Quantum Gibbs Sampling
summary
Construction of a continuous-time Lindbladian gives a quantum Gibbs sampler that is efficiently implementable on a fault-tolerant device and has the Gibbs state as a fixed point; implementation uses energy-filtered jump operators obtained by Heisenberg evolution plus a Fourier transform to pick transitions and apply Boltzmann weights. The recipe replaces discrete rejection with continuous rewinding to avoid destructive measurements, yields a purified Gibbs state, and costs scale with Hamiltonian-simulation time × beta; mixing time of the resulting quantum Markov chain remains the sampling bottleneck.
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chapters (16)
- 0:00Introduction
- 1:13Task
- 5:34Hardness
- 11:51Quantum Monte Carlo
- 14:18Classical Monte Carlo
- 17:56Detailed Balance
- 21:54Metropolis Hasting
- 23:28Summary
- 25:20Main Course
- 29:25Challenges
- 31:06Algorithm
- 32:39Continuous Time
- 40:02Main Result
- 47:14Intuition
- 51:14Locality
- 56:06Log dependencies
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