AQC 2016 - Scaling Analysis & Instantons for Thermally-Assisted Tunneling and Quantum MC Simulations

A Google TechTalk, June 28, 2016, presented by Zhang Jiang (NASA) ABSTRACT: We develop an instantonic calculus to derive an analytical expression for the thermally-assisted tunneling decay rate of a metastable state in a fully connected quantum spin model. The tunneling decay problem can be mapped onto the Kramers escape problem of a classical random dynamical field. This dynamical field is simulated efficiently by path integral Quantum Monte Carlo (QMC). We show analytically that the exponential scaling with the number of spins of the thermally-assisted quantum tunneling rate and the escape rate of the QMC process with periodic boundary conditions are identical. We relate this effect to the existence of a dominant instantonic tunneling path. The instanton trajectory is described by nonlinear dynamical mean-field theory equations for a single site magnetization vector, which we solve exactly. Finally, we derive scaling relations for the spiky barrier shape when the spin tunneling and QMC rates scale polynomially with the number of spins N while a purely classical over-the-barrier activation rate scales exponentially with N. Vadim N. Smelyanskiy, Google, Sergei V. Isakov, Google, Sergio Boixo, Google, Guglielmo Mazzola, ETH Zurich, Matthias Troyer, ETH Zurich, Hartmut Neven, Google Presented at the Adiabatic Quantum Computing Conference, June 26-29, 2016, at Google's Los Angeles office.