Sample Complexity of Learning Quantum Circuits
- URL: http://arxiv.org/abs/2107.09078v1
- Date: Mon, 19 Jul 2021 18:00:04 GMT
- Title: Sample Complexity of Learning Quantum Circuits
- Authors: Haoyuan Cai, Qi Ye, Dong-Ling Deng
- Abstract summary: We prove that physical quantum circuits are PAC learnable on a quantum computer via empirical risk minimization.
Our results provide a valuable guide for quantum machine learning in both theory and experiment.
- Score: 4.329298109272386
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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
$\tilde{O}(n^{c+1})$. 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 $n^c$ elementary gates. Our results provide a valuable guide for
quantum machine learning in both theory and experiment.
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