Quantum geometric machine learning for quantum circuits and control

Elija Perrier,Dacheng Tao,Chris Ferrie

doi:10.1088/1367-2630/abbf6b

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 for 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 whitebox models (which encode 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.

Highlights

IntroductionOverview Machine learning-based approaches to solving theoretical and applied problems in quantum control have gained considerable traction over recent years as researchers leverage access to enhanced computational resources in order to solve numerical optimisation problems
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 time-optimal, routes and (b) synthesise those circuits
New contributions In this work, we report a number of experimental results based upon simulations of machine learning models for quantum circuit synthesis

Summary

Introduction

Overview Machine learning-based approaches to solving theoretical and applied problems in quantum control have gained considerable traction over recent years as researchers leverage access to enhanced computational resources in order to solve numerical optimisation problems. The synthesis of geometry and quantum information has recently emerged of interest to researchers in complexity geometry [5, 6]. It is natural that the intersection between geometric and machine learning techniques in quantum control emerge as a cross-disciplinary research direction. Understanding such synergies between techniques within geometric control, quantum information processing and machine learning offers promising techniques within theoretical and applied quantum computational research, with potential application across other research domains

Results

Discussion

Conclusion