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Sample complexity of learning parametric quantum circuits
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DOI：10.1088/2058-9565/ac4f30.png)
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Quantum computers hold unprecedented potentials for machine learning applications. Here, we prove that physical quantum circuits are probably approximately correct learnable on a quantum computer via empirical risk minimization: to learn a parametric quantum circuit with at most n(c) gates and each gate acting on a constant number of qubits, the sample complexity is bounded by O(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` elementary gates. Our results provide a valuable guide for quantum machine learning in both theory and practice.
Keyword:
quantum machine learning
sample complexity
PAC learnable
quantum circuit
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