Analytical determination of lifted quantum Tanner-code parameters

Determine the parameters of the lifted quantum Tanner codes analytically and provide a rigorous analysis beyond the numerical computations used for the reported examples.

Background

The paper introduces lifted quantum Tanner codes and studies explicit examples primarily through computational experiments. The authors explain that determining their parameters analytically is challenging, so they generate finite covers of selected input codes and use GAP and QDistRnd to obtain numerical distance upper bounds for codes of moderate length.

A rigorous analytical treatment of the parameters—such as dimension, distance, and related code characteristics—remains to be developed beyond the reported numerical data. This problem is included because the authors explicitly defer that analysis to future work.

References

It has proven challenging to determine analytically the parameters of our lifted Tanner codes. We hence choose to follow a numerical approach. For some chosen input quantum Tanner codes, we generate all possible lifts of index 1 to 30, producing codes with length less than 800 qubits. An upper bound for the distance is calculated with GAP and the package QDistRnd . We only report the codes with the best parameters and leave a more rigorous analysis for future work.

— Moderate-length lifted quantum Tanner codes  (2502.20297 - Guemard et al., 27 Feb 2025) in Introduction

We suspect it may be possible to apply a similar strategy to that in \cref{thm:achievable-depth_qTanner-local-codes} to the quadripartite case.

— Local Automorphism-Aware Syndrome Compilation for General Quantum LDPC Codes  (2609.40319 - Rocha et al., 30 Sep 2026) in Section 4, immediately following Theorem 4.6 (Theorem~\ref{thm:achievable-depth_qTanner-local-codes})

An exact characterization of a layer code built from a quantum Tanner input therefore remains open. What would change that is not more computation but a theorem making explicit the constant in the construction's distance bound.

— Layer codes as quantum memories: syndrome extraction, thresholds and idle robustness  (2609.39522 - Sun et al., 30 Sep 2026) in Section 6.1, “Negative results and limitations,” subsection “Quantum Tanner inputs”