Training Gaussian Boson Sampling Distributions

Abstract

Gaussian Boson Sampling (GBS) is a near-term platform for photonic quantum computing. Applications have been developed which rely on directly programming GBS devices, but the ability to train and optimize circuits has been a key missing ingredient for developing new algorithms. In this work, we derive analytical gradient formulas for the GBS distribution, which can be used to train devices using standard methods based on gradient descent. We introduce a parametrization of the distribution that allows the gradient to be estimated by sampling from the same device that is being optimized. In the case of training using a Kullback-Leibler divergence or log-likelihood cost function, we show that gradients can be computed classically, leading to fast training. We illustrate these results with numerical experiments in stochastic optimization and unsupervised learning. As a particular example, we introduce the variational Ising solver, a hybrid algorithm for training GBS devices to sample ground states of a classical Ising model with high probability.

15 pages, 3 figures

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• Information processing at the speed of light
• Fast optimization of parametrized quantum optical circuits
• Riemannian optimization of photonic quantum circuits in phase and Fock space
• Protocols for classically training quantum generative models on probability distributions
• A Quadratic Speedup in the Optimization of Noisy Quantum Optical Circuits
• Universal compiling and (No-)Free-Lunch theorems for continuous variable quantum learning
• Gaussian boson sampling and multi-particle event optimization by machine learning in the quantum phase space
• Gaussian Boson Sampling for binary optimization
• Classical modelling of a bosonic sampler with photon collisions