LDGM-Based Quantum Codes for Fault-Tolerant Quantum Computation
Information Theory
Summary
The authors create a new type of quantum error-correcting codes by using special matrices from classical codes called LDGM codes and modifying them to fit quantum needs. They use an iterative decoding method with message passing to correct errors, and they optimize performance for a common noise model in quantum systems. Their design allows control over certain code properties, making the codes suitable for fault-tolerant quantum computing while maintaining strong error correction. Overall, their approach offers flexible and effective quantum codes.
Authors
Yumin Li, Kejing Liu, Hanqing Lou, Javier Garcia-Frias
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.