Quantum state discrimination (QSD) is a fundamental task in quantum information processing with numerous applications. We present a variational quantum algorithm that performs the minimum-error QSD, called the variational quantum state discriminator (VQSD). The VQSD uses a parameterized quantum circuit that is trained by minimizing a cost function derived from the QSD, and finds the optimal positive-operator valued measure (POVM) for distinguishing target quantum states. The VQSD is capable of discriminating even unknown states, eliminating the need for expensive quantum state tomography. Our numerical simulations and comparisons with semidefinite programming demonstrate the effectiveness of the VQSD in finding optimal POVMs for minimum-error QSD of both pure and mixed states. In addition, the VQSD can be utilized as a supervised machine learning algorithm for multi-class classification. The area under the receiver operating characteristic curve obtained in numerical simulations with the Iris flower dataset ranges from 0.97 to 1 with an average of 0.985, demonstrating excellent performance of the VQSD classifier.

中文翻译：

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用于监督机器学习的变分量子态鉴别器


量子态辨别（QSD）是量子信息处理中的一项基本任务，具有广泛的应用。我们提出了一种执行最小误差 QSD 的变分量子算法，称为变分量子态鉴别器（VQSD）。 VQSD 使用参数化量子电路，该电路通过最小化源自 QSD 的成本函数进行训练，并找到用于区分目标量子态的最佳正算子值测度 (POVM)。 VQSD 甚至能够区分未知状态，从而无需昂贵的量子态断层扫描。我们的数值模拟以及与半定规划的比较证明了 VQSD 在寻找纯状态和混合状态的最小误差 QSD 的最佳 POVM 方面的有效性。此外，VQSD 还可用作多类分类的监督机器学习算法。在鸢尾花数据集的数值模拟中获得的接收器操作特征曲线下面积范围为0.97到1，平均值为0.985，展示了VQSD分类器的优异性能。