Reversible circuit synthesis by genetic programming using dynamic gate libraries

We have defined a new method for automatic construction of reversible logic circuits by using the genetic programming approach. The choice of the gate library is 100% dynamic. The algorithm is capable of accepting all possible combinations of the following gate types: NOT TOFFOLI, NOT PERES, NOT CNOT TOFFOLI, NOT CNOT SWAP FREDKIN, NOT CNOT TOFFOLI SWAP FREDKIN, NOT CNOT PERES, NOT CNOT SWAP FREDKIN PERES, NOT CNOT TOFFOLI PERES and NOT CNOT TOFFOLI SWAP FREDKIN PERES. Our method produced near optimum circuits in some cases when a particular subset of gate types was used in the library. Meanwhile, in some cases, optimal circuits were produced due to the heuristic nature of the algorithm. We compared the outcomes of our method with several existing synthesis methods, and it was shown that our algorithm performed relatively well compared to the previous synthesis methods in terms of the output efficiency of the algorithm and execution time as well.

[1]  O A Mukhanov,et al.  Energy-Efficient Single Flux Quantum Technology , 2011, IEEE Transactions on Applied Superconductivity.

[2]  M. Mosca,et al.  A Meet-in-the-Middle Algorithm for Fast Synthesis of Depth-Optimal Quantum Circuits , 2012, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[3]  A. Al-Rabadi.  Reversible Logic Synthesis: From Fundamentals to Quantum Computing , 2012 .

[4]  Morteza Saheb Zamani,et al.  Reversible circuit synthesis using a cycle-based approach , 2010, JETC.

[5]  Rolf Drechsler,et al.  Exact sat-based toffoli network synthesis , 2007, GLSVLSI '07.

[6]  T. Toffoli,et al.  Conservative logic , 2002, Collision-Based Computing.

[7]  Barenco,et al.  Elementary gates for quantum computation. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[8]  John P. Hayes,et al.  Data structures and algorithms for simplifying reversible circuits , 2006, JETC.

[9]  Md. Selim Al Mamun,et al.  Quantum Cost Optimization for Reversible Sequential Circuit , 2014, ArXiv.

[10]  Anas N. Al-Rabadi,et al.  A General Decomposition for Reversible Logic , 2001 .

[11]  Michael S. Hsiao,et al.  Reversible logic synthesis through ant colony optimization , 2010, 2010 Design, Automation & Test in Europe Conference & Exhibition (DATE 2010).

[12]  Martin Lukac,et al.  Evolving quantum circuits using genetic algorithm , 2002, Proceedings 2002 NASA/DoD Conference on Evolvable Hardware.

[13]  Dmitri Maslov,et al.  A Study of Optimal 4-Bit Reversible Toffoli Circuits and Their Synthesis , 2011, IEEE Transactions on Computers.

[14]  V. K. Agrawal,et al.  An Exact approach for Complete Test Set Generation of Toffoli-Fredkin-Peres based Reversible Circuits , 2016, J. Electron. Test..

[15]  Dmitri Maslov,et al.  Comparison of the cost metrics through investigation of the relation between optimal NCV and optimal NCT three-qubit reversible circuits , 2007, IET Comput. Digit. Tech..

[16]  Gerhard W. Dueck,et al.  Techniques for the synthesis of reversible Toffoli networks , 2006, TODE.

[17]  Guowu Yang,et al.  Fast synthesis of exact minimal reversible circuits using group theory , 2005, Proceedings of the ASP-DAC 2005. Asia and South Pacific Design Automation Conference, 2005..

[18]  A. Adamski,et al.  Design of Reversible Logic Circuits by Means of Control Gates , 2000, PATMOS.

[19]  Ahmed Younes,et al.  On the Universality of n-bit Reversible Gate Libraries , 2015 .

[20]  Anas N. Al-Rabadi.  Reversible Logic Synthesis , 2003 .

[21]  Leo Storme,et al.  Group Theoretical Aspects of Reversible Logic Gates , 1999, J. Univers. Comput. Sci..

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

[23]  Morteza Saheb Zamani,et al.  Rule-based optimization of reversible circuits , 2010, 2010 15th Asia and South Pacific Design Automation Conference (ASP-DAC).

[24]  Mircea Vladutiu,et al.  Genetic algorithm based quantum circuit synthesis with adaptive parameters control , 2009, 2009 IEEE Congress on Evolutionary Computation.

[25]  Pawel Kerntopf,et al.  Reducing Quantum Cost in Reversible Toffoli Circuits , 2011, ArXiv.

[26]  Morteza Saheb Zamani,et al.  A library-based synthesis methodology for reversible logic , 2010, Microelectron. J..

[27]  Michitaka Kameyama,et al.  Evolutionary Quantum Logic Synthesis of Boolean Reversible Logic Circuits Embedded in Ternary Quantum Space using Heuristics , 2011, ArXiv.

[28]  Masaki Nakanishi,et al.  An efficient conversion of quantum circuits to a linear nearest neighbor architecture , 2011, Quantum Inf. Comput..

[29]  Robert Wille,et al.  Quantified Synthesis of Reversible Logic , 2008, 2008 Design, Automation and Test in Europe.

[30]  Gerhard W. Dueck,et al.  Quantum Circuit Simplification and Level Compaction , 2006, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[31]  D J Newman,et al.  On the symmetry of logic , 1995 .

[32]  Maher Mofeid Hawash,et al.  Methods for Efficient Synthesis of Large Reversible Binary and Ternary Quantum Circuits and Applications of Linear Nearest Neighbor Model , 2013 .

[33]  Shah Mohammad Bahauddin,et al.  Permutation Algebra for Constructing Reversible Circuits , 2012 .

[34]  Ahmed Younes,et al.  Tight Bounds on the Synthesis of 3-Bit Reversible Circuits: Nffr Library , 2013, J. Circuits Syst. Comput..

[35]  Morteza Saheb Zamani,et al.  Depth-optimized reversible circuit synthesis , 2012, Quantum Inf. Process..

[36]  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.

[37]  Hitoshi Iba,et al.  Genetic Algorithms for Quantum Circuit Design –Evolving a Simpler Teleportation Circuit– , 2000 .

[38]  Morteza Saheb Zamani,et al.  Moving forward: A non-search based synthesis method toward efficient CNOT-based quantum circuit synthesis algorithms , 2008, 2008 Asia and South Pacific Design Automation Conference.

[39]  Dmitry V. Zakablukov.  Application of Permutation Group Theory in Reversible Logic Synthesis , 2016, RC.

[40]  Gerhard W. Dueck,et al.  Fredkin/Toffoli Templates for Reversible Logic Synthesis , 2003, ICCAD 2003.

[41]  Colin P. Williams,et al.  Optimal quantum circuits for general two-qubit gates (5 pages) , 2003, quant-ph/0308006.

[42]  A. Bautu,et al.  QUANTUM CIRCUIT DESIGN BY MEANS OF GENETIC PROGRAMMING ê , 2007 .

[43]  Robert Wille,et al.  BDD-based synthesis of reversible logic for large functions , 2009, 2009 46th ACM/IEEE Design Automation Conference.

[44]  William C. Athas,et al.  Reversible logic issues in adiabatic CMOS , 1994, Proceedings Workshop on Physics and Computation. PhysComp '94.

[45]  John P. Hayes,et al.  Synthesis of reversible logic circuits , 2003, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[46]  I. Chuang,et al.  Quantum Computation and Quantum Information: Bibliography , 2010 .

[47]  Alexander G. Gray,et al.  Automated Design of Quantum Circuits , 1998, QCQC.

[48]  Tommaso Toffoli,et al.  Reversible Computing , 1980, ICALP.

[49]  Robert Wille,et al.  Realizing reversible circuits using a new class of quantum gates , 2012, DAC Design Automation Conference 2012.

[50]  John P. Hayes,et al.  Reversible logic circuit synthesis , 2002, IWLS.

[51]  Igor L. Markov,et al.  Synthesis and optimization of reversible circuits—a survey , 2011, CSUR.

[52]  Gerhard W. Dueck,et al.  Quantum circuit simplification using templates , 2005, Design, Automation and Test in Europe.

[53]  John P. Hayes,et al.  Optimal synthesis of linear reversible circuits , 2008, Quantum Inf. Comput..

[54]  Pawel Kerntopf,et al.  A new heuristic algorithm for reversible logic synthesis , 2004, Proceedings. 41st Design Automation Conference, 2004..

[55]  D. V. Zakablukov.  Fast synthesis of invertible circuits based on permutation group theory , 2014 .

[56]  Trailokya Nath Sasamal,et al.  Reversible Logic Circuit Synthesis and Optimization Using Adaptive Genetic Algorithm , 2015 .

[57]  Niraj K. Jha,et al.  Reversible logic synthesis with Fredkin and Peres gates , 2008, JETC.

[58]  Ahmed Younes,et al.  Reducing Quantum Cost of Reversible Circuits for Homogeneous Boolean Functions , 2010, J. Circuits Syst. Comput..

[59]  Kaushik Roy,et al.  Energy recovery circuits using reversible and partially reversible logic , 1996 .

[60]  Gerhard W. Dueck,et al.  IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION ( VLSI ) SYSTEMS , VOL . ? ? ? , NO . ? ? ? , ? ? ? , 2003 .

[61]  Benjamin I. P. Rubinstein.  Evolving quantum circuits using genetic programming , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[62]  Alexis De Vos,et al.  The decomposition of an arbitrary reversible logic circuit , 2006 .

[63]  Lee Spector,et al.  Automatic Quantum Computer Programming: A Genetic Programming Approach (Genetic Programming) , 2004 .

[64]  Gerhard W. Dueck,et al.  A transformation based algorithm for reversible logic synthesis , 2003, Proceedings 2003. Design Automation Conference (IEEE Cat. No.03CH37451).

[65]  Niraj K. Jha,et al.  An Algorithm for Synthesis of Reversible Logic Circuits , 2006, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[66]  M. Thornton,et al.  ESOP-based Toffoli Gate Cascade Generation , 2007, 2007 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing.

[67]  Robert Wille,et al.  Reversible Logic Synthesis with Output Permutation , 2009, 2009 22nd International Conference on VLSI Design.

[68]  Dmitri Maslov,et al.  Reversible Circuit Optimization Via Leaving the Boolean Domain , 2011, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[69]  Dmitri Maslov,et al.  Polynomial-Time T-Depth Optimization of Clifford+T Circuits Via Matroid Partitioning , 2013, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.