Quantum Thermal State Preparation
arXiv:2303.18224
Abstract
Preparing ground states and thermal states is essential for simulating quantum systems on quantum computers. Despite the hope for practical quantum advantage in quantum simulation, popular state preparation approaches have been challenged. Monte Carlo-style quantum Gibbs samplers have emerged as an alternative, but prior proposals have been unsatisfactory due to technical obstacles rooted in energy-time uncertainty. We introduce simple continuous-time quantum Gibbs samplers that overcome these obstacles by efficiently simulating Nature-inspired quantum master equations (Lindbladians). In addition, we construct the first provably accurate and efficient algorithm for preparing certain purified Gibbs states (called thermal field double states in high-energy physics) of rapidly thermalizing systems; this algorithm also benefits from a quantum walk speedup. Our algorithms' costs have a provable dependence on temperature, accuracy, and the mixing time (or spectral gap) of the relevant Lindbladian. We complete the first rigorous proof of finite-time thermalization for physically derived Lindbladians by developing a general analytic framework for nonasymptotic secular approximation and approximate detailed balance. Given the success of classical Markov chain Monte Carlo (MCMC) algorithms and the ubiquity of thermodynamics, we anticipate that quantum Gibbs sampling will become indispensable in quantum computing.
arXiv comment79 pages, 12 figures; v2 modified table 1 and improved presentation and bounds
Cited by in corpus (8)
- Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions
- On the Sample Complexity of Quantum Boltzmann Machine Learning
- Designing open quantum systems with known steady states: Davies generators and beyond
- Gibbs Sampling gives Quantum Advantage at Constant Temperatures with O(1)-Local Hamiltonians
- Variational post-selection for ground states and thermal states simulation
- Chemically Motivated Simulation Problems are Efficiently Solvable by a Quantum Computer
- Variational Quantum Algorithms for Gibbs State Preparation
- Quantum algorithms based on quantum trajectories