The Perturbed Ferromagnetic Chain: A Tuneable Test of Quantum Hardness in the Transverse-Field Ising Model

TL;DR

This paper introduces the perturbed ferromagnetic chain as a tunable testbed for quantum hardness, demonstrating that quantum dynamics outperform classical methods in solving this frustrated system.

Contribution

It presents a new frustrated chain model with tunable hardness, enabling comparison of classical and quantum annealing, highlighting quantum advantages in certain regimes.

Findings

Quantum dynamics stay in ground state more effectively than classical methods.

Classical SVMC methods get trapped in excited states.

Quantum evolution yields higher ground state probabilities.

Abstract

Quantum annealing in the transverse-field Ising model (TFIM) with open-system dynamics is known to use thermally-assisted tunneling to drive computation. However, it is still subject to debate whether quantum systems in the presence of decoherence are more useful than those using classical dynamics to drive computation. We contribute to this debate by introducing the perturbed ferromagnetic chain (PFC), a chain of frustrated sub-systems where the degree of frustration scales inversely with the perturbation introduced by a tunable parameter. This gives us an easily embeddable gadget whereby problem hardness can be tuned for systems of constant size. We outline the properties of the PFC and compare classical spin-vector Monte Carlo (SVMC) variants with the adiabatic quantum master equation. We demonstrate that SVMC methods get trapped in the exponentially large first-excited-state manifold when solving this frustrated problem, whereas evolution using quantum dynamics remains in the lowest energy eigenstates. This results in significant differences in ground state probability when using either classical or quantum annealing dynamics in the TFIM.