The Smallest Perfect Quantum Accumulate Codes
Khoirul Anwar, Mujib Ramadhan · 2021
Quantum has many unique characteristics for future applications in the sixth telecommunication generation (6G) 2030 based on entanglement and quantum teleportation. However, quantum communications are still vulnerable to errors and require quantum error corrections (QECC). This paper proposes quantum accumulate codes, where idea is coming from the classical accumulate codes that can provide good performances to remove or minimize the error-floor in classical communications. The proposed quantum codes can exactly satisfy both Hamming and Singleton bounds resulting in one of the smallest perfect quantum codes. This paper explains in details the steps to construct the codewords, syndrome extraction, error correction, and the quantum circuits. We perform a series of computer simulations to evaluate the quantum word error rate (QWR) and quantum fidelity performances under the depolarizing channels. Our results confirm that the stabilizers of the proposed codes can extract the syndrome and distinguish all error patterns of any single qubit errors of Pauli X, Y, and Z providing performances confirmed by the theoretical QWER curves. The results are expected to provide contributions to the development of quantum communications and future security issues.