Implementation of a Hamming-Distance-Like Genomic Quantum Classifier Using Inner Products on IBMQX4 and IBMQX16

Motivated by the problem of classifying individuals with a disease versus controls using functional genomic attributes as input, we encode the input as a string of 1s (presence) or 0s (absence) of the genomic attribute across the genome. Blocks of physical regions in the subdivided genome serve as the feature dimensions, which takes full advantage of remaining in the computational basis of a quantum computer. Given that a natural distance between two binary strings is the Hamming distance and that this distance shares properties with an inner product between qubits, we developed two Hamming-distance-like classifiers which apply two different kinds of inner products ("active" and "symmetric") to directly and efficiently classify a test input into either of two training classes. To account for multiple disease and control samples, each train class can be composed of an arbitrary number of bit strings (i.e., number of samples) that can be compressed into one input string per class. Thus, our circuits require the same number of qubits regardless of the number of training samples. These algorithms, which implement a training bisection decision plane, were simulated and implemented on IBMQX4 and IBMQX16. The latter allowed for encoding of $64$ training features across the genome for $2$ (disease and control) training classes.