Approximate level-by-level maximum-likelihood decoding based on the Chase algorithm for high-rate concatenated stabilizer codes
Takeshi Kakizaki
TL;DR
This work addresses decoding for high-rate concatenated stabilizer codes in fault-tolerant quantum computation by introducing LMLD-CA, a Chase-based extension of level-by-level decoding. LMLD-CA integrates a constrained ML search over a subset of physical errors with inner-code candidate lists and reliability-driven test patterns to approximate the global ML decoding. Through simulations on two- and three-level concatenated Hamming codes under bit-flip noise, it demonstrates substantial performance gains over HDD and symbol-MAP, especially when multiple logical qubits per level are present. The approach trades increased computational complexity for significantly improved decoding accuracy, offering a practical framework for high-rate stabilizer-code decoding beyond many-hypercube constructions.
Abstract
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.