论文标题
用痕量速度量化Grover算法的计算优势
Quantifying Computational Advantage of Grover's Algorithm with the Trace Speed
论文作者
论文摘要
尽管进行了深入的研究，但量子算法提供的加速速度的物理起源仍然神秘。没有一般的物理数量，例如纠缠，可以将其视为必不可少的有用资源。在这里，我们报告了用纯净和伪岩石状态实现的Grover搜索算法中的痕量速度与量子加速之间的密切联系。对于无噪声算法，我们发现量子加速与伪岩石状态的极化之间的一对一对应关系，可以将其连接到宽类量子统计速度。对于时间依赖性的部分去极化和中断的Grover搜索，加速度是由算法操作过程中发生的最大痕量速度特异性的。我们的结果用实验可测量的物理资源量化了量子加速，并且与多部分纠缠和量子相干性有关。
Despite intensive research, the physical origin of the speed-up offered by quantum algorithms remains mysterious. No general physical quantity, like, for instance, entanglement, can be singled out as the essential useful resource. Here we report a close connection between the trace speed and the quantum speed-up in Grover's search algorithm implemented with pure and pseudo-pure states. For a noiseless algorithm, we find a one-to-one correspondence between the quantum speed-up and the polarization of the pseudo-pure state, which can be connected to a wide class of quantum statistical speeds. For time-dependent partial depolarization and for interrupted Grover searches, the speed-up is specifically bounded by the maximal trace speed that occurs during the algorithm operations. Our results quantify the quantum speed-up with a physical resource that is experimentally measurable and related to multipartite entanglement and quantum coherence.
