Reservoir Computing and Quantum Systems

Abstract

The current era of quantum computing is characterized by scale and noise: we are able to engineer quantum systems with an unprecedented number of degrees of freedom which can be controlled and read-out. However, their application to practical computation is hindered by unavoidable noise in these platforms, our inability to correct for the resulting errors in the current computational paradigm, and limited precision with which quantum states can be measured. In this thesis we explore the intersection of engineered quantum systems and reservoir computing. Reservoir computing is a machine learning framework which uses a physical dynamical system to perform computation, in a manner agnostic to noise or errors and without detailed optimization. We will show, both through theoretical analysis and experiments on cloud quantum computers, that operating current quantum platforms as reservoir computers is a powerful computational paradigm which offers solutions to the above issues, while avoiding training difficulties typically associated with quantum machine learning.We study both gate-based and continuously-evolving qubit networks as reservoir computers, with an emphasis on their performance in the presence of noise and limited measurement resources. We develop an intuitive analysis which allows for the construction of measured observables that are maximally robust to this noise, optimizing the performance of a given quantum reservoir computer. We naturally obtain a metric, the expressible capacity, which quantifies how much information can be extracted from a quantum system in practice with limited measurement shots. This encompasses the input, algorithm, physical device, and measurement — ideal for a full-stack analysis of current quantum computers, and the critical unsolved problem of informing ansatz design in quantum machine learning. Finally, instead of quantum systems as reservoirs, we consider the application of reservoir computing to the problem of quantum measurement. We show that a small oscillator network sharing the same chip as a quantum computer can process quantum measurement signals with greater accuracy, lower latency, and less calibration overhead than conventional approaches. This reservoir computer co-processor is naturally realizable using components already present in the measurement chain of superconducting circuits, and adaptable to practical tasks such as parity monitoring and tomography.