A Constructive Algorithm for Reversible Logic Synthesis

This paper presents a constructive synthesis algorithm for any n-qubit reversible function. Given any n-qubit reversible function, there are N distinct input patterns different from their corresponding outputs, where N les 2ⁿ, and the other (2ⁿ - N) input patterns will be the same as their outputs. We show that this circuit can be synthesized by at most 2nldrN ´(n - 1)´-CNOT gates and 4n² ldr N NOT gates. The time complexity of our algorithm has asymptotic upper bound O(n ldr 4ⁿ). The space complexity of our synthesis algorithm is also O(n ldr 2ⁿ). The computational complexity of our synthesis algorithm is exponentially lower than the complexity of breadth-first search based synthesis algorithm.