Design and synthesis of improved reversible circuits using AIG‐ and MIG‐based graph data structures

Abstract

Reversible logic synthesis is one of the best suited ways which act as the intermediate step for synthesising Boolean functions on quantum technologies. For a given Boolean function, there are multiple possible intermediate representations (IRs), based on functional abstraction, e.g. truth table, decision diagrams or circuit abstraction, e.g. binary decision diagram (BDD), and-inverter graph (AIG) and majority inverter graph (MIG). These IRs play an important role in building circuits as the choice of an IR directly impacts on cost parameters of the design. In the authors' work, they are analysing the effects of different graphbased IRs (BDD, AIG and MIG) and their usability in making efficient circuit realisations. Although applications of BDDs as an IR to represent large functions has already been studied, here they are demonstrating a synthesis scheme by taking AIG and MIG as IRs and making a comprehensive comparative analysis over all these three graph-based IRs. In experimental evaluation, it is being observed that for small functions BDD gives more compact circuits than the other two IRs but when the input size increases, then MIG as IR makes substantial improvements in cost parameters as compared with BDD by reducing quantum cost by 39% on an average. Along with the experimental results, a detailed analysis over the different IRs is also included to find their easiness in designing circuits.

Reversible Circuit Synthesis Method by Combining Factoring and Boolean Expression Diagram

“…如采用与-非图(and-inverter graph, AIG) [14] 、表决器-非图(majority-inverter graph, MIG) [14] 或布尔表达式 图(Boolean expression diagram, BED) [15] 作为函数表 示模型.…”

Quantum Circuit Synthesis Using Projective Simulation

“…Quantum circuit synthesis is mainly made through the synthesis of reversible boolean circuits [2][3][24] [12]. These techniques focus on generating a classical reversible circuit and then matching it with an equivalent quantum circuit.…”

Conversion between Logic and Algebraic Expressions of Boolean Control Networks

“…Boolean control network (BCN) is a logical system pioneered by Kauffman in [1] for initially describing genetic regulatory networks, which provides useful modeling tools for dynamical systems whose state-variables take only two values ('True' or 'False'). With the development of information technologies, BCNs have become an effective way to analyze and design circuits by algebraic means in terms of logic gates, and have served as a fundamental approach to digital circuit design, computer programming, and so on (see, e.g., [2][3][4][5][6][7]). With the development of digital circuit, the research on logic synthesis becomes particularly important.…”

“…Recently, Rushdi and Ahmad [5] used a novel method for obtaining the parametric general solutions of the 'big' Boolean equation, which cover the most prominent type among basic problems of digital circuit design. Bandyopadhyay et al [4] analyzed the effects of different graph-based intermediate representations, inclutding binary decision diagram, and-inverter graph and majority inverter graph, and their usability in making efficient circuit realisations. Wang and Tao [3] introduced the Karnaugh maps of logical systems and used in the analysis and design of clocked sequential circuits and in the simplification of multioutput gate circuits.…”