Sample Complexity of Learning Quantum Circuits
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Quantum computers hold unprecedented potentials for machine learning applications. Here, we prove that physical quantum circuits are PAC (probably approximately correct) learnable on a quantum computer via empirical risk minimization: to learn a quantum circuit with at most n^c gates and each gate acting on a constant number of qubits, the sample complexity is bounded by Õ(n^c+1). In particular, we explicitly construct a family of variational quantum circuits with O(n^c+1) elementary gates arranged in a fixed pattern, which can represent all physical quantum circuits consisting of at most n^c elementary gates. Our results provide a valuable guide for quantum machine learning in both theory and experiment.
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