Sample complexity of learning parametric quantum circuits

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.

Automated summary

This article proves that physical quantum circuits can be learned through empirical risk minimization on a quantum computer, and provides valuable guidance for the development of quantum machine learning in both theory and practice.