Abstract-The problem of minimizing the number of garbage outputs is an important issue in reversible logic design. We start with the analysis of the number of garbage outputs that must be added to a multiple output function to make it reversible. We give a precise formula for the theoretical minimum of the required number of garbage outputs. For some benchmark functions, we calculate the garbage required by some proposed reversible design methods and compare it to the theoretical minimum. Based on the information about minimal garbage, we suggest a new reversible design method that uses the minimum number of garbage outputs. We show that any Boolean function can be realized as a reversible network in terms of this new approach by giving the theoretical method of finding such a network. Using a heuristics synthesis approach, we create a program and run it to compare results of our synthesis to the previously reported synthesis results for the benchmark functions with up to ten variables. Finally, we show that the synthesis for the proposed model can be accomplished with lower cost than the synthesis of EXOR programmable logic arrays. Index Terms-Logic synthesis, minimal garbage, quantum computing, reversible logic.
In REF it has been showed that the minimum number of garbage bits required to make a boolean function reversible is log(M ) , where M is the maximum of number of times an output pattern is repeated in the truth table.
Reversible cascades with minimal garbage
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Computer Science