Cantori, Simone (2025) Combining classical deep learning and quantum computing. [Tesi di dottorato]

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Abstract

Quantum computers hold the promise of solving problems that are intractable for classical computers. However, their usefulness is limited by the noise that comes from imperfect hardware. In this thesis, we show how classical deep learning can be used to benchmark quantum computers, mitigate noise in quantum device outputs, and implement hybrid classical-quantum algorithms. To begin with, we demonstrate that scalable neural networks can accurately predict the expectation values of certain types of quantum circuits, even when they are significantly larger than those used during training. This allows us to benchmark large quantum systems that are otherwise too complex for standard classical simulations. We also examine the boundaries of this method when applied to parameterized quantum circuits. Next, we explore the use of deep learning for mitigating quantum computational errors. In this context, neural networks are trained on small, noisy quantum circuits to learn how to correct their output expectation values. Once trained, the same networks can be used to infer the ideal expectation values of larger circuits, for which only noisy outputs are available. We also introduce a complementary strategy that simulates training circuits using the circuit knitting technique. This approach is used to improve the accuracy of the Variational Quantum Eigensolver (VQE) algorithm through a deep learning-based error mitigation scheme. Finally, we present a method to tackle quantum many-body problems using autoregressive neural networks to identify key configurations in the sample-based diagonalization (SBD) approach. We further propose a basis transformation technique that makes the ground state more localized, an important requirement for the success of SBD methods. These basis changes can be implemented on actual quantum hardware, leading to a generalized VQE algorithm featuring the sampling of more input bitstrings.

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