Sample Complexity of Learning Parametric Quantum Circuits [article]

Haoyuan Cai, Qi Ye, Dong-Ling Deng
2022 arXiv   pre-print
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 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 Õ(n^c+1). In particular, we explicitly construct a family of variational quantum circuits with O(n^c+1) elementary
more » ... 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 practice.
arXiv:2107.09078v2 fatcat:w34x5ig4tfgwzos5rg7ru4bb24