Quantum Fair Machine Learning

In this paper, we inaugurate the field of quantum fair machine learning. We undertake a comparative analysis of differences and similarities between classical and quantum fair machine learning algorithms, specifying how the unique features of quantum computation alter measures, metrics and remediation strategies when quantum algorithms are subject to fairness constraints. We present the first results in quantum fair machine learning by demonstrating the use of Grover's search algorithm to satisfy statistical parity constraints imposed on quantum algorithms. We provide lower-bounds on iterations needed to achieve such statistical parity within $\epsilon$-tolerance. We extend canonical Lipschitz-conditioned individual fairness criteria to the quantum setting using quantum metrics. We examine the consequences for typical measures of fairness in machine learning context when quantum information processing and quantum data are involved. Finally, we propose open questions and research programmes for this new field of interest to researchers in computer science, ethics and quantum computation.

Computability, Complexity, Consistency and Controllability: A Four C's Framework for cross-disciplinary Ethical Algorithm Research

The ethical consequences of, constraints upon and regulation of algorithms arguably represent the defining challenges of our age, asking us to reckon with the rise of computational technologies whose potential to radically transforming social and individual orders and identity in unforeseen ways is already being realised. Yet despite the multidisciplinary impact of this algorithmic turn, there remains some way to go in motivating the crossdisciplinary collaboration that is crucial to advancing feasible proposals for the ethical design, implementation and regulation of algorithmic and automated systems. In this work, we provide a framework to assist cross-disciplinary collaboration by presenting a Four C's Framework covering key computational considerations researchers across such diverse fields should consider when approaching these questions: (i) computability, (ii) complexity, (iii) consistency and (iv) controllability. In addition, we provide examples of how insights from ethics, philosophy and population ethics are relevant to and translatable within sciences concerned with the study and design of algorithms. Our aim is to set out a framework which we believe is useful for fostering cross-disciplinary understanding of pertinent issues in ethical algorithmic literature which is relevant considering the feasibility of ethical algorithmic governance, especially the impact of computational constraints upon algorithmic governance.

Quantum Geometric Machine Learning for Quantum Circuits and Control

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.