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

TL;DR

This paper proves that finite-dimensional spin systems undergoing quantum annealing do not experience a quantum first-order transition in transverse magnetization, challenging previous assumptions about their difficulty.

Contribution

It provides a rigorous proof that appropriate quantum annealing avoids first-order transitions in transverse magnetization for finite-dimensional spin systems.

Findings

Quantum annealing has no first-order transition in transverse magnetization.

This result applies to finite-dimensional spin-glass systems.

First-order transitions may not be the main obstacle in quantum optimization.

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.