Quantum Geometric Machine Learning for Quantum Circuits and Control

TL;DR

This paper explores how deep learning can enhance geometric control methods for quantum circuits, improving time-optimal synthesis and verification of quantum gates on Lie group manifolds.

Contribution

It introduces novel deep learning algorithms, including greybox models, to approximate geodesics and optimize quantum circuit synthesis on Lie groups like SU(2), SU(4), and SU(8).

Findings

Greybox models outperform traditional algorithms in quantum circuit approximation.

Deep learning enhances the verification of geodesic routes in quantum circuit synthesis.

Results demonstrate improved time-optimal control in low-dimensional multi-qubit systems.

Abstract

The application of machine learning techniques to solve problems in quantum control together with established geometric methods for solving optimisation problems leads naturally to an exploration of how machine learning approaches can be used to enhance geometric approaches to solving problems in quantum information processing. In this work, we review and extend the application of deep learning to quantum geometric control problems. Specifically, we demonstrate enhancements in time-optimal control in the context of quantum circuit synthesis problems by applying novel deep learning algorithms in order to approximate geodesics (and thus minimal circuits) along Lie group manifolds relevant to low-dimensional multi-qubit systems, such as SU(2), SU(4) and SU(8). We demonstrate the superior performance of greybox models, which combine traditional blackbox algorithms with prior domain knowledge of quantum mechanics, as means of learning underlying quantum circuit distributions of interest. Our results demonstrate how geometric control techniques can be used to both (a) verify the extent to which geometrically synthesised quantum circuits lie along geodesic, and thus time-optimal, routes and (b) synthesise those circuits. Our results are of interest to researchers in quantum control and quantum information theory seeking to combine machine learning and geometric techniques for time-optimal control problems.