nt - p h / 02 07 00 1 v 4 2 7 Fe b 20 03 Synthesis of Reversible Logic Circuits ∗

Reversible or information-lossless circuits have applications in digital signal processing, communication, computer graphics and cryptography. They are also a fundamental requirement in the emerging field of 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 prove constructively that every even permutation can be implemented without temporary storage using NOT, CNOT and TOFFOLI gates. We describe an algorithm for the synthesis of optimal circuits and study the reversible functions on three wires, reporting the distribution of circuit sizes. Finally, in an application important to quantum computing, we synthesize oracle circuits for Grover’s search algorithm, and show a significant improvement over a previously proposed synthesis algorithm. ∗This work was partially supported by the Undergraduate Summer Research Program at the University of Michigan and by the DARPA QuIST program. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing official policies or endorsements, either expressed or implied, of the Defense Advanced Research Projects Agency (DARPA) or the U.S. Government.