Hearing the Shape of the Ising Model with a Programmable Superconducting-Flux Annealer

TL;DR

This paper explores the use of a programmable superconducting flux annealer to distinguish graph structures by analyzing quantum and classical spectra of the Ising model, revealing the quantum spectrum's superior invariance.

Contribution

It introduces refined spectral invariants for the Ising model and demonstrates experimentally that classical spectral refinements outperform quantum spectra in graph distinction.

Findings

Quantum spectrum is a stronger invariant than classical spectrum.

Classical spectral refinements can distinguish non-isomorphic graphs.

Quantum spectra did not distinguish the graphs in experiments.

Abstract

Two objects can be distinguished if they have different measurable properties. Thus, distinguishability depends on the Physics of the objects. In considering graphs, we revisit the Ising model as a framework to define physically meaningful spectral invariants. In this context, we introduce a family of refinements of the classical spectrum and consider the quantum partition function. We demonstrate that the energy spectrum of the quantum Ising Hamiltonian is a stronger invariant than the classical one without refinements. For the purpose of implementing the related physical systems, we perform experiments on a programmable annealer with superconducting flux technology. Departing from the paradigm of adiabatic computation, we take advantage of a noisy evolution of the device to generate statistics of low energy states. The graphs considered in the experiments have the same classical partition functions, but different quantum spectra. The data obtained from the annealer distinguish non-isomorphic graphs via information contained in the classical refinements of the functions but not via the differences in the quantum spectra.