Simulated Quantum Annealing is Efficient on the Spike Hamiltonian

TL;DR

This paper demonstrates that Simulated Quantum Annealing (SQA) efficiently solves the Spike Hamiltonian, a toy model for quantum tunneling, showing no exponential advantage over quantum annealing in this context.

Contribution

The study extends previous analysis to the full polynomial regime of the Spike Hamiltonian, proving SQA's efficiency and its comparable performance to quantum annealing.

Findings

SQA runs in polynomial time on the Spike Hamiltonian.

No exponential speedup of QA over SQA is observed.

The analysis covers the remaining polynomial regime of energy gaps.

Abstract

In this work we study the convergence of a classical algorithm called Simulated Quantum Annealing (SQA) on the Spike Hamiltonian, a specific toy model Hamiltonian for quantum-mechanical tunneling introduced by [FGG02]. This toy model Hamiltonian encodes a simple bit-symmetric cost function f in the computational basis, and is used to emulate local minima in more complex optimization problems. In previous work [CH16] showed that SQA runs in polynomial time in much of the regime of spikes that QA does, pointing to evidence against an exponential speedup through tunneling. In this paper we extend their analysis to the remaining polynomial regime of energy gaps of the spike Hamiltonian, to show that indeed QA presents no exponential speedup with respect to SQA on this family of toy models.