Algebraic Characterization of Reversible Logic Gates

Abstract Reversible logic plays an important role in quantum computing. This paper investigates the universality and composition power of various known and new reversible gates. We present the algebraic characterization of selected new families of Boolean reversible gates. Some theoretical results on the relation between reversible w*w gates and the corresponding symmetric group are derived. Different combinations of reversible gate classes are proven to generate the entire class of reversible w*w gates.

[1]  DiVincenzo,et al.  Five two-bit quantum gates are sufficient to implement the quantum Fredkin gate. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[2]  M. I. Kargapolov,et al.  Fundamentals of the theory of groups , 1979 .

[3]  Tommaso Toffoli,et al.  Bicontinuous extensions of invertible combinatorial functions , 1981, Mathematical systems theory.

[4]  Yongwook Chung,et al.  A Practical Method of Constructing Quantum Combinational Logic Circuits , 1999 .

[5]  J. Dixon,et al.  Permutation Groups , 1996 .

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

[7]  K. Igeta,et al.  Quantum mechanical computers with single atom and photon fields , 1988 .

[8]  Jaehyun Kim,et al.  Implementation of the refined Deutsch-Jozsa algorithm on a three-bit NMR quantum computer , 1999, quant-ph/9910015.

[9]  Martin Lukac,et al.  A Hierarchical Approach to Computer-Aided Design of Quantum Circuits , 2003 .

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

[11]  Jaehyun Kim,et al.  Implementing unitary operators in quantum computation , 2000 .

[12]  Anas N. Al-Rabadi,et al.  Regularity and Symmetry as a Base for Efficient Realization of Reversible Logic Circuits , 2001 .

[13]  R. Feynman.  Quantum mechanical computers , 1986 .

[14]  J. Cirac,et al.  Quantum Computations with Cold Trapped Ions. , 1995, Physical review letters.

[15]  Pérès,et al.  Reversible logic and quantum computers. , 1985, Physical review. A, General physics.

[16]  David J. Wineland,et al.  Manipulating the Motion of a Single Trapped Atom , 1996 .

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

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