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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)

- Nabila Abdessaied, Mathias Soeken, Michael Kirkedal Thomsen, Rolf Drechsler
- Inf. Process. Lett.
- 2014

We present tighter upper bounds on the number of Toffoli gates needed in reversible circuits. Both multiple controlled Toffoli gates and mixed polarity Toffoli gates have been considered for this purpose. The calculation of the bounds is based on a synthesis approach based on Young subgroups that results in circuits using a more generalized gate library.… (More)

- Nabila Abdessaied, Mathias Soeken, Robert Wille, Rolf Drechsler
- ISMVL
- 2013

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)

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)

Due to its fault-tolerant gates, the Clifford+T library consisting of Hadamard (denoted by H), T , and CNOT gates has attracted interest in the synthesis of quantum circuits. Since the implementation of T gates is expensive, recent research is aiming at minimizing the use of such gates. It has been shown that T -depth optimizations can be implemented… (More)

- Nabila Abdessaied, Matthew Amy, Mathias Soeken, Rolf Drechsler
- ISMVL
- 2016

The Clifford+T quantum gate library has attracted much interest in the design of quantum circuits, particularly since the contained operations can be implemented in a faulttolerant manner. Since fault tolerant implementations of the T gate have very high latency, synthesis and optimization are aiming at minimizing the number of T stages, referred to as the… (More)

- Mathias Soeken, Nabila Abdessaied, Rolf Drechsler
- ArXiv
- 2014

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)

- Nabila Abdessaied, Mathias Soeken, Gerhard W. Dueck, Rolf Drechsler
- VLSI-SoC
- 2015

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 subcircuits 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)