Quantum machine learning promises great speedups over classical algorithms, but it often requires repeated computations to achieve a desired level of accuracy for its point estimates. Bayesian learning focuses more on sampling from posterior distributions than on point estimation, thus it might be more forgiving in the face of additional quantum noise. We propose a quantum algorithm for Bayesian neural network inference, drawing on recent advances in quantum deep learning, and simulate its empirical performance on several tasks. We find that already for small numbers of qubits, our algorithm approximates the true posterior well, while it does not require any repeated computations and thus fully realizes the quantum speedups.
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