Using Small Dimensional Quantum Error Correction Codes for High-Performance Quantum Communication.

For achieving long-distance quantum communication, Quantum Repeaters (QRs) have to be used, with commu-nication range and reliability increased by using intermediate stations. The physical requirements of second generation QRs may be achievable in the near future. They use Quantum Error Correction Codes (QECC) to protect logical qubits against environmental interaction using physical redundancy. In this work, we study the types of errors that can corrupt quantum codewords in intermediate stations. Our studies show that the errors are distance-dependent, and also consist of correlated errors and biased errors. To mitigate this error model, we use non-symmetric CSS codes as well as mirrored structure coding. We show that using non-symmetric CSS codes results in better performance. Also, we prove the logical CZ gate transversality of the mirrored structure coding. The effectiveness of the proposed methods is verified by numerical simulations.