Gebhart Valentin, Pezzè Luca, Smerzi Augusto
QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, 50125, Firenze, Italy.
Università degli Studi di Napoli Federico II, Via Cinthia 21, 80126, Napoli, Italy.
Sci Rep. 2021 Jan 14;11(1):1288. doi: 10.1038/s41598-020-80153-z.
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.
尽管进行了深入研究，但量子算法所提供加速的物理起源仍然神秘莫测。没有任何一个通用的物理量，比如纠缠，能够被明确认定为至关重要的有用资源。在此，我们报告了在使用纯态和准纯态实现的格罗弗搜索算法中，迹速度与量子加速之间的紧密联系。对于无噪声算法，我们发现量子加速与准纯态的极化之间存在一一对应关系，这可以与一大类量子统计速度相联系。对于随时间变化的部分退极化以及中断的格罗弗搜索，加速具体受到算法操作过程中出现的最大迹速度的限制。我们的结果用量子加速来量化一种物理资源，这种资源在实验上是可测量的，并且与多体纠缠和量子相干相关。
