Condensed Matter Seminars

Motivated by the problem of classifying individuals with a disease versus controls using a functional genomic attribute as input, we developed a general-purpose inner product–based kernel classifier to classify the test as a normal or disease sample. We encoded each training patient sample as a string of 1s and 0s representing the presence and absence, respectively of a relevant genomic feature (e.g., single nucleotide variant) across the subdivided human genome. The classifier implements an inner product between N = 2^n dimension test and train vectors using n quantum gates. Moreover, each training class can be composed of an arbitrary number m of samples that can be classically summed into one input string to effectively execute all test-train inner products simultaneously. Thus, our circuit requires the same number of qubits for any number of training samples and is O(logN) in gate complexity after the states are prepared. This represents an exponential speedup in computing the test-train inner products compared to the classical approach. However, there are two major problems with this method, especially for genome-scale input features. The encoding approach described above is an amplitude encoding of classical data into highly entangled multi-qubit states. This suffers from a well-known problem that inputting the data requires solving a set of N equations to arrive at the correct gate settings, which destroys the exponential gain of the overall performance of the classifier compared to one implemented on a classical computer. The second problem is that the genomic classifier detailed above yields a linear decision boundary in the space of the encoded training data. A recent method termed quantum metric learning, in which a learned quantum embedding maximally separates data into classes, addresses both of these problems. We show that quantum metric learning applied to a breast cancer diagnostic dataset accurately predicts benign and malignant tumors on hold out test data as long as the number of model parameters are notably less than the number training samples.