Evolutionary quantum logic synthesis of Boolean reversible logic circuits embedded in ternary quantum space using structural restrictions

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. We describe the experiments that we conducted using GPU programming. Various approaches to fitness function formulation were applied to obtain various realizations of well known universal Boolean reversible quantum gates.

[1]  G. Milburn,et al.  Linear optical quantum computing with photonic qubits , 2005, quant-ph/0512071.

[2]  Samira Manabi Khan,et al.  Quantum Realization of Some Ternary Circuits Using Muthukrishnan-Stroud Gates , 2007, 37th International Symposium on Multiple-Valued Logic (ISMVL'07).

[3]  William J. Munro,et al.  Generalized Toffoli gates using qudit catalysis , 2009, 0903.4123.

[4]  T. Ralph,et al.  Demonstration of an all-optical quantum controlled-NOT gate , 2003, Nature.

[5]  L. Brown.  Dirac ’ s The Principles of Quantum Mechanics * , 2006 .

[6]  Martin Lukac,et al.  Quantum Mechanical Model of Emotional Robot Behaviors , 2007, 37th International Symposium on Multiple-Valued Logic (ISMVL'07).

[7]  Guang-Can Guo,et al.  Methods for a linear optical quantum Fredkin gate , 2008, 0804.0992.

[8]  Marek A. Perkowski,et al.  Reversible Logic Synthesis by Iterative Compositions , 2002, IWLS.

[9]  P. Dirac.  Principles of Quantum Mechanics , 1982 .

[10]  T. Rudolph,et al.  Resource-efficient linear optical quantum computation. , 2004, Physical review letters.

[11]  Gerhard W. Dueck,et al.  Synthesis of Quantum Multiple-Valued Circuits , 2006, J. Multiple Valued Log. Soft Comput..

[12]  T.C.Ralph,et al.  Efficient Toffoli Gates Using Qudits , 2008, 0806.0654.

[13]  Jr.,et al.  Multivalued logic gates for quantum computation , 2000, quant-ph/0002033.

[14]  Martin Lukac,et al.  Evolutionary approach to quantum symbolic logic synthesis , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[15]  Alan Mishchenko,et al.  Automated Synthesis of Generalized Reversible Cascades using Genetic Algorithms , 2002 .

[16]  Gerhard W. Dueck,et al.  GARBAGE IN REVERSIBLE DESIGN OF MULTIPLE OUTPUT FUNCTIONS , 2003 .

[17]  Guowu Yang,et al.  Quantum logic synthesis by symbolic reachability analysis , 2004, Proceedings. 41st Design Automation Conference, 2004..

[18]  D. M. Miller.  Spectral and two-place decomposition techniques in reversible logic , 2002, The 2002 45th Midwest Symposium on Circuits and Systems, 2002. MWSCAS-2002..

[19]  James E. Baker,et al.  Reducing Bias and Inefficienry in the Selection Algorithm , 1987, ICGA.

[20]  Marco Barbieri,et al.  Simplifying quantum logic using higher-dimensional Hilbert spaces , 2009 .

[21]  V.V. Shende,et al.  Synthesis of quantum-logic circuits , 2006, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[22]  Martin Lukac,et al.  Quantum inductive learning and quantum logic synthesis , 2009 .

[23]  D. Michael Miller,et al.  QMDD: A Decision Diagram Structure for Reversible and Quantum Circuits , 2006, 36th International Symposium on Multiple-Valued Logic (ISMVL'06).

[24]  Kyusik Chung,et al.  Evolutionary Approach to Quantum and Reversible Circuits Synthesis , 2003, Artificial Intelligence Review.

[25]  M. Nielsen.  Optical quantum computation using cluster States. , 2004, Physical review letters.

[26]  Guowu Yang,et al.  Optimal synthesis of multiple output Boolean functions using a set of quantum gates by symbolic reachability analysis , 2006, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[27]  Jaromir Fiurasek,et al.  Linear optical Fredkin gate based on partial-SWAP gate , 2008, 0809.3228.

[28]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[29]  T. Jennewein,et al.  Quantum computing using shortcuts through higher dimensions , 2008 .

[30]  Herbert Walther,et al.  Quantum computation with trapped ions in an optical cavity. , 2002, Physical review letters.

[31]  D. Gammon,et al.  An All-Optical Quantum Gate in a Semiconductor Quantum Dot , 2003, Science.