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The synthesis of Boolean functions, as they are found in many quantum algorithms, is usually conducted in two steps. First, the function is realized in terms of a reversible circuit followed by a mapping into a corresponding quantum realization. During this process, the number of lines and the quantum costs of the resulting circuits have mainly been… (More)

—In order to verify natural language assertions from a specification automatically, they need to be translated into formal representations. This process is error-prone and can lead to a product that does not meet the initial intentions. We automate this process by first partitioning all assertions into subsets based on sentence similarity and then providing… (More)

—Reversible logic is an emerging research area that has shown promising results in applications such as quantum computing, low power design, and optical computing. Since the synthesis of minimal circuits is a cumbersome task, many synthesis algorithms apply heuristics and can therefore not provide a minimal solution. As a consequence, post synthesis methods… (More)

Reversible single-target gates are a generalization of Toffoli gates which are a helpful formal representation for the description of synthesis algorithms but are too general for an actual implementation based on some technology. There is an exponential lower bound on the number of Toffoli gates required to implement any reversible function, however, there… (More)

We review combinational results to enumerate and classify reversible functions and investigate the application to circuit complexity. In particularly, we consider the effect of negating and permuting input and output variables and the effect of applying linear and affine transformations to inputs and outputs. We apply the results to reversible circuits and… (More)

—This paper presents a rule based approach to optimize the quantum cost of reversible circuits using circuit rewriting rules that handle positive and negative controls. Since incremental optimization cannot guarantee optimality, we consider the application of simulated annealing to find further sub-circuits that could be replaced with smaller ones.… (More)

Quantum computing offers a promising emerging technology due to the potential theoretical capacity of solving many important problems with exponentially less complexity. Since most of the known quantum algorithms include Boolean components, the design of quantum computers is often conducted by a two-stage approach. In a first step, the Boolean component is… (More)