Quantum geometric machine learning for quantum circuits and control

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.

QDataSet, quantum datasets for machine learning

“…Such pulses are characterised by for example a single parameter, being the amplitude of the waveform applied to the quantum system (this manifests as we discuss below as an amplitude applied to the algebraic generators of unitary evolution (see refs. 14 , 28 for an example)). Other models of pulses (such as Gaussian) are more complex and require more sophisticated parametrisation and encoding with machine learning architectures in order to simulate.…”

“…To this end, hybrid classical-quantum QML architectures which are able to optimise classical controls or inputs for quantum systems have wider, more near-term applicability for both experiments and NISQ 11 , 12 devices. Recent literature on hybrid classical-quantum algorithms for quantum control 13 , 14 , noisy control 15 and noise characterisation 13 present examples of this approach. Other recent approaches include the hybrid use of quantum algorithms and classical objective functions for natural language processing 16 .…”

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

“…5.3.3 and 5.3.4, highlight that QOCT as a general optimization tool is not only interesting for the computation of timedependent control pulses, but also in other optimization problems of interest in quantum technologies. In this framework, geometric control has been combined with machine learning techniques in order to improve the synthesis of quantum circuits [457].…”

Multi-Axis Control of a Qubit in the Presence of Unknown Non-Markovian Quantum Noise

“…Part of the model uses blackbox structures such as neural networks, while other parts uses whitebox structures such as calculating a unitary given a Hamiltonian. This approach has been developed to model and control various quantum systems [14][15][16][17][18][19]. In this paper, we consider the optimization of open-loop controls for single qubit gate synthesis when the a qubit that is in contact with an a priori unknown non-Markovian quantum environment (which is not a quantum white noise process), and analyze its performance.…”