Description
Quantum error correction promises a practical pathway to fault-tolerant quantum computing; however, typical error-correcting codes, such as the surface code, suffer from asymptotically vanishing code rates and high resource overheads. Quantum low-density parity-check (QLDPC) codes have emerged as promising candidates to overcome these limitations. However, designing high-performance QLDPC codes remains challenging. In this work, we produce a diverse ensemble of quasi-cyclic symmetric lifted-product (LP-QLDPC) codes by randomly selecting seed matrices and lifting parameters, and employ the Belief Propagation with Ordered Statistics Decoding (BP+OSD) algorithm to analyze the distance of these generated codes. For codes with 825 physical qubits encoding 45 and 53 logical qubits, we demonstrate that code distances of 20 to 24 can be achieved with a 40% frequency, reaching an upper bound of 24. Furthermore, for 1122 physical qubits encoding 148 and 160 logical qubits, distances of 16 to 18 can be achieved with a 32.3% frequency. Our findings demonstrate that a wide variety of large-distance LP-QLDPC codes can be efficiently constructed through randomized parameter selection. Because these randomly generated codes exhibit diverse parity-check matrix structures, they offer flexible design choices tailored to the specific connectivity of distinct hardware platforms such as photonics and neutral atom systems. Ultimately, our results can guide future experimental efforts in selecting and implementing optimal, hardware-efficient codes for scalable quantum processors.
| I am the presenting author | Yes |
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