Quantum Error Correction beyond the Bounded Distance Decoding Limit

Abstract

In this paper, we consider quantum error correction over depolarizing channels with non-binary low-density parity-check codes defined over Galois field of size $2^p$ . The proposed quantum error correcting codes are based on the binary quasi-cyclic CSS (Calderbank, Shor and Steane) codes. The resulting quantum codes outperform the best known quantum codes and surpass the performance limit of the bounded distance decoder. By increasing the size of the underlying Galois field, i.e., $2^p$, the error floors are considerably improved.

To appear in IEEE Transactions on Information Theory

References in corpus (4)

• Good Quantum Error-Correcting Codes Exist
• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• Sparse Graph Codes for Quantum Error-Correction
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• A decoding algorithm for CSS codes using the X/Z correlations
• A characterization of entanglement-assisted quantum low-density parity-check codes
• Log-domain decoding of quantum LDPC codes over binary finite fields
• On the probabilistic quantum error correction
• Performance of polar codes for quantum and private classical communication
• Quantum Error Correction near the Coding Theoretical Bound
• Error Correction for Reliable Quantum Computing
• Capacity-Achieving Entanglement Purification Protocol for Pauli Dephasing Channel