Improved Boltzmann machines with error corrected quantum annealing

Abstract

Boltzmann machines are the basis of several deep learning methods that have been successfully applied to both supervised and unsupervised machine learning tasks. These models assume that a dataset is generated according to a Boltzmann distribution, and the goal of the training procedure is to learn the set of parameters that most closely match the input data distribution. Training such models is difficult due to the intractability of traditional sampling techniques, and proposals using quantum annealers for sampling hope to mitigate the sampling cost. However, real physical devices will inevitably be coupled to the environment, and the strength of this coupling affects the effective temperature of the distributions from which a quantum annealer samples. To counteract this problem, error correction schemes that can effectively reduce the temperature are needed if there is to be some benefit in using quantum annealing for problems at a larger scale, where we might expect the effective temperature of the device to not be sufficiently low. To this end, we have applied nested quantum annealing correction (NQAC) to do unsupervised learning with a small bars and stripes dataset, and to do supervised learning with a coarse-grained MNIST dataset. For both datasets we demonstrate improved training and a concomitant effective temperature reduction at higher noise levels relative to the unencoded case. We also find better performance overall with longer anneal times and offer an interpretation of the results based on a comparison to simulated quantum annealing and spin vector Monte Carlo. A counterintuitive aspect of our results is that the output distribution generally becomes less Gibbs-like with increasing nesting level and increasing anneal times, which shows that improved training performance can be achieved without equilibration to the target Gibbs distribution.

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Cited by in corpus (15)

• Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond
• Prospects for Quantum Enhancement with Diabatic Quantum Annealing
• High-quality Thermal Gibbs Sampling with Quantum Annealing Hardware
• Boltzmann machine learning with a variational quantum algorithm
• Signatures of Open and Noisy Quantum Systems in Single-Qubit Quantum Annealing
• Preparing ground states of the XXZ model using the quantum annealing with inductively coupled superconducting flux qubits
• A hybrid quantum-classical approach for inference on restricted Boltzmann machines
• Localization transition induced by programmable disorder
• Perils of Embedding for Quantum Sampling
• Discriminating Non-Isomorphic Graphs with an Experimental Quantum Annealer
• Demonstration of error-suppressed quantum annealing via boundary cancellation
• Using copies to improve precision in continuous-time quantum computing
• Reducing quantum annealing biases for solving the graph partitioning problem
• Frustration-enhanced quantum annealing correction models with additional inter-replica interactions
• Training Hybrid Classical-Quantum Classifiers via Stochastic Variational Optimization