标题： 浅层量子标量积与相位信息 显示英文标题

标题： Shallow Quantum Scalar Products with Phase Information

摘要： 两个向量之间的标量积的测量是科学计算中的常见任务，进而也是量子计算中的常见任务。 在本工作中，我们引入了两种替代的量子电路，用于计算带有相位信息的标量积，结合了交换测试、真空测试和哈达玛测试的结构。 这些新的框架被称为零控制和一控制测试，在访问两个量子态之间的标量积时，它们在电路深度和量子比特数量之间表现出不同的权衡。 我们证明，与哈达玛测试相比，我们的方法显著减少了大量量子比特的门数，并降低了量子需求的扩展规模。 显示英文摘要

摘要： The measurement of scalar products between two vectors is a common task in scientific computing and, by extension, in quantum computing. In this work, we introduce two alternative quantum circuits for computing scalar products with phase information, combining the structure of the swap test, the vacuum test, and the Hadamard test. These novel frameworks, called the zero-control and one-control tests, present different trade-offs between circuit depth and qubit count for accessing the scalar product between two quantum states. We demonstrate that our approach significantly reduces the gate count for large numbers of qubits and decreases the scaling of quantum requirements compared to the Hadamard test.