Quantum

Temporal Degeneracy Limits Message Passing Decoding of QLDPC Codes Under Repeated Noisy Syndrome Measurements

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Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 26/10/2026, 04:13:25 UTC.

Briefings

A new study reveals that repeated noisy syndrome measurements in QLDPC codes create temporal degeneracy, causing deterministic message-passing decoders to fail under specific conditions. The research identifies elementary temporal codewords of weight d_v+2 and derives counting bounds showing these patterns occur with multiplicity Theta(nr) in blocklength n and r measurement rounds. Monte carlo simulations confirm these failures for min-sum decoders, while space-time anisotropic decoding is proposed as a solution with linear complexity. The findings apply to bivariate bicycle codes where the degenerate error weight equals four, though the isolation assumption limits the scope of the failure analysis.

Key points

• Temporal degeneracy in QLDPC codes arises from repeated noisy syndrome measurements, creating elementary temporal codewords of weight d_v+2 that cause deterministic decoders to fail.
• For bivariate bicycle codes, the identified degenerate error patterns have a weight of four, and Monte carlo simulations quantify their harmful impact on min-sum decoders beyond the isolation assumption.

Context

This research addresses the challenge of practical quantum computations requiring logical error rates of 10^-12 or lower, where QLDPC codes offer low qubit overhead but face decoding difficulties. The study characterizes temporal degeneracy in the space-time decoding graph and proposes space-time anisotropic min-sum decoding as a solution, though the findings are based on theoretical analysis and simulations rather than experimental validation.

Limitations

The analysis relies on theoretical characterizations and Monte carlo simulations rather than experimental data, limiting the direct applicability to real-world quantum hardware. The isolation assumption constrains the scope of failure analysis, and the study focuses on bivariate bicycle codes with fixed degrees, restricting generalizability to other code types.

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