Classification Of Measurement-based Quantum Wire In Stabilizer PEPS

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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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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.

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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).

Popular summary

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.

► BibTeX data

@article{Herringer2023classificationof, doi = {10.22331/q-2023-06-12-1041}, url = {https://doi.org/10.22331/q-2023-06-12-1041}, title = {Classification of measurement-based quantum wire in stabilizer {PEPS}}, author = {Herringer, Paul and Raussendorf, Robert}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {7}, pages = {1041}, month = jun, year = {2023}<br /> }

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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).

The above citations are from SAO/NASA ADS (last updated successfully 2023-06-12 23:53:38). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2023-06-12 23:53:37).

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.