Bayesian Learning of Parameterised Quantum Circuits

Abstract

Currently available quantum computers suffer from constraints including hardware noise and a limited number of qubits. As such, variational quantum algorithms that utilise a classical optimiser in order to train a parameterised quantum circuit have drawn significant attention for near-term practical applications of quantum technology. In this work, we take a probabilistic point of view and reformulate the classical optimisation as an approximation of a Bayesian posterior. The posterior is induced by combining the cost function to be minimised with a prior distribution over the parameters of the quantum circuit. We describe a dimension reduction strategy based on a maximum a posteriori point estimate with a Laplace prior. Experiments on the Quantinuum H1-2 computer show that the resulting circuits are faster to execute and less noisy than the circuits trained without the dimension reduction strategy. We subsequently describe a posterior sampling strategy based on stochastic gradient Langevin dynamics. Numerical simulations on three different problems show that the strategy is capable of generating samples from the full posterior and avoiding local optima.

arXiv comment11 pages, 7 figures

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Cited by in corpus (5)

• Stochastic noise can be helpful for variational quantum algorithms
• Generalized Bayesian Likelihood-Free Inference
• Enhancing qubit readout with Bayesian Learning
• Bayesian mitigation of measurement errors in multiqubit experiments
• Multivariate unbounded quantum regression via log-ratio probabilities mitigating barren plateaus