并行哈达玛测试
Parallel Hadamard Test
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中文总结 AI 辅助
研究针对量子计算算法中哈达玛测试存在的问题，提出并行哈达玛测试方法，将多个测试合并为一种电路类型，适用于三类工作负载，能减少电路类型数量，降低计算时间和成本，在特定工作负载中还可减少测量次数。
中文摘要 AI 辅助
哈达玛测试是许多量子计算算法中广泛使用的基本构建块，用于估计$\langle \psi \vert U \vert \psi \rangle$的实部或虚部。然而在许多算法中，需要估计许多这样的量，导致电路类型众多、计算时间长和成本高。本文提出并行哈达玛测试，将多个哈达玛测试合并为一种电路类型。展示了其适用于三类工作负载，比较了并行与传统测试的成本。该方法显著减少了不同电路类型的数量，在固定电路开销占主导时可降低计算时间和成本，在Gram矩阵工作负载中，典型非对角重叠小时还可减少总测量次数。
英文摘要
The Hadamard test is a fundamental building block widely used in many quantum computing algorithms. It estimates the real or imaginary part of $\langle ψ\vert U \vert ψ\rangle$, where $\vert ψ\rangle$ is a quantum state and $U$ is a unitary operator. In many algorithms, however, many such quantities must be estimated, leading to a large number of distinct circuit types, long computational times, and high financial costs. In this work, we propose the parallel Hadamard test, which combines multiple Hadamard tests into a single circuit type. We demonstrate how the parallel Hadamard test applies to three structural classes of workloads: arbitrary sets of unitary operators, prefix-product arrays, and Gram-matrix elements. For each class, we compare the cost of the parallel Hadamard test with that of the conventional one. Our unified approach significantly reduces the number of distinct circuit types, and can lower both computational time and financial costs in regimes where fixed per-circuit overheads dominate the total cost. In Gram-matrix workloads, it can also reduce the total number of shots when typical off-diagonal overlaps are small.
