  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.
