Nonequilibrium work performed in quantum annealing

Abstract

Quantum annealing is a generic solver of classical optimization problems that makes full use of quantum fluctuations. We consider work statistics given by a repetition of quantum annealing processes by employing the Jarzynski equality proposed in nonequilibrium statistical physics. In particular, we analyze the distribution of the work performed by a transverse field. A special symmetry, gauge symmetry, leads to a non-trivial relationship between quantum annealing toward different targets in the theory of spin glasses. We believe that our results will be a step toward an alternative realization of efficient quantum computation as well as our better understanding of nonequilibrium behavior of systems under quantum control.

4pages, Proceedings of International Symposium "Nanoscience and Quantum Physics 2011" (nanoPHYS'11) Title is changed and some typos are fixed

References in corpus (7)

• Mathematical Foundation of Quantum Annealing
• Fluctuation Theorem for Arbitrary Open Quantum Systems
• First order phase transition in the Quantum Adiabatic Algorithm
• Simple Glass Models and their Quantum Annealing
• Quantum annealing with Jarzynski equality
• Gauge Theory for Quantum Spin Glasses
• Non-equilibrium Relations for Spin Glasses with Gauge Symmetry

Cited by in corpus (6)

• Benchmark test of Black-box optimization using D-Wave quantum annealer
• Mathematical understanding of detailed balance condition violation and its application to Langevin dynamics
• Statistical-mechanical analysis of compressed sensing for Hamiltonian estimation of Ising spin glass
• Message-passing algorithm of quantum annealing with nonstoquastic Hamiltonian
• Stochastic gradient method with accelerated stochastic dynamics
• Statistical mechanical models of integer factorization problem