Subsystem relaxation and a calibrated sampling diagnostic for programmable quantum annealers

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.