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日期
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2026-07-21 |
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時間
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11:00-12:00 |
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地點
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Meeting Room, 2F, QFort, NCKU |
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領域
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Quantum Information Science |
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講者
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魏子傑 教授 - 美國紐約州立大學石溪分校 |
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題目
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Measurement-Based Preparation of Higher-Dimensional AKLT States and Their Quantum Computational Power |
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摘要
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It was shown previously that Affleck-Kenney-Lieb-Tasaki (AKLT) states on several 2D lattices are universal resource for measurement-based quantum computation and that their parent Hamiltonians have a nonzero spectral gap. Here, 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. 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 AKLT construction. We show that these 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 random-bond AKLT states possess similar quantum computational power as the original singlet-bond AKLT states via the percolation perspective. |
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