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Paper 1

Analytical Theory of Greedy Peeling for Bivariate Bicycle Codes and Two-Shot Streaming Decoding

Anton Pakhunov

Year

2026

Journal

arXiv preprint

DOI

arXiv:2604.11352

arXiv

2604.11352

We present an analytical theory of greedy peeling decoding for bivariate bicycle (BB) codes under circuit-level noise. The deferred greedy decoder achieves 330x latency reduction over belief propagation (BP) at p = 10^{-3} while maintaining identical logical error rate. Our main theoretical contribution is a closed-form collision resolution factor A_0 = |true collisions| / |birthday collisions|, derived from XOR syndrome analysis with no free parameters, that quantifies the fraction of detector-sharing fault pairs genuinely blocking iterative peeling. For the [[144,12,12]] Gross code, A_0 = 0.8685 (within 0.5% of the empirical value), with shared-2 pairs (4-cycles) always resolving under peeling. We show A_0 depends on the mean fault-graph degree d-bar rather than code size: A_0 = 0.87 for d-bar = 52 (Gross family) versus A_0 = 0.76 for d-bar = 17 ([[32,8,6]]). We establish a syndrome code stopping distance d_S = n/4.5 for the Gross family and demonstrate that [[32,8,6]] (d_S = 4) enables two-shot streaming decoding: T = 2 rounds achieve 89% peeling success with 1.29 +/- 0.03 LER ratio versus T = 12, at estimated latency ~50 ns. The full formula P_peel = exp(-A_0 * gamma_analytic * exp(-BTp) * n * p^2) is validated across five BB codes, four noise levels, and four values of T with R^2 = 0.86. Cross-platform reproduction of the Kunlun [[18,4,4]] experiment matches their hardware LER within 0.73 percentage points.

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Paper 2

Fast surgery for quantum LDPC codes

Nouédyn Baspin, Lucas Berent, Lawrence Z. Cohen

Year

2025

Journal

arXiv preprint

DOI

arXiv:2510.04521

arXiv

2510.04521

Quantum LDPC codes promise significant reductions in physical qubit overhead compared with topological codes. However, many existing constructions for performing logical operations come with distance-dependent temporal overheads. We introduce a scheme for performing generalized surgery on quantum LDPC codes using a constant number of rounds of syndrome measurement. The merged code in our scheme is constructed by taking the total complex of the base code and a suitably chosen homomorphic chain complex. We demonstrate the applicability of our scheme on an example multi-cycle code and assess the performance under a phenomenological noise model, showing that fast surgery performs comparably to standard generalized surgery with multiple rounds. Our results pave the way towards fault-tolerant quantum computing with LDPC codes with both low spatial and temporal overheads.

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