High-quality Thermal Gibbs Sampling with Quantum Annealing Hardware

Abstract

Quantum Annealing (QA) was originally intended for accelerating the solution of combinatorial optimization tasks that have natural encodings as Ising models. However, recent experiments on QA hardware platforms have demonstrated that, in the operating regime corresponding to weak interactions, the QA hardware behaves like a noisy Gibbs sampler at a hardware-specific effective temperature. This work builds on those insights and identifies a class of small hardware-native Ising models that are robust to noise effects and proposes a novel procedure for executing these models on QA hardware to maximize Gibbs sampling performance. Experimental results indicate that the proposed protocol results in high-quality Gibbs samples from a hardware-specific effective temperature and that the QA annealing time can be used to adjust the effective temperature of the output distribution. The procedure proposed in this work provides a new approach to using QA hardware for Ising model sampling presenting potential new opportunities for applications in machine learning and physics simulation.

On the challenges of using D-Wave computers to sample Boltzmann Random Variables

“…As Boltzmann distributions are to be reached in equilibrium setting, one may hope that such a pause would give the system enough time to reach such an equilibrium. This direction is explored in [11], where authors experimentally determine on simple problems which pauses yield the results that are closer to an actual Boltzmann distribution. Yet despite the theoretical and experimental insights provided, the road towards Boltzmann sampling is still full of pitfalls as:…”

“…• upon experimentally determining which pause of the anneal schedule yields a sampleset that is the closest to a Boltzmann distribution, authors of [11] retrofit an Ising model corresponding to this distribution. Hence, even if a pause-based protocol could yield a Boltzmann distribution, it would a priori not be the target distribution (thus not solving the sampling problem);…”

“…c) Compensating for α Assuming thermal equilibrium to be reached, compensating for α is still a nontrivial task. Nelson et al [11] retrofit an Ising Hamiltonian to get a Boltzmann distribution. They consider processes in which they aim to sample according to a target distribution: x) , Z = x ′ e −ain H(x ′ ) Upon sampling and thus getting a sample set S, they then numerically determine the parameter:…”