  One of the major approaches to neuromorphic computing is using memristors as
analogue synapses. We propose unitary quantum gates that exhibit memristive
behaviours, including Ohm's law, pinched hysteresis loop and synaptic
plasticity. Hysteresis depending on the quantum phase and long-term plasticity
that encodes the quantum state are observed. We also propose a three-layer
neural network with the capability of universal quantum computing. Quantum
state classification on the memristive neural network is demonstrated. Our
results pave the way towards brain-inspired quantum computing. We obtain these
results in numerical simulations and experiments on the superconducting quantum
computer ibmq_vigo.
