Quantum Topological Error Correction Codes: The Classical-to-Quantum Isomorphism Perspective

Daryus Chandra, Zunaira Babar, Hung Viet Nguyen, Dimitrios Alanis, Panagiotis Botsinis, Soon Xin Ng, Lajos Hanzo
2018 IEEE Access  
We conceive and investigate the family of classical topological error correction codes (TECCs), which have the bits of a codeword arranged in a lattice structure. We then present the classical-to-quantum isomorphism to pave the way for constructing their quantum dual pairs, namely the quantum topological error correction codes (QTECCs). Finally, we characterize the performance of QTECCs in the face of the quantum depolarizing channel in terms of both the quantum-bit error rate (QBER) and
more » ... y. Specifically, from our simulation results, the threshold probability of the QBER curves for the colour codes, rotated-surface codes, surface codes and toric codes are given by 1.8 × 10 −2 , 1.3 × 10 −2 , 6.3 × 10 −2 and 6.8 × 10 −2 , respectively. Furthermore, we also demonstrate that we can achieve the benefit of fidelity improvement at the minimum fidelity of 0.94, 0.97 and 0.99 by employing the 1/7-rate colour code, the 1/9-rate rotatedsurface code and 1/13-rate surface code, respectively. Index Terms-quantum error correction codes, quantum stabilizer codes, quantum topological codes, lattice code, LDPC The authors are with the
doi:10.1109/access.2017.2784417 fatcat:qoqlrsus3be2necelaojeskwaa