Abstract 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 c elementary gates. Our results provide a valuable guide for quantum machine learning in both theory and practice.

中文翻译：

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学习参量量子电路的样本复杂度

摘要 量子计算机在机器学习应用方面具有前所未有的潜力。在这里，我们证明物理量子电路可能通过经验风险最小化在量子计算机上近似正确地学习：学习一个参数量子电路，最多具有 nc 门，每个门都作用于恒定数量的量子比特，. 特别是，我们明确地构建了一系列变分量子电路，其中 O(n c+1) 个基本门以固定模式排列，可以表示最多由 nc 个基本门组成的所有物理量子电路。我们的结果为量子机器学习的理论和实践提供了有价值的指导。