Quantum computation with machine-learning-controlled quantum stuff

Abstract

We formulate the control over quantum matter, so as to perform arbitrary quantum computation, as an optimization problem. We then provide a schematic machine learning algorithm for its solution. Imagine a long strip of ‘quantum stuff’, endowed with certain assumed physical properties, and equipped with regularly spaced wires to provide input settings and to read off outcomes. After showing how the corresponding map from settings to outcomes can be construed as a quantum circuit, we provide a machine learning framework to tomographically ‘learn’ which settings implement the members of a universal gate set. To that end, we devise a loss function measuring how badly a proposed encoding has failed to implement a given circuit, and prove the existence of ‘tomographically complete’ circuit sets: should a given encoding minimize the loss function for each member of such a set, it also will for an arbitrary circuit. At optimum, arbitrary quantum gates, and thus arbitrary quantum programs, can be implemented using the stuff.