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Optimal Locality and Parameter Tradeoffs for Subsystem Codes

Authors Samuel Dai , Ray Li , Eugene Tang

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Subject Classification

ACM Subject Classification
  • Hardware → Quantum error correction and fault tolerance
  • Theory of computation → Error-correcting codes
Keywords
  • Quantum Error Correcting Code
  • Locality
  • Subsystem Code
  • Commuting Projector Code

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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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.TQC.2025.4

Author Details

Samuel Dai
  • Department of Physics, Northeastern University, Boston, MA, USA
Ray Li
  • Math & CS Department, Santa Clara University, CA, USA
Eugene Tang
  • Departments of Math and Physics, Northeastern University, Boston, MA, USA

Funding

  • Li, Ray: Supported by NSF grant CCF-2347371.

Acknowledgements

We thank Andy Liu, Shouzhen Gu, Zhiyang He for helpful feedback on our manuscript.

References

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