A Novel Least-Entanglement-Assisted Asymmetric Quantum Codes Based on Sliding Grill

We propose new methods for constructing novel entanglement-assisted asymmetric quantum codes based on combinatorial designs and sliding grill. Based on a special case of combinatorial designs, our proposed method can construct a type of parity check matrix with greater column weight and better decoding performance. Combined with the characteristic of asymmetric quantum channel, we propose new method of sliding grill. Mother matrix and submatrix can be constructed. The null space of the parity-check matrix gives entanglement-assisted asymmetric quantum code. Tanner graph of the code has a girth of at least 6. Our proposed quantum code has higher code rate with the same error correction capability. These families of entanglement-assisted asymmetric quantum codes consume only one copy of maximally entangled state (ebit), and outperform other quantum codes based on similar construction method according to our numerical computation.