LDGM-Based Quantum Codes for Fault-Tolerant Quantum Computation
This work addresses the challenge in fault-tolerant quantum computing of simultaneously achieving high error-correction performance and low stabilizer weight. By leveraging low-density generator matrix (LDGM) codes and the Calderbank–Shor–Steane (CSS) construction, the authors design a new class of quantum error-correcting codes. Through flexible row operations, the code rate is efficiently tuned, while message-passing iterative decoding on graphs—combined with discrete density evolution analysis—enables significantly reduced stabilizer generator weights without compromising error-correction capability. The resulting quantum codes exhibit outstanding performance under the depolarizing channel, offering both low decoding complexity and high practicality. This approach provides an efficient and scalable coding solution for fault-tolerant quantum computation.