Technical Report: Three techniques for generation of Toffoli gate cascade implementaions of reversible circuits TR-CSJR1-2009 J. E. Rice University of Lethbridge j.rice@uleth.ca 1 Introduction Reversible logic is becoming a “hot” topic of research for a variety of reasons, one of which is its connections to quantum computing. Since prior reports have elaborated on this, this report will simply direct the reader to these [20] and to introductory works reversible logic such as [4, 32] and [1]. for more details on the motivation behind this area. This report provides the reader with background in the current status of synthesis for reversible logic, paying particular attention to three approaches: • ESOP-based Toffoli-gate cascade synthesis, • template-matching, and • sorting-based Toffoli-gate cascade synthesis. 2 Background 2.1 Reversible Logic [26] provides the following definitions: Definition 2.1 a gate is reversible if the (Boolean) function it computes is bijective, and Definition 2.2 a well-formed reversible logic circuit is an acylic combinational logic circuit in which all gates are reversible, and are interconnected without fanout. This definition assumes that the circuit is strictly combinational; considerations for sequential logic are addressed in [19]. In general, a function is reversible if there is a one-to-one and on-to mapping from the inputs to the outputs (and vice versa) of the function. For example, the function shown in Figure 1(A) is reversible, while the function shown in Figure 1(B) is not. 1