Classification of measurement-based quantum wire in stabilizer PEPS
Department of Physics and Astronomy, University of British Columbia, Vancouver, Canada
Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, Canada
Published: | 2023-06-12, volume 7, page 1041 |
Eprint: | arXiv:2207.00616v3 |
Doi: | https://doi.org/10.22331/q-2023-06-12-1041 |
Citation: | Quantum 7, 1041 (2023). |
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Abstract
We consider a class of translation-invariant 2D tensor network states with a stabilizer symmetry, which we call stabilizer PEPS. The cluster state, GHZ state, and states in the toric code belong to this class. We investigate the transmission capacity of stabilizer PEPS for measurement-based quantum wire, and arrive at a complete classification of transmission behaviors. The transmission behaviors fall into 13 classes, one of which corresponds to Clifford quantum cellular automata. In addition, we identify 12 other classes.

Featured image: Transmission capacity for measurement-based quantum wire as a function of the circumference (vertical axis) and depth (horizontal axis) of a cylindrical stabilizer PEPS falls into one of 13 classes. Shown here are characteristic plots for 8 of these classes, including the class of Clifford quantum cellular automata (bottom right).
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Cited by
[1] David T. Stephen, Wen Wei Ho, Tzu-Chieh Wei, Robert Raussendorf, and Ruben Verresen, "Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits", arXiv:2209.06191, (2022).
[2] Michael de Oliveira, Luís S. Barbosa, and Ernesto F. Galvão, "Quantum advantage in temporally flat measurement-based quantum computation", arXiv:2212.03668, (2022).
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