Quantum

Local enhancement of finite-strength code preparation: recoverability and Wilson coherence

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Briefings

This article investigates how finite measurement strength affects quantum error-correcting codes, specifically examining Wilson coherence and logical leakage. The authors demonstrate that local logical leakage obstructs asymptotically faithful recovery in finite-strength codes, requiring measurement strength to grow logarithmically with code distance. They prove this obstruction can be removed locally by enhancing only a vanishing fraction of checks near logical supports. Additionally, the study establishes a dimensional distinction in logical operations: in the 3D deconfined phase, enhanced tubes restore equivalence between macroscopically separated representatives, whereas in 2D, recoverability alone does not ensure this equivalence.

Key points

• Local logical leakage obstructs asymptotically faithful recovery in finite-strength codes, forcing measurement strength to grow logarithmically with code distance.
• Enhancing only a vanishing fraction of checks near logical supports can remove the obstruction to recovery in fixed toric registers.

Context

Quantum error-correcting codes rely on stabilizer measurements to prepare long-range entangled states, but finite measurement strength can coherently deform the encoding map. This study addresses how local errors affect recovery and logical operations in these codes.

Limitations

The findings apply to fixed toric registers under sufficiently weak local-stochastic errors. The 2D equivalence distinction remains unproven for general cases, and the specific conditions for local enhancement are not fully detailed.

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