Instantons in Quantum Annealing: Thermally Assisted Tunneling Vs Quantum Monte Carlo SimulationsRecent numerical result (arXiv:1512.02206) from Google suggested that the D-Wave quantum annealer may have an asymptotic speed-up than simulated annealing, however, the asymptotic advantage disappears when it is compared to quantum Monte Carlo (a classical algorithm despite its name). We show analytically that the asymptotic scaling of quantum tunneling is exactly the same as the escape rate in quantum Monte Carlo for a class of problems. Thus, the Google result might be explained in our framework. We also found that the transition state in quantum Monte Carlo corresponds to the instanton solution in quantum tunneling problems, which is observed in numerical simulations.
Document ID
20160001101
Acquisition Source
Ames Research Center
Document Type
Presentation
Authors
Jiang, Zhang (SGT, Inc. Moffett Field, CA, United States)
Smelyanskiy, Vadim N. (Google, Inc. Venice, CA, United States)
Boixo, Sergio (Google, Inc. Venice, CA, United States)
Isakov, Sergei V. (Google, Inc. Venice, CA, United States)
Neven, Hartmut (Google, Inc. Venice, CA, United States)