Generate Seed Generators for Quantum Stabilizer Codes

Stabilizer is a very important description method of quantum error-correcting code. Before to generate quantum codes based on the stabilizer it needs to generate seed generator. The problem of finding seed generators is transformed into the problems of determining linear independence or linear dependence of vectors and finding the solutions of equations; we also present quick determinant method, sort and find method and solve equations method to verify the validity of the operator; we present the total number of seed generators of the stabilizer code. The method introduced in this paper can be applied to the quantum stabilizer code contains both type 1 and type 2 generator; and also can be applied to the quantum stabilizer code contains only type 1 generators. Through standardize the generator of the stabilizer and the seed generators at the same time; it can quickly get the quantum encoding circuit. It also presented the number of 2-qubit gates and 1-qubit gates needed for the encoding circuit.