Measurement-Based Loss Tolerance in Graph-GKP Codes through Syndrome-Resolved Pauli-Frame Decoding

• URL: http://arxiv.org/abs/2608.00830v1
• Date: Sat, 01 Aug 2026 19:14:42 GMT
• Title: Measurement-Based Loss Tolerance in Graph-GKP Codes through Syndrome-Resolved Pauli-Frame Decoding
• Abstract summary: We develop a causal framework that unifies these mechanisms for measurement-based loss tolerance under pure loss.<n>We derive decoder-conditioned branch restriction, signed-outcome reconstruction, Pauli-frame updating, and syndrome-resolved logical fusion.<n>The resulting graph-GKP interface provides a unified causal control layer for fault-tolerant MBQC, fusion-based computation, and all-photonic repeaters.
• Score: 46.2474896050764
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Graph codes offer multiple physical representatives of logical observables, while Gottesman-Kitaev-Preskill (GKP) codes retain analog information about bosonic displacement noise. We develop a causal framework that unifies these mechanisms for measurement-based loss tolerance under pure loss followed by quantum-limited amplification. In this framework, each local GKP recovery produces a refreshed logical block, a continuous syndrome record, and a confidence score for the inferred Pauli class. Low-confidence outcomes are deliberately converted into located erasures, so the availability pattern is generated directly from the bosonic data rather than sampled independently. Both accepted and rejected syndromes contribute to a syndrome-resolved posterior over the graph branch, which determines accessible logical representatives and the outgoing logical Pauli frame. We derive decoder-conditioned branch restriction, signed-outcome reconstruction, Pauli-frame updating, recursive concatenation of graph-GKP modules, and syndrome-resolved logical fusion. Numerical simulations across several squeezing levels identify task-dependent loss-tolerance behavior and finite-depth pseudothresholds for square and hexagonal GKP lattices. The resulting graph-GKP interface provides a unified causal control layer for fault-tolerant MBQC, fusion-based computation, and all-photonic repeaters.

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