Proof of avoidability of the quantum first-order transition in transverse magnetization in quantum annealing of finite-dimensional spin glasses

Abstract

It is rigorously shown that an appropriate quantum annealing for any finite-dimensional spin system has no quantum first-order transition in transverse magnetization. This result can be applied to finite-dimensional spin-glass systems, where the ground state search problem is known to be hard to solve. Consequently, it is strongly suggested that the quantum first-order transition in transverse magnetization is not fatal to the difficulty of combinatorial optimization problems in quantum annealing.

26 pages, no figure

References in corpus (6)

• Quantum annealing with antiferromagnetic fluctuations
• Size dependence of the minimum excitation gap in the Quantum Adiabatic Algorithm
• Energy gaps in quantum first-order mean-field-like transitions: The problems that quantum annealing cannot solve
• The performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs
• Absence of replica symmetry breaking in the random field Ising model
• Squeezed ensemble for systems with first-order phase transitions