Bayesian Deep Learning on a Quantum Computer

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.

arXiv comment11 pages, 3 figures. RevTeX 4.1. Code is available at https://gitlab.com/apozas/bayesian-dl-quantum/ V3: Updated to match published version

References in corpus (17)

• Quantum Machine Learning
• Quantum algorithm for solving linear systems of equations
• Quantum support vector machine for big data classification
• Quantum machine learning in feature Hilbert spaces
• Exponential algorithmic speedup by quantum walk
• The quest for a Quantum Neural Network
• On the relationship between continuous- and discrete-time quantum walk
• Hamiltonian simulation with nearly optimal dependence on all parameters
• A quantum linear system algorithm for dense matrices
• Quantum algorithm and circuit design solving the Poisson equation
• Higher Order Decompositions of Ordered Operator Exponentials
• Quantum singular value decomposition of non-sparse low-rank matrices
• 16-qubit IBM universal quantum computer can be fully entangled
• Learning Relevant Features of Data with Multi-scale Tensor Networks
• Hamiltonian Simulation with Optimal Sample Complexity
• Quantum Circuit Design for Solving Linear Systems of Equations
• Black-box Hamiltonian simulation and unitary implementation

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