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Paper 1
Approximate level-by-level maximum-likelihood decoding based on the Chase algorithm for high-rate concatenated stabilizer codes
Takeshi Kakizaki
- Year
- 2026
- Journal
- arXiv preprint
- DOI
- arXiv:2601.18743
- arXiv
- 2601.18743
Fault-tolerant quantum computation (FTQC) is expected to address a wide range of computational problems. To realize large-scale FTQC, it is essential to encode logical qubits using quantum error-correcting codes. High-rate concatenated codes have recently attracted attention due to theoretical advances in fault-tolerant protocols with constant-space-overhead and polylogarithmic-time-overhead, as well as practical developments of high-rate many-hypercube codes equipped with a high-performance level-by-level minimum-distance decoder (LMDD). We propose a general, high-performance decoder for high-rate concatenated stabilizer codes that extends LMDD by leveraging the Chase algorithm to generate a suitable set of candidate errors. Our simulation results demonstrate that the proposed decoder outperforms conventional decoders for high-rate concatenated Hamming codes under bit-flip noise.
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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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