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DOI: 10.4230/LIPIcs.TQC.2025.4

Optimal Locality and Parameter Tradeoffs for Subsystem Codes

Authors: Samuel Dai, Ray Li, and Eugene Tang

Published in: LIPIcs, Volume 350, 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)

Abstract

We study the tradeoffs between the locality and parameters of subsystem codes. We prove lower bounds on both the number and lengths of interactions in any D-dimensional embedding of a subsystem code. Specifically, we show that any embedding of a subsystem code with parameters [[n,k,d]] into R^D must have at least M^* interactions of length at least 𝓁^*, where M^* = Ω(max(k,d)), and 𝓁^* = Ω(max(d/(n^((D-1)/D)), ((kd^(1/(D-1))/n))^((D-1)/D))). We also give tradeoffs between the locality and parameters of commuting projector codes in D-dimensions, generalizing a result of Dai and Li [Dai and Li, 2025]. We provide explicit constructions of embedded codes that show our bounds are optimal in both the interaction count and interaction length.

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Samuel Dai, Ray Li, and Eugene Tang. Optimal Locality and Parameter Tradeoffs for Subsystem Codes. In 20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 4:1-4:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dai_et_al:LIPIcs.TQC.2025.4,
  author =	{Dai, Samuel and Li, Ray and Tang, Eugene},
  title =	{{Optimal Locality and Parameter Tradeoffs for Subsystem Codes}},
  booktitle =	{20th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2025)},
  pages =	{4:1--4:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-392-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{350},
  editor =	{Fefferman, Bill},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2025.4},
  URN =		{urn:nbn:de:0030-drops-240539},
  doi =		{10.4230/LIPIcs.TQC.2025.4},
  annote =	{Keywords: Quantum Error Correcting Code, Locality, Subsystem Code, Commuting Projector Code}
}

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Optimal Locality and Parameter Tradeoffs for Subsystem Codes

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