Ground-state statistics from annealing algorithms: Quantum vs classical approaches

Abstract

We study the performance of quantum annealing for systems with ground-state degeneracy by directly solving the Schrödinger equation for small systems and quantum Monte Carlo simulations for larger systems. The results indicate that naive quantum annealing using a transverse field may not be well suited to identify all degenerate ground-state configurations, although the value of the ground-state energy is often efficiently estimated. An introduction of quantum transitions to all states with equal weights is shown to greatly improve the situation but with a sacrifice in the annealing time. We also clarify the relation between the spin configurations in the degenerate ground states and the probabilities that those states are obtained by quantum annealing. The strengths and weaknesses of quantum annealing for problems with degenerate ground states are discussed in comparison with classical simulated annealing.

12 pages, 16 epsfiles

References in corpus (4)

• Quantum Annealing in the Transverse Ising Model
• Quantum Annealing: A New Method for Minimizing Multidimensional Functions
• Finding Low-Temperature States with Parallel Tempering, Simulated Annealing and Simple Monte Carlo
• Optimization by Quantum Annealing: Lessons from Simple Cases

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