On Quantum Weight Reduction

• URL: http://arxiv.org/abs/2102.10030v3
• Date: Thu, 27 Jul 2023 18:06:00 GMT
• Title: On Quantum Weight Reduction
• Authors: M. B. Hastings
• Abstract summary: We introduce a new technique that we call "coning" to effectively induce high weight stabilizers in an LDPC code. As one application, any LDPC code (with arbitrary $O(1)$ stabilizer weights) may be turned into a code where all stabilizers have weight at most $5$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We give a general procedure for weight reducing quantum codes. This corrects a previous work\cite{owr}, and introduces a new technique that we call "coning" to effectively induce high weight stabilizers in an LDPC code. As one application, any LDPC code (with arbitrary $O(1)$ stabilizer weights) may be turned into a code where all stabilizers have weight at most $5$ at the cost of at most a constant factor increase in number of physical qubits and constant factor reduction in distance. Also, by applying this technique to a quantum code whose $X$-stabilizers are derived from a classical log-weight random code and whose $Z$-stabilizers have linear weight, we construct an LDPC quantum code with distance $\tilde \Omega(N^{2/3})$ and $\tilde\Omega(N^{2/3})$ logical qubits.

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