Quantum Locally Testable Code with Constant Soundness

• URL: http://arxiv.org/abs/2209.11405v3
• Date: Tue, 08 Oct 2024 22:22:41 GMT
• Title: Quantum Locally Testable Code with Constant Soundness
• Authors: Andrew Cross, Zhiyang He, Anand Natarajan, Mario Szegedy, Guanyu Zhu,
• Abstract summary: 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. 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.
• Score: 1.5559957709246597
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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.

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