Classification of measurement-based quantum wire in stabilizer PEPS

Paul Herringer and Robert Raussendorf

Department of Physics and Astronomy, University of British Columbia, Vancouver, Canada
Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, Canada

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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.

Symmetry is ubiquitous in nature, and it helps us simplify and classify phenomena of the physical world. In this paper, we leverage symmetry to classify a family of many-body quantum states by their entanglement structure. With the help of single-particle measurements, entanglement can be harnessed to transmit quantum information in a process known as measurement-based quantum wire. Consequently, our findings establish a classification of quantum states based on their suitability for measurement-based quantum wire. In doing so, we lay the groundwork for a future classification of quantum states and phases by their usefulness for universal measurement-based quantum computation.

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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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