论文标题
量子光子处理器及以后的学习理论
A learning theory for quantum photonic processors and beyond
论文作者
论文摘要
我们考虑通过连续变化（CV）量子电路产生的学习量子状态，测量和通道的任务。这个电路家族适合描述光学量子技术，特别是它包括能够显示量子优势的最先进的光子处理器。我们定义了绘制经典变量的函数类别的类别，该变量编码为CV电路参数，以在这些电路上评估的结果概率。然后，我们通过计算其伪维数或覆盖数字来建立此类类别的有效学习性保证，表明可以以样品复杂性与电路的大小（即模式数量）多样地缩放CV量子电路。我们的结果表明，可以使用许多训练样本对CV电路进行有效训练，这些训练样品与有限维度对应物不同，这些样品与电路深度不相比。
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.
