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arXiv 2209.03075quant-phcs.CCcs.ITcs.LGmath-phmath.ITmath.MP

量子光子处理器及更广泛场景的学习理论

A learning theory for quantum photonic processors and beyond

Università Roma Tre(罗马第三大学)

Matteo Rosati

AI总结:

本研究针对连续变量量子电路的量子态、测量与信道学习任务,通过计算伪维度和覆盖数界建立高效可学习性保证,证明其样本复杂度随模式数多项式增长且不随电路深度增长。

摘要:

我们研究学习由连续变量(CV)量子电路生成的量子态、测量和信道的任务。这类电路适用于描述光学量子技术,尤其涵盖了能够展现量子优势的最先进光子处理器。我们定义了若干函数类,它们将编码进CV电路参数的经典变量映射为在这些电路上计算得到的输出概率。随后我们通过计算其伪维度或覆盖数的界,为此类函数建立了高效可学习性保证,表明CV量子电路的学习样本复杂度与电路规模(即模式数)呈多项式关系。我们的结果显示,与有限维对应电路不同,CV电路可使用不随电路深度增长的训练样本量实现高效训练。

英文摘要:

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.

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