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Link to original content: https://doi.org/10.48550/arXiv.2209.11405
[2209.11405] Quantum Locally Testable Code with Constant Soundness
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Computer Science > Information Theory

arXiv:2209.11405 (cs)
[Submitted on 23 Sep 2022 (v1), last revised 8 Oct 2024 (this version, v3)]

Title:Quantum Locally Testable Code with Constant Soundness

Authors:Andrew Cross, Zhiyang He, Anand Natarajan, Mario Szegedy, Guanyu Zhu
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Abstract:In this paper, we present two constructions of quantum locally testable codes (QLTC) with constant soundness. In the first approach, we introduce an operation called check product, and show how this operation gives rise to QLTCs of constant soundness, constant rate, and distance scaling with locality. In the second approach, we consider hypergraph product of a quantum code and a classical repetition code, and observe a special case in which the soundness of component codes is preserved. This insight leads us to construct QLTCs of constant soundness, scalable rate and distance, and constant average locality. Our work marks a step towards constructing QLTCs of high soundness and distance, which would give a different construction to the No Low-Energy Trivial States (NLTS) theorem.
Comments: Updated manuscript
Subjects: Information Theory (cs.IT); Quantum Physics (quant-ph)
Cite as: arXiv:2209.11405 [cs.IT]
  (or arXiv:2209.11405v3 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.2209.11405
Journal reference: Quantum 8, 1501 (2024)
Related DOI: https://doi.org/10.22331/q-2024-10-18-1501

Submission history

From: Zhiyang He [view email]
[v1] Fri, 23 Sep 2022 04:38:01 UTC (22 KB)
[v2] Wed, 26 Jul 2023 21:46:31 UTC (28 KB)
[v3] Tue, 8 Oct 2024 22:22:41 UTC (49 KB)
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