Understanding Quantum Tunneling through Quantum Monte Carlo Simulations.
The tunneling between the two ground states of an Ising ferromagnet is a typical example of many-body tunneling processes between two local minima, as they occur during quantum annealing. Performing quantum Monte Carlo (QMC) simulations we find that the QMC tunneling rate displays the same scaling with system size, as the rate of incoherent tunneling. The scaling in both cases is O(Δ^{2}), where Δ is the tunneling splitting (or equivalently the minimum spectral gap). An important consequence is that QMC simulations can be used to predict the performance of a quantum annealer for tunneling through a barrier. Furthermore, by using open instead of periodic boundary conditions in imaginary time, equivalent to a projector QMC algorithm, we obtain a quadratic speedup for QMC simulations, and achieve linear scaling in Δ. We provide a physical understanding of these results and their range of applicability based on an instanton picture.
Google, 8002 Zurich, Switzerland.
Sergei V
SV
Isakov
Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland.
Guglielmo
G
Mazzola
Google, Venice, California 90291, USA.
Vadim N
VN
Smelyanskiy
QuAIL, NASA Ames Research Center, Moffett Field, California 94035, USA.|Stinger Ghaffarian Technologies Inc., 7701 Greenbelt Rd., Suite 400, Greenbelt, Maryland 20770, USA.
Zhang
Z
Jiang
Google, Venice, California 90291, USA.
Sergio
S
Boixo
Google, Venice, California 90291, USA.
Hartmut
H
Neven
Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland.
Matthias
M
Troyer