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Quantum computing crucially relies on the ability to efficiently characterizethe quantum states output by quantum hardware. Conventional methods which probethese states through direct measurements and classically computed correlationsbecome computationally expensive when increasing the system size. Quantumneural networks tailored to recognize specific features of quantum states bycombining unitary operations, measurements and feedforward promise to requirefewer measurements and to tolerate errors. Here, we realize a quantumconvolutional neural network (QCNN) on a 7-qubit superconducting quantumprocessor to identify symmetry-protected topological (SPT) phases of a spinmodel characterized by a non-zero string order parameter. We benchmark theperformance of the QCNN based on approximate ground states of a family ofcluster-Ising Hamiltonians which we prepare using a hardware-efficient,low-depth state preparation circuit. We find that, despite being composed offinite-fidelity gates itself, the QCNN recognizes the topological phase withhigher fidelity than direct measurements of the string order parameter for theprepared states.

Realizing Quantum Convolutional Neural Networks on a Superconducting Quantum Processor to Recognize Quantum Phases