Subsystem bivariate bicycle codes achieve high-rate BB logical qubits with local four-qubit gauge checks, yielding examples such as [[108,12,6]] that outperform surface-code alternatives.
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arXiv preprint arXiv:2403.18901 (2024)
18 Pith papers cite this work, alongside 3 external citations. Polarity classification is still indexing.
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Pith papers citing it
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abstract
We introduce a sliding window decoder based on belief propagation (BP) with guided decimation for the purposes of decoding quantum low-density parity-check codes in the presence of circuit-level noise. Windowed decoding keeps the decoding complexity reasonable when, as is typically the case, repeated rounds of syndrome extraction are required to decode. Within each window, we employ several rounds of BP with decimation of the variable node that we expect to be the most likely to flip in each round, Furthermore, we employ ensemble decoding to keep both decimation options (guesses) open in a small number of chosen rounds. We term the resulting decoder BP with guided decimation guessing (GDG). Applied to bivariate bicycle codes, GDG achieves a similar logical error rate as BP with an additional OSD post-processing stage (BP+OSD) and combination-sweep of order 10. For a window size of three syndrome cycles, a multi-threaded CPU implementation of GDG achieves a worst-case decoding latency of 3ms per window for the [[144,12,12]] code.
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representative citing papers
Routed tile codes on a 2D nearest-neighbor grid achieve circuit-level thresholds of 0.11%-0.13% under SI1000 noise and become more qubit-efficient than the surface code below a physical error rate of 0.08%.
LightStim automates DEM construction for QEC protocols via a record-augmented Pauli tableau tracker, validated across memory, logical operations, distillation, and a novel cross-code lattice surgery design.
Z_N bivariate-bicycle codes have essential topological properties determined by their Z_p prime-factor counterparts, enabling generalization of algebraic-geometric methods to anyon fusion rules and resolution of quasifractonic behavior via symmetry-enriched topological order.
An algorithm converts topological data of 2D bulk stabilizer codes into 1D boundary subsystem codes via operator algebra and normal forms, enabling automatic generation of boundaries and defects demonstrated on toric, color, and other codes.
The Frontier decoder approximates optimal quantum LDPC decoding via narrow-frontier dynamic programming, achieving near-optimal thresholds for surface and color codes plus state-of-the-art circuit-level performance with small retained lists.
Degeneracy in quantum LDPC codes equals classical code shortening at the decoder, enabling impulse decoding that beats BP+OSD plus a residual-error follow-up step.
DART-Q shows that cached state organization, overload policies, and service capacity determine whether real-time QLDPC decoders can meet deadlines under finite memory and varying load.
Extending affine subcode ensemble decoding to quantum codes with overcomplete matrices improves BP convergence and reduces logical error rates on toric and generalized bicycle codes.
Edge-coloring eliminates automorphisms in low-weight stabilizer subgraphs of generalized bicycle codes, enabling improved anisotropic min-sum decoding.
A tree-encoded fusion scheme and MemTree compiler suppress fusion erasure errors in photonic MBQC, achieving large execution-time reductions over prior compilers with real-hardware validation.
A trapped-ion architecture based on LDPC codes and cat-state factories achieves 110 logical qubits and one million T gates per day using 2514 physical qubits, with estimates for Heisenberg model simulation on 100 sites in one month using 10000 qubits.
Bivariate bicycle codes achieve an asymptotic threshold of approximately 0.488 on the quantum erasure channel with BP-OSD decoding, offering modest threshold edge and 12x lower overhead than toric codes under fair baselines.
Local syndrome-based preprocessing accelerates BP decoders for quantum LDPC codes, delivering up to 10x speedup on the [[144,12,12]] code while maintaining or improving logical error rates.
FPGA emulator tests 10^13 error patterns in 20 days and diversity BP decoder matches BP+OSD logical error rates with 30-80% average speed gains and far less post-processing for QLDPC codes.
Quantum Margulis codes are constructed from classical Margulis LDPC codes via two-block group algebra, enabling linear-complexity min-sum decoding and better error-floor performance than bivariate bicycle codes under code-capacity noise.
Simulations show non-local CNOT achieves up to 10x lower logical error than teleportation and distributed qLDPC needs d≈11 at p=10^{-4} or d≈29 at p=10^{-3} (with p_ebit=10p) for <10^{-12} error.
A two-level decoder scheduling framework reduces classical processing requirements for quantum error correction by 10-40% on fault-tolerant benchmarks by managing bursty workloads as shared resources.
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Fair Decoder Baselines and Rigorous Finite-Size Scaling for Bivariate Bicycle Codes on the Quantum Erasure Channel
Bivariate bicycle codes achieve an asymptotic threshold of approximately 0.488 on the quantum erasure channel with BP-OSD decoding, offering modest threshold edge and 12x lower overhead than toric codes under fair baselines.
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Accelerating BP-based decoders for QLDPC Codes with Local Syndrome-Based Preprocessing
Local syndrome-based preprocessing accelerates BP decoders for quantum LDPC codes, delivering up to 10x speedup on the [[144,12,12]] code while maintaining or improving logical error rates.
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Diversity Methods for Improving Convergence and Accuracy of Quantum Error Correction Decoders Through Hardware Emulation
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