Abstract: Quantum reversible logic circuit synthesis is one of the key techniques to construct the quantum computer．Bidirectional reversible logic circuit synthesis algorithm based on matrix elementary transformation was proposed in this paper．The algorithm can construct reversible logic circuit of any given permutation by using the circuit transformation rules of the adjacent matrix and the method of exchanging either the row number or the elements of the matrix in terms of hamming distance of two numbers．Compared with the other algorithms,the time-space complexity of our algorithm has been decreased greatly because of without exhaustive searching．Moreover,the types of the quantum reversible logic circuits synthesized by our algorithm are even and odd permutation because using n-qubit extended general Toffoli gates,and the number of quantum gates in the circuit is cut down.

Key words: Quantum reversible logic circuit,Quantum computation,Toffoli gate