🤖 AI Summary
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.
📝 Abstract
We construct a new family of Calderbank-Shor-Steane (CSS) codes using the generator and parity-check matrices of Low-Density Generator Matrix (LDGM) codes, with row operations applied to both matrices in order to achieve the desired quantum rate. Decoding is performed in an iterative manner, by applying message passing over the associated graph, and discrete Density Evolution (DDE) is used to optimize performance in the depolarizing channel. The proposed construction offers high flexibility and easiness in the design, producing quantum codes that possess excellent error correction capabilities. By properly designing the structure of the code, we are able to control and bound the weight of the stabilizer generators to a small value, which results in codes particularly well suited for fault-tolerant quantum computation. At the same time, these codes achieve very good performance in terms of error correction capability.