Classical simulation and theory of quantum annealing in a thermal environment
arXiv:2102.02570 · doi:10.1103/PhysRevLett.128.170502
Abstract
We study quantum annealing in the quantum Ising model coupled to a thermal environment. When the speed of quantum annealing is sufficiently slow, the system evolves following the instantaneous thermal equilibrium. This quasistatic and isothermal evolution, however, fails near the end of annealing because the relaxation time grows infinitely, therefore yielding excess energy from the thermal equilibrium. We develop a phenomenological theory based on this picture and derive a scaling relation of the excess energy after annealing. The theoretical results are numerically confirmed using a novel non-Markovian method that we recently proposed based on a path-integral representation of the reduced density matrix and the infinite time evolving block decimation. In addition, we discuss crossovers from weak to strong coupling as well as from the adiabatic to quasistatic regime, and propose experiments on the D-Wave quantum annealer.
8 pages, 6 fugures
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Cited by in corpus (8)
- Quantum Annealing: An Overview
- Quantum Optimisation of Complex Systems with a Quantum Annealer
- Heat Current in Non-Markovian Open Systems
- Kibble-Zurek scaling due to environment temperature quench in the transverse field Ising model
- Non-Markovian effects in stochastic resonance in a two level system
- Half Landau-Zener ramp to a quantum phase transition in a dissipative single spin sodel
- Improving quantum annealing by engineering the coupling to the environment
- Solving Helmholtz problems with finite elements on a quantum annealer