Space-group codes—CSS codes whose stabilizers use crystallographic point-group symmetries—can be topologically ordered and geometrically local, and some match or beat bivariate-bicycle benchmarks.
Scalable Neural Decoders for Practical Fault-Tolerant Quantum Computation
11 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have recently emerged as a promising route to efficient fault tolerance, current decoding algorithms do not allow one to realize the full potential of these codes in practical settings. Here, we introduce a convolutional neural network decoder that exploits the geometric structure of QEC codes, and use it to probe a novel "waterfall" regime of error suppression, demonstrating that the logical error rates required for large-scale fault-tolerant algorithms are attainable with modest code sizes at current physical error rates, and with latencies within the real-time budgets of several leading hardware platforms. For example, for the $[144, 12, 12]$ Gross code, the decoder achieves logical error rates up to $\sim 17$x below existing decoders - reaching logical error rates $\sim 10^{-10}$ at physical error $p=0.1\%$ - with 3-5 orders of magnitude higher throughput. This decoder also produces well-calibrated confidence estimates that can significantly reduce the time overhead of repeat-until-success protocols. Taken together, these results suggest that the space-time costs associated with fault-tolerant quantum computation may be significantly lower than previously anticipated.
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A symmetry-co-designed high-rate QEC architecture with parallel STAR injection on bivariate bicycle codes achieves ~5.5x space savings for TFIM and Fermi-Hubbard simulations versus surface-code STAR.
Transformer neural networks estimate coherent information thresholds for the surface code under code capacity, phenomenological, and circuit-level noise, outperforming minimum weight perfect matching decoding and enabling optimal soft post-selection.
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.
Concatenating quantum Reed-Solomon codes over the gross code via Galois qudits reaches teraquop regime at uniform 10^{-3} noise with reduced overhead.
A forced-gap post-selection strategy using repeated Relay-BP decoder runs improves logical error rates by over 4x on 72- and 144-qubit bivariate bicycle codes at fixed post-selection rate.
Neutral-atom system delivers state-of-the-art CZ gate fidelity of 99.854% (99.941% postselected) and demonstrates coherent rearrangement for nonlocal quantum circuits.
New structural conditions on affine permutation matrices yield ultra-high-rate quantum LDPC codes (rate >1/2) with near-teraquop logical error rates under circuit-level noise on reconfigurable atom arrays.
Biased-noise ancillas (phase flips only) in bicycle bivariate and cyclic hypergraph product QLDPC codes increase effective fault distance, reduce short loops, and improve logical error rate by nearly 10x at 2e-3 circuit noise when bit flips are 50x rarer.
GNN decoder logit outperforms MWPM logical gap for post-selection, yielding lower logical error rates on surface code syndromes under circuit-level noise.
A benchmarking framework for hybrid quantum error correction shows belief propagation reduces weighted correction volume by 48-57% compared to MWPM-family decoders while preserving input sparsity.
citing papers explorer
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Topological Codes from Space Groups: A Route beyond Translation Invariance
Space-group codes—CSS codes whose stabilizers use crystallographic point-group symmetries—can be topologically ordered and geometrically local, and some match or beat bivariate-bicycle benchmarks.
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Fast and Parallel High-Rate STAR Architecture for Megaquop Quantum Simulation
A symmetry-co-designed high-rate QEC architecture with parallel STAR injection on bivariate bicycle codes achieves ~5.5x space savings for TFIM and Fermi-Hubbard simulations versus surface-code STAR.
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Machine Learning Optimal Quantum Error Correction Thresholds
Transformer neural networks estimate coherent information thresholds for the surface code under code capacity, phenomenological, and circuit-level noise, outperforming minimum weight perfect matching decoding and enabling optimal soft post-selection.
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Approximating optimal decoding of quantum LDPC codes with narrow frontiers
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.
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Concatenating Algebraic Codes over High-Rate Quantum LDPC Codes
Concatenating quantum Reed-Solomon codes over the gross code via Galois qudits reaches teraquop regime at uniform 10^{-3} noise with reduced overhead.
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Forced Gap Post-Selection for Quantum LDPC Codes and their Operations
A forced-gap post-selection strategy using repeated Relay-BP decoder runs improves logical error rates by over 4x on 72- and 144-qubit bivariate bicycle codes at fixed post-selection rate.
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High-fidelity entangling gates and nonlocal circuits with neutral atoms
Neutral-atom system delivers state-of-the-art CZ gate fidelity of 99.854% (99.941% postselected) and demonstrates coherent rearrangement for nonlocal quantum circuits.
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Towards Ultra-High-Rate Quantum Error Correction with Reconfigurable Atom Arrays
New structural conditions on affine permutation matrices yield ultra-high-rate quantum LDPC codes (rate >1/2) with near-teraquop logical error rates under circuit-level noise on reconfigurable atom arrays.
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Untangling QLDPC Codes with Biased Noise Ancilla
Biased-noise ancillas (phase flips only) in bicycle bivariate and cyclic hypergraph product QLDPC codes increase effective fault distance, reduce short loops, and improve logical error rate by nearly 10x at 2e-3 circuit noise when bit flips are 50x rarer.
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Neural network decoder confidence as a learned proxy for the logical gap
GNN decoder logit outperforms MWPM logical gap for post-selection, yielding lower logical error rates on surface code syndromes under circuit-level noise.
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A Unified Hardware-to-Decoder Architecture for Hybrid Continuous-Variable and Discrete-Variable Quantum Error Correction in LiDMaS+
A benchmarking framework for hybrid quantum error correction shows belief propagation reduces weighted correction volume by 48-57% compared to MWPM-family decoders while preserving input sparsity.