Reversible, or information-lossless, circuits have applications in digital signal processing, communication, computer graphics and cryptography. They are also a fundamental requirement for quantum computation. We investigate the synthesis of reversible circuits that employ a minimum number of gates and contain no redundant input-output line-pairs (temporary storage channels). We propose new constructions for reversible circuits composed of NOT, Controlled-NOT, and TOFFOLI gates (the CNT gate library) based on permutation theory. A new algorithm is given to synthesize optimal reversible circuits using an arbitrary gate library, and we describe much faster heuristic algorithms. We also pursue applications of the proposed techniques to the synthesis of quantum circuits.
Vivek V. Shende, Aditya K. Prasad, Igor L. Markov,