Griffiths-McCoy singularity on the diluted Chimera graph: Monte Carlo simulations and experiments on the quantum hardware

TL;DR

This study investigates the Griffiths-McCoy singularity in disordered quantum spin systems using Monte Carlo simulations and experiments on a D-Wave quantum annealer, demonstrating the phenomenon's presence and exploring the hardware's capabilities.

Contribution

First experimental evidence of Griffiths-McCoy singularity on a quantum annealer, combining simulations and hardware experiments to assess analog quantum simulation of disordered quantum systems.

Findings

Evidence of Griffiths-McCoy singularity in simulations.

Experimental results are consistent with simulation findings.

Highlights limitations and potential of D-Wave quantum hardware for such studies.

Abstract

The Griffiths-McCoy singularity is a phenomenon characteristic of low-dimensional disordered quantum spin systems, in which the magnetic susceptibility shows singular behavior as a function of the external field even within the paramagnetic phase. We study whether this phenomenon is observed in the transverse-field Ising model with disordered ferromagnetic interactions on the quasi-two-dimensional diluted Chimera graph both by quantum Monte Carlo simulations and by extensive experiments on the D-Wave quantum annealer used as a quantum simulator. From quantum Monte Carlo simulations, evidence is found for the existence of the Griffiths-McCoy singularity in the paramagnetic phase. The experimental approach on the quantum hardware produces results that are less clear-cut due to the intrinsic noise and errors in the analog quantum device but can nonetheless be interpreted to be consistent with the existence of the Griffiths-McCoy singularity as in the Monte Carlo case. This is the first experimental approach based on an analog quantum simulator to study the subtle phenomenon of Griffiths-McCoy singularities in a disordered quantum spin system, through which we have clarified the capabilities and limitations of the D-Wave quantum annealer as a quantum simulator.