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Artificial neural networks are becoming an integral part of digital solutionsto complex problems. However, employing neural networks on quantum processorsfaces challenges related to the implementation of non-linear functions usingquantum circuits. In this paper, we use repeat-until-success circuits enabledby real-time control-flow feedback to realize quantum neurons with non-linearactivation functions. These neurons constitute elementary building blocks thatcan be arranged in a variety of layouts to carry out deep learning tasksquantum coherently. As an example, we construct a minimal feedforward quantumneural network capable of learning all 2-to-1-bit Boolean functions byoptimization of network activation parameters within the supervised-learningparadigm. This model is shown to perform non-linear classification andeffectively learns from multiple copies of a single training state consistingof the maximal superposition of all inputs.

Realization of a quantum neural network using repeat-until-success circuits in a superconducting quantum processor