A family of permutationally invariant quantum codes

Arda Aydin1, Max A. Alekseyev2, and Alexander Barg1

1Department of ECE and Institute for Systems Research, University of Maryland, College Park, MD 20742
2Department of Mathematics, The George Washington University, Washington, DC 20052

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Abstract

We construct a new family of permutationally invariant codes that correct $t$ Pauli errors for any $t\ge 1$. We also show that codes in the new family correct quantum deletion errors as well as spontaneous decay errors. Our construction contains some of the previously known permutationally invariant quantum codes as particular cases, which also admit transversal gates. In many cases, the codes in the new family are shorter than the best previously known explicit permutationally invariant codes for Pauli errors and deletions. Furthermore, our new code family includes a new $((4,2,2))$ optimal single-deletion-correcting code. As a separate result, we generalize the conditions for permutationally invariant codes to correct $t$ Pauli errors from the previously known results for $t=1$ to any number of errors. For small $t$, these conditions can be used to construct new examples of codes by computer.

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Cited by

[1] Yingkai Ouyang, "A new take on permutation-invariant quantum codes", Quantum Views 8, 80 (2024).

[2] Eric Kubischta and Ian Teixeira, "The Not-So-Secret Fourth Parameter of Quantum Codes", arXiv:2310.17652, (2023).

[3] Yingkai Ouyang, "Robust projective measurements through measuring code-inspired observables", arXiv:2402.04093, (2024).

The above citations are from Crossref's cited-by service (last updated successfully 2024-05-26 12:23:51) and SAO/NASA ADS (last updated successfully 2024-05-26 12:23:52). The list may be incomplete as not all publishers provide suitable and complete citation data.

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