Avoiding local minima in Variational Quantum Algorithms with Neural Networks

Abstract

Variational Quantum Algorithms have emerged as a leading paradigm for near-term quantum computation. In such algorithms, a parameterized quantum circuit is controlled via a classical optimization method that seeks to minimize a problem-dependent cost function. Although such algorithms are powerful in principle, the non-convexity of the associated cost landscapes and the prevalence of local minima means that local optimization methods such as gradient descent typically fail to reach good solutions. In this work we suggest a method to improve gradient-based approaches to variational quantum circuit optimization, which involves coupling the output of the quantum circuit to a classical neural network. The effect of this neural network is to peturb the cost landscape as a function of its parameters, so that local minima can be escaped or avoided via a modification to the cost landscape itself. We present two algorithms within this framework and numerically benchmark them on small instances of the Max-Cut optimization problem. We show that the method is able to reach deeper minima and lower cost values than standard gradient descent based approaches. Moreover, our algorithms require essentially the same number of quantum circuit evaluations per optimization step as the standard approach since, unlike the gradient with respect to the circuit, the neural network updates can be estimated in parallel via the backpropagation method. More generally, our approach suggests that relaxing the cost landscape is a fruitful path to improving near-term quantum computing algorithms.

arXiv comment12 pages (12 figures) + 1 page Supplementary material (2 figures). Comments are welcome

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Cited by in corpus (9)

• Theory of overparametrization in quantum neural networks
• Graph neural network initialisation of quantum approximate optimisation
• Quantum algorithms for the generalized eigenvalue problem
• Expressivity of Variational Quantum Machine Learning on the Boolean Cube
• Efficient and Robust Parameter Optimization of the Unitary Coupled-Cluster Ansatz
• Approaching Collateral Optimization for NISQ and Quantum-Inspired Computing
• Variational post-selection for ground states and thermal states simulation
• Using machine learning for quantum annealing accuracy prediction
• Generative flow-based warm start of the variational quantum eigensolver