The swap test is a quantum algorithm capable of computing the absolute value of the scalar product of two arbitrary wavefunctions. Scalar products represent a crucial ingredient to many quantum machine learning (QML) methods, but their evaluation is not straightforward at all. For this reason, many research efforts have been made without achieving an efficient and robust implementation. Here, we present an integrated photonic circuit designed to implement the swap test algorithm. Our approach relies solely on linear optical integrated components and qudits, represented by single photons from an attenuated laser beam propagating through a set of waveguides. By utilizing 2³ spatial degrees of freedom for the qudits, we can configure all the necessary arrangements to set any two-qubit state and perform the swap test. This simplifies the requirements on the circuitry elements and eliminates the need for non-linearity, heralding, or post-selection to achieve multi-qubit gates. Our photonic swap test circuit successfully encodes two qubits and estimates their scalar product with a measured root mean square error smaller than 0.05. This result paves the way for the development of integrated photonic architectures capable of performing QML tasks with robust devices operating at room temperature.

中文翻译：

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用于量子核估计的线性光子交换测试电路


交换测试是一种量子算法，能够计算两个任意波函数的标量乘积的绝对值。标量产品是许多量子机器学习 （QML） 方法的关键组成部分，但它们的评估根本不简单。出于这个原因，已经进行了许多研究工作，但没有实现高效和稳健的实施。在这里，我们提出了一个集成光子电路，旨在实现交换测试算法。我们的方法完全依赖于线性光学集成元件和 qudits，由来自通过一组波导传播的衰减激光束的单光子表示。通过对 qudit 使用 2^{个 3} 个空间自由度，我们可以配置所有必要的安排来设置任何双量子比特状态并执行交换测试。这简化了对电路元件的要求，并且无需非线性、先兆或后选即可实现多量子比特门。我们的光子交换测试电路成功地编码了两个量子比特，并以小于 0.05 的测得均方根误差估计它们的标量积。这一结果为集成光子架构的开发铺平了道路，这些架构能够在室温下运行稳健的器件中执行 QML 任务。