Researchers have developed new quantum low-density parity-check (LDPC) codes based on circulant permutation matrices (CPMs). These Calderbank-Shor-Steane (CSS) type codes are crucial for quantum computing, as they enable the protection of quantum information from errors inherent in qubits. The construction is parameterized by column weight J, row weight L, and prime lift size P, and uses an array of pair partitions to impose linear equations that ensure CSS orthogonality.

Quantum LDPC codes are a promising avenue for quantum error correction due to their sparse structure, which facilitates decoding. Specific examples presented include a (J,L)=(4,12) code with a rate of 0.349 and a distance [[372,130,16]], and another (J,L)=(4,14) code with a rate of 0.440 and a distance [[518,228,16]]. Instances of (J,L)=(3,8) with distances [[472,122,14]] and [[488,126,14]] for lift sizes P=59 and P=61, respectively, are also reported.

The distance of these codes has been established through exhaustive low-weight exclusion and the use of explicit non-stabilizer witnesses, ensuring their ability to detect and correct errors. The improvement in the coding rate and minimum distance of these new LDPC codes is a significant step towards the construction of fault-tolerant quantum computers, a fundamental requirement for the development of large-scale quantum computing.