Subsystem relaxation and a calibrated sampling diagnostic for programmable quantum annealers

TL;DR

This paper develops a validation protocol for quantum annealers, analyzing subsystem relaxation behavior and introducing a diagnostic to detect memory loss and trapping during sampling.

Contribution

It presents a subsystem-environment protocol and a calibrated diagnostic for assessing relaxation and memory retention in programmable quantum annealers.

Findings

Large or strongly coupled environments lead to initial-state independence.

Disorder and atypical states hinder relaxation.

The diagnostic flags rare trapping events effectively.

Abstract

Programmable quantum annealers are used as open-system samplers, but it is unclear when reverse annealing erases preparation memory and what the readout represents. Here we implement a subsystem-environment protocol on two D-Wave quantum annealers, varying environment size, coupling, disorder, preparation, geometry and QPU generation. A six-qubit subsystem becomes initial-state independent when the environment is large or strongly coupled, while quenched disorder and atypical environment states arrest relaxation. Pairing the memory order parameter with the distance to a calibrated conditional-Boltzmann reference yields a diagnostic that flags rare wrong-basin trapping memory loss alone misses; memory-retaining conditions stay far from the reference (median 0.35). Relaxed ferromagnetic readouts are near-deterministic, so small distances there are a consistency check, not a thermometric test. In a mixed-frustration benchmark, the local-update model practitioners assume mispredicts QPU relaxation roughly sevenfold, whereas non-local classical sampling recovers it. We provide a subsystem-level validation protocol for quantum-annealer sampling.