Storage capacity and learning capability of quantum neural networks

Abstract We study the storage capacity of quantum neural networks (QNNs), described by completely positive trace preserving (CPTP) maps acting on an N -dimensional Hilbert space. demonstrate that attractor QNNs can store in a non-trivial manner up to linearly independent pure states. For n qubits, reach exponential capacity, O ( 2 n stretchy="false">) , clearly outperforming standard classical whose scales with number neurons . estimate, employing Gardner program, relative volume CPTP M ⩽ stationary states and show this decreases exponentially shrinks zero for ⩾ + 1. generalize our results storing mixed as well input–output relations feed-forward QNNs. Our approach opens path relate properties features This paper is dedicated memory Peter Wittek.