Quantum versus classical annealing: insights from scaling theory and results for spin glasses on 3-regular graphs

Abstract

We discuss an Ising spin glass where each $S=1/2$ spin is coupled antiferromagnetically to three other spins (3-regular graphs). Inducing quantum fluctuations by a time-dependent transverse field, we use out-of-equilibrium quantum Monte Carlo simulations to study dynamic scaling at the quantum glass transition. Comparing the dynamic exponent and other critical exponents with those of the classical (temperature-driven) transition, we conclude that quantum annealing is less efficient than classical simulated annealing in bringing the system into the glass phase. Quantum computing based on the quantum annealing paradigm is therefore inferior to classical simulated annealing for this class of problems. We also comment on previous simulations where a parameter is changed with the simulation time, which is very different from the true Hamiltonian dynamics simulated here.

5 pages, 3 figures

References in corpus (7)

• Universal adiabatic dynamics across a quantum critical point
• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Size dependence of the minimum excitation gap in the Quantum Adiabatic Algorithm
• The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective
• The performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs
• Potts Glass on Random Graphs
• Comparative Study of the Performance of Quantum Annealing and Simulated Annealing

Cited by in corpus (5)

• Kibble-Zurek scaling in the Yang-Lee edge singularity
• Direct comparison of quantum and simulated annealing on a fully-connected Ising ferromagnet
• Scaling in driven dynamics starting in the vicinity of a quantum critical point
• Dynamic scaling in the 2D Ising spin glass with Gaussian couplings
• Nonequilibrium critical dynamics in the quantum chiral clock model