Quantum Metropolis Sampling via Weak Measurement

Understand

Gibbs sampling is a crucial computational technique used in physics, statistics, and many other scientific fields.

• For classical Hamiltonians, the most commonly used Gibbs sampler is the Metropolis algorithm, known for having the Gibbs state as its unique fixed point.
• For quantum Hamiltonians, designing provably correct Gibbs samplers has been more challenging.
• [TOV+11] introduced a novel method that uses quantum phase estimation (QPE) and the Marriot-Watrous rewinding technique to mimic the classical Metropolis algorithm for quantum Hamiltonians.