Quantum Generalizations of Glauber and Metropolis Dynamics | Quantum Colloquium

Classical Markov Chain Monte Carlo methods, such as Metropolis and Glauber dynamics, have been essential for simulating statistical physical systems and have proven well applicable to other systems with complex degrees of freedom. There have been several proposals for quantum variants of the Metropolis algorithms with different pros and cons, which promise efficient---heuristic, but physically plausible---solutions to the notorious low-energy state preparation problem in quantum computing.

What would be a natural quantum analogue of Metropolis and Glauber dynamics in continuous and discrete time? Are they physically motivated and efficiently implementable on a quantum computer? What intuition survives from classical detailed balance in the quantum case and what breaks down? What are the important connections and differences to thermodynamics? We try to answer the above questions based on a series of recent breakthroughs.

Joint work with: Chi-Fang Chen, Joao F. Doriguello, Michael J. Kastoryano
 

Panel Discussion: Fernando Brandao (AWS & Caltech), Shayan Gharan (University of  Washington), and Matt Hastings (Microsoft)