We consider the tasks of learning quantum states, measurements and channels generated by continuous-variable (CV) quantum circuits. This family of circuits is suited to describe optical quantum technologies and in particular it includes state-of-the-art photonic processors capable of showing quantum advantage. We define classes of functions that map classical variables, encoded into the CV circuit parameters, to outcome probabilities evaluated on those circuits. We then establish efficient learnability guarantees for such classes, by computing bounds on their pseudo-dimension or covering numbers, showing that CV quantum circuits can be learned with a sample complexity that scales polynomially with the circuit's size, i.e., the number of modes. Our results show that CV circuits can be trained efficiently using a number of training samples that, unlike their finite-dimensional counterpart, does not scale with the circuit depth.

中文翻译：

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量子光子处理器及其他领域的学习理论


我们考虑学习连续变量（CV）量子电路生成的量子态、测量和通道的任务。该电路系列适合描述光量子技术，特别是它包括能够显示量子优势的最先进的光子处理器。我们定义了一些函数类，这些函数将编码到 CV 电路参数中的经典变量映射到在这些电路上评估的结果概率。然后，我们通过计算它们的伪维度或覆盖数的界限，为此类建立有效的可学习性保证，表明可以通过与电路大小（即模式数量）成多项式缩放的样本复杂度来学习 CV 量子电路。我们的结果表明，可以使用大量训练样本来有效地训练 CV 电路，这些训练样本与有限维对应的样本不同，不会随电路深度而缩放。