Synthesis of Reversible Circuits with No Ancilla Bits for Large Reversible Functions Specified with Bit Equations

This paper presents a new algorithm MP(multiple pass) to synthesize large reversible binary circuits without ancilla bits. The MMD algorithm requires to store a truth table (or a Reed-Muller -RM transform) as a 2^n vector for a reversible function of n variables. This representation prohibits synthesis of large functions. However, in MP we do not store such an exponentially growing data structure. The values of minterms are calculated in MP dynamically, one-by-one, from a set of logic equations that specify the reversible circuit to be designed. This allows for synthesis of large scale reversible circuits (30-bits), which is not possible with existing algorithms. In addition, our unique multipass approach where the circuit is synthesized with various, yet specific, minterm orders yields optimal solution. The algorithm returns a description of the optimal circuit with respect to gate count or quantum cost. Although the synthesis process is relatively slower, the solution is found in real-time for smaller circuits of 8 bits or less