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Ambiguity Clustering: an accurate and efficient decoder for qLDPC codes
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Error correction allows a quantum computer to preserve states long beyond the decoherence time of its physical qubits. Key to any scheme of error correction is the decoding algorithm, which estimates the error state of qubits from the results of syndrome measurements. The leading proposal for quantum error correction, the surface code, has fast and accurate decoders, but several recently proposed quantum low-density parity check (qLDPC) codes allow more logical information to be encoded in significantly fewer physical qubits. The state-of-the-art decoder for general qLDPC codes, BP-OSD, has a cheap Belief Propagation stage, followed by linear algebra and search stages which can each be slow in practice. We introduce the Ambiguity Clustering decoder (AC) which, after the Belief Propagation stage, divides the measurement data into clusters that can be decoded independently. We benchmark AC on the recently proposed bivariate bicycle qLDPC codes and find that, with 0.3% circuit-level depolarising noise, AC is up to 27x faster than BP-OSD with matched accuracy. Our implementation of AC decodes the 144-qubit Gross code in 135us per round of syndrome extraction on an M2 CPU, already fast enough to keep up with neutral atom and trapped ion systems.
Forward citations
Cited by 9 Pith papers
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Pauli stabilizer formalism for topological quantum field theories and generalized statistics
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Unfolded distillation prepares an |X^{1/4}> magic state with logical error 3e-7 using 53 biased-noise qubits and 5.5 rounds, by unfolding the 3D Reed-Muller X-stabilizers into a 2D layout.
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Improved belief propagation is sufficient for real-time decoding of quantum memory
Relay-BP, a message-passing decoder using disordered memory strengths and relay ensembling, matches or beats benchmark decoders for bivariate-bicycle and surface codes within a real-time iteration budget.
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Scalable decoding protocols for fast transversal logic in the surface code
The paper presents windowed decoding protocols that restore modularity and locality to decoding of fast transversal logic, enabling constant-time logical gates with scalable error correction.
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A matching decoder for bivariate bicycle codes
The authors introduce symatch, a minimum-weight matching decoder for bivariate bicycle quantum LDPC codes that uses code symmetries and a cylinder trick, and show it is competitive with BP-OSD and tesseract under code...
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Degeneracy Cutting: A Local and Efficient Post-Processing for Belief Propagation Decoding of Quantum Low-Density Parity-Check Codes
A local O(n) post-processor called degeneracy cutting prunes one low-probability qubit per stabilizer and reruns belief propagation, matching or beating BP+OSD accuracy in several qLDPC settings.
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Efficient Post-Selection for General Quantum LDPC Codes
Cluster-size and cluster-LLR norm fractions from BP+LSD decoding suppress logical error rates by orders of magnitude at low abort rates on surface, bivariate bicycle, and hypergraph product codes.
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Fully Parallelized BP Decoding for Quantum LDPC Codes Can Outperform BP-OSD
A syndrome-flipping belief-propagation decoder with parallel trial attempts matches BP-OSD logical error rates while avoiding Gaussian elimination and shortening average latency.
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Leveraging biased noise for more efficient quantum error correction at the circuit-level with two-level qubits
Bias-preserving CZ gates plus small residual CNOT bias enable a 90% threshold improvement and up to 75% footprint reduction for the XZZX code in two-level qubits.
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