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arXiv 2602.07201quant-ph
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基于测量的高维AKLT态制备及其量子计算能力

Measurement-Based Preparation of Higher-Dimensional AKLT States and Their Quantum Computational Power

C. N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook(纽约州立大学石溪分校杨振宁理论物理研究所);Department of Physics and Astronomy, State University of New York at Stony Brook(纽约州立大学石溪分校物理与天文学系);Department of Physics, University of Illinois Urbana-Champaign(伊利诺伊大学厄巴纳-香槟分校物理系);IBM Quantum, IBM Research Cambridge(IBM量子,IBM剑桥研究院)

Wenhan Guo, Mikhail Litvinov, Tzu-Chieh Wei, Abid Khan, Kevin C. Smith

AI总结:

本文提出了一种常数时间测量基方案,用于制备高维AKLT态,并展示了其在量子计算中的等效计算能力。

摘要:

我们研究了一种常数时间、融合测量基的方案,用于在超过一维的图上创建AKLT态。我们证明,在给定的图上可以制备此类态,直至随机的自旋-1'装饰,每个对应于沿边插入顶点的概率性插入。在研究其在测量基量子计算中的用途时,我们证明任何随机装饰的AKLT态至少具有与非随机态相同的计算能力,例如那些在三价平面晶格上的态。对于Bethe晶格及其装饰版本,我们展示了其制备存在确定性的常数时间方案。除了随机装饰的AKLT态外,我们还考虑了随机键AKLT态,其构造涉及任何标准的贝尔态在键自由度中,而不是仅仅在原始构造中的singlet态。此类态自然出现在对随机装饰的AKLT态的所有装饰自旋-1站点进行测量时。我们证明,那些在三价晶格上的随机键AKLT态在对所有站点应用相同的POVM后,可以转换为编码的随机图态。我们还论证了这些随机键AKLT态与原始singlet键AKLT态具有相似的量子计算能力,通过渗透视角。

英文摘要:

We investigate a constant-time, fusion measurement-based scheme to create AKLT states beyond one dimension. We show that it is possible to prepare such states on a given graph up to random spin-1 `decorations', each corresponding to a probabilistic insertion of a vertex along an edge. In investigating their utility in measurement-based quantum computation, we demonstrate that any such randomly decorated AKLT state possesses at least the same computational power as non-random ones, such as those on trivalent planar lattices. For AKLT states on Bethe lattices and their decorated versions we show that there exists a deterministic, constant-time scheme for their preparation. In addition to randomly decorated AKLT states, we also consider random-bond AKLT states, whose construction involves any of the canonical Bell states in the bond degrees of freedom instead of just the singlet in the original construction. Such states naturally emerge upon measuring all the decorative spin-1 sites in the randomly decorated AKLT states. We show that those random-bond AKLT states on trivalent lattices can be converted to encoded random graph states after acting with the same POVM on all sites. We also argue that these random-bond AKLT states possess similar quantum computational power as the original singlet-bond AKLT states via the percolation perspective.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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