Fast Constructions of Quantum Codes Based on Residues Pauli Block Matrices

Table 1

Computation complexity of the fast algorithm based on Pauli block matrices. For simplicity, Add and Mul denote the number of additions and multiplications. The notations 𝐿^𝜎_𝑝 and 𝐿^𝜎_𝑞 express the number of nonidentity matrices 𝜎₀ in Pauli block matrices 𝑄_𝑝 and 𝑄_𝑞.

	Direct approach	Proposed algorithm	Proposed algorithm
Add	(𝑛−1)𝑛	(𝑝−1)𝑛𝑚	𝑝𝑛+𝑞𝑛−2𝑛
Mul	𝑛^2	𝐿^𝜎𝑝𝑛𝑚	𝐿^𝜎𝑝𝑚𝑛+𝐿^𝜎𝑞𝑠𝑛