# Thermalization, freeze-out and noise: deciphering experimental quantum annealers

## TL;DR

This study compares two quantum annealers at different temperatures, revealing that their output distributions often do not match classical Boltzmann distributions and are influenced by freeze-out effects, impacting their use as Boltzmann samplers.

## Contribution

The paper introduces a method to estimate effective temperatures from annealer outputs and demonstrates the non-classical thermalization behavior in large-scale spin-glass instances.

## Key findings

- Output distributions often deviate from classical Boltzmann distributions.
- Effective temperatures are higher than physical temperatures in thermalized instances.
- Temperature fluctuations increase with problem size and programming cycles.

## Abstract

By contrasting the performance of two quantum annealers operating at different temperatures, we address recent questions related to the role of temperature in these devices and their function as `Boltzmann samplers'. Using a method to reliably calculate the degeneracies of the energy levels of large-scale spin-glass instances, we are able to estimate the instance-dependent effective temperature from the output of annealing runs. Our results show that the output distributions of the annealers do not in general correspond to classical Boltzmann distributions. For the small fraction of the instances for which classical thermalization takes place, we find that the effective temperatures are significantly higher than the physical temperatures. Our results in this regime provide further evidence for the `freeze-out' picture in which the output is sampled from equilibrium distributions determined at a point in time earlier in the quantum annealing process. We also find that the effective temperatures at different programming cycles fluctuate greatly, with the effect worsening with problem size. We discuss the implications of our results for the design of future quantum annealers to act as efficient Boltzmann samplers and for the programming of such annealers.