Supervised Learning with Quantum Reservoir Computing

Abstract

In this thesis we adopt an approach inspired by Reservoir Computing (RC) [10] to gate-based quantum processors. The RC paradigm presents a universal framework for encoding computation into the natural time-evolution of any physical system that is sufficiently complex. There have been attempts at porting the RC paradigm to quantum mechanical systems [5], and recent results indicate they may present universal approximators for arbitrary functions on input data [2]. The goal of this work is to devise a distinct RC approach readily implementable on quantum processors to handle nontrivial machine learning tasks such as handwritten digit recognition [14]. We fulfill this objective by presenting a quantum RC approach that leverages (1) partial quantum measurement of a multi-qubit register, (2) a fixed gate-set, and (3) multi-time cumulants. We subsequently benchmark the most promising architecture against the Quantum Perceptron Algorithm (QPA) to classify a 2 × 2 pixel dataset [20], finding gate-complexity that appears to be scalable. We then address handwritten digit classification tasks of various sizes drawn from the MNIST database, which in the largest instance included the full MNIST 28 × 28 multi-classification task of digits 0-9, achieving 84.7% accuracy in a 6-qubit circuit simulation. We analyze the impact of sources of decoherence and noise, and implement an 8 × 8 MNIST binary classification on IBM Q’s 7-qubit Casablanca device, obtaining a 95% testing accuracy. Our results indicate that we are likely limited by the number of qubits available to us to carry out the full MNIST classification with high accuracy on a quantum processor.