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Evolutionary Quantum Logic Synthesis of Boolean Reversible Logic Circuits Embedded in Ternary Quantum Space using Heuristics

Maartin Lukac, Marek Perkowski, Michitaka Kameyama
Department of Information Sciences, Tohoku University, Sendai, Japan
arXiv:1107.3383v1 [quant-ph] (18 Jul 2011)

@article{2011arXiv1107.3383N,

   author={nLukac}, M. and {Perkowski}, M. and {Kameyama}, M.},

   title={"{Evolutionary Quantum Logic Synthesis of Boolean Reversible Logic Circuits Embedded in Ternary Quantum Space using Heuristics}"},

   journal={ArXiv e-prints},

   archivePrefix={"arXiv"},

   eprint={1107.3383},

   primaryClass={"quant-ph"},

   keywords={Quantum Physics, Computer Science – Artificial Intelligence},

   year={2011},

   month={jul},

   adsurl={http://adsabs.harvard.edu/abs/2011arXiv1107.3383N},

   adsnote={Provided by the SAO/NASA Astrophysics Data System}

}

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It has been experimentally proven that realizing universal quantum gates using higher-radices logic is practically and technologically possible. We developed a Parallel Genetic Algorithm that synthesizes Boolean reversible circuits realized with a variety of quantum gates on qudits with various radices. In order to allow synthesizing circuits of medium sizes in the higher radix quantum space we performed the experiments using a GPU accelerated Genetic Algorithm. Using the accelerated GA we compare heuristic improvements to the mutation process based on cost minimization, on the adaptive cost of the primitives and improvements due to Baldwinian vs. Lamarckian GA. We also describe various fitness function formulations that allowed for various realizations of well known universal Boolean reversible or quantum-probabilistic circuits.
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