Bidirectional matrix-based algorithm for 4-qubit reversible logic circuits synthesis

Quantum reversible logic circuits synthesis is one of the key technologies to construct quantum computer. The algebraic model for quantum information processing is a unitary matrix operator. Matrix can better reflect the quantum state evolution and the properties of quantum computation. Bidirectional matrix-based algorithm for quantum reversible logic circuits synthesis is proposed in this paper. The matrix representation of quantum reversible circuit and the circuit transformation rules of adjacent matrix are employed to construct any quantum reversible circuit in this paper. Compared with [11, 12], the computational complexity of our algorithm has been decreased exponentially and the speed has been increased by about 105 times. In addition, the types of the quantum reversible circuits synthesized by our algorithm are extended from only even permutations in [11, 12] to even and odd ones. we have synthesized 13!=6227020800 quantum reversible circuits, which can't be done by other algorithms.