Bayesian Deep Learning on a Quantum Computer

TL;DR

This paper introduces a quantum algorithm for Bayesian deep learning that leverages Gaussian process connections, offering potential polynomial speedups and demonstrating feasibility on current quantum hardware.

Contribution

It develops a novel quantum algorithm for Bayesian deep learning by connecting neural networks with Gaussian processes, enabling efficient quantum matrix inversion.

Findings

Quantum algorithm achieves polynomial speedup over classical methods.

Algorithm successfully executed on current quantum hardware.

Robustness analyzed under realistic noise conditions.

Abstract

Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to deep architectures has remained a major challenge. Recent results connected deep feedforward neural networks with Gaussian processes, allowing training without backpropagation. This connection enables us to leverage a quantum algorithm designed for Gaussian processes and develop a new algorithm for Bayesian deep learning on quantum computers. The properties of the kernel matrix in the Gaussian process ensure the efficient execution of the core component of the protocol, quantum matrix inversion, providing an at least polynomial speedup over classical algorithms. Furthermore, we demonstrate the execution of the algorithm on contemporary quantum computers and analyze its robustness with respect to realistic noise models.