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Local Tests Reached Constant Rate and Distance
An explicit qubit-code construction combines constant rate, constant relative distance and constant-soundness local tests.
Summary
An explicit qubit-code construction combines constant rate, constant relative distance and constant-soundness local tests.
Quantum locally testable codes aim to diagnose global encoding errors through checks that touch only a constant number of qubits. This work gives explicit qubit-based quantum LDPC CSS code families that are asymptotically good: their information rate and relative distance remain constant as the code grows. Their testers also keep constant weight and constant soundness. The result is a mathematical construction rather than a hardware demonstration, but it closes a central combination of parameters for locally testable quantum error correction.
Why it matters
An explicit qubit-code construction combines constant rate, constant relative distance and constant-soundness local tests.
Limits and context
- Quantum locally testable codes aim to diagnose global encoding errors through checks that touch only a constant number of qubits.
- This work gives explicit qubit-based quantum LDPC CSS code families that are asymptotically good: their information rate and relative distance remain constant as the code grows.
Key claims
An explicit qubit-code construction combines constant rate, constant relative distance and constant-soundness local tests.
Qualification: Quantum locally testable codes aim to diagnose global encoding errors through checks that touch only a constant number of qubits.
Evidence: source-2026-09-18-013
Sources
- arXiv preprint 2609.20780arXiv · primary research
Corrections
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