A transformation based algorithm for reversible logic synthesis

Abstract

A digital combinational logic circuit is reversible if it maps each input pattern to a unique output pattern. Such circuits are of interest in quantum computing, optical computing, nanotechnology and low-power CMOS design. Synthesis approaches are not well developed for reversible circuits even for small numbers of inputs and outputs.In this paper, a transformation based algorithm for the synthesis of such a reversible circuit in terms of n × n Toffoli gates is presented. Initially, a circuit is constructed by a single pass through the specification with minimal lookahead and no back-tracking. Reduction rules are then applied by simple template matching. The method produces near-optimal results for 3-input circuits and also produces very good results for larger problems.

Rule-based optimization of reversible circuits

“…The application of rule set was extended in [5] where the authors introduced several transformation rules based on a set of predefined patterns called templates. According to [5], a template T is a circuit with identity function which contains m gates g 1 , g 2 , · · · , g m .…”

“…According to [5], a template T is a circuit with identity function which contains m gates g 1 , g 2 , · · · , g m . Consider the first k (k > m/2) gates of T (i.e., g 1 , g 2 , · · · g k ) and suppose that these gates are applied in a reversible circuit in sequence.…”

“…It is worth noting that none of the examples, except Example 6 and Example 7, can be simplified by using the previously published optimization methods [5,8,9]. Since the proposed approach can use negative controls to reduce the quantum cost, it outperforms the available methods.…”

“…In this scenario, a realization is found from a given specification first and then, further optimizations are applied in a post-processing step to improve various cost metrics (e.g., quantum cost). Local transformation [4], templates matching [5][6][7][8], and data-structure-based optimization [9] were used to simplify synthesized circuits in the past.…”

Automatic synthesis of composable sequential quantum Boolean circuits

“…Iwama et al [6] propose transformation rules for optimize Controlled-Not-based combinational quantum Boolean circuits and point out a design theory for a sequential quantum circuit is very interesting. Miller et al [15] propose a transformation based algorithm for synthesizing the combinational circuits and reduction rules for optimizing the synthesized circuits. Younes and Miller [17] propose an automated method to build CNOT based quantum circuits for Boolean functions.…”