-math/beyond-lindblad-system-bath

Terminology

• Spectral Gap — 67× in this paper · explained in 5 episodes
• Accuracy — 18× in this paper · explained in 1 episode
• Hubbard Model — 14× in this paper · explained in 3 episodes
• Fidelity — 11× in this paper · explained in 2 episodes
• Lindblad Dynamics — 10× in this paper · explained in 2 episodes
• ANNNI model — 6× in this paper · explained in 1 episode
• Robustness — 6× in this paper · explained in 5 episodes
• Trace — 4× in this paper · explained in 2 episodes
• Generalization — 3× in this paper · explained in 13 episodes
• Gibbs State — 2× in this paper · explained in 2 episodes
• Adiabatic Evolution — 1× in this paper · explained in 2 episodes
• Block Encoding — 1× in this paper · explained in 4 episodes
• Computational overhead — 1× in this paper · explained in 2 episodes
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Secular Approximation — 1× in this paper · explained in 2 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes
• Trace Distance — 1× in this paper · explained in 3 episodes

Sources

• Dissipative ground state preparation and the Dissipative Quantum Eigensolver
• Quantum generalizations of Glauber and Metropolis dynamics
• Universal cooling of quantum systems via randomized measurements
• Polynomial-Time Preparation of Low-Temperature Gibbs States for 2D Toric Code
• Polynomial Time Quantum Gibbs Sampling for Fermi-Hubbard Model at any Temperature
• Optimal quantum algorithm for Gibbs state preparation
• Quantum Thermal State Preparation
• Towards Efficient Quantum Thermal State Preparation via Local Driving: Lindbladian Simulation with Provable Guarantees
• Quantum thermal state preparation for near-term quantum processors
• Simple and efficient end-to-end quantum thermal and ground state preparation
• Preparing thermal states on noiseless and noisy programmable quantum processors
• The Thermodynamic Cost of Ignorance: Thermal State Preparation with One Ancilla Qubit
• Unified error bounds for perturbations of non-Markovian open quantum systems in Gaussian environments
• Overcoming the Lamb Shift in System-Bath Interaction Models via KMS Detailed Balance: High-Accuracy Thermalization with Time-Bounded Interactions
• Thermalization in open many-body systems and KMS detailed balance
• An efficient and exact noncommutative quantum Gibbs sampler

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• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
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