Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits

Abstract At first sight, quantum computing is completely different from classical computing. Nevertheless, a link is provided by reversible computation. Whereas an arbitrary quantum circuit, acting...

[1]  Steven Vandenbrande,et al.  The Group of Dyadic Unitary Matrices , 2012, Open Syst. Inf. Dyn..

[2]  Alexis De Vos,et al.  The NEGATOR as a Basic Building Block for Quantum Circuits , 2013, Open Syst. Inf. Dyn..

[3]  Dominique de Werra Path colorings in bipartite graphs , 2005, Eur. J. Oper. Res..

[4]  Alexis De Vos,et al.  Matrix Calculus for Classical and Quantum Circuits , 2014, JETC.

[5]  Lin Chen,et al.  Decomposition of bipartite and multipartite unitary gates into the product of controlled unitary gates , 2015, 1501.02708.

[6]  Olle Ingemar Elgerd,et al.  Control systems theory , 1967 .

[7]  Charles Clos,et al.  A study of non-blocking switching networks , 1953 .

[8]  Alexis De Vos,et al.  Block-Z X Z synthesis of an arbitrary quantum circuit , 2015, 1512.07240.

[9]  D. Michael Miller,et al.  Transforming MCT Circuits to NCVW Circuits , 2011, RC.

[10]  H. Jonathan Chao,et al.  Matching algorithms for three-stage bufferless Clos network switches , 2003, IEEE Commun. Mag..

[11]  Peter Selinger,et al.  Efficient Clifford+T approximation of single-qubit operators , 2012, Quantum Inf. Comput..

[12]  A. Galindo,et al.  Information and computation: Classical and quantum aspects , 2001, quant-ph/0112105.

[13]  Jan De Beule,et al.  Computing with the Square Root of NOT , 2009 .

[14]  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.

[15]  Alexis De Vos,et al.  Reversible computing: from mathematical group theory to electronical circuit experiment , 2005, CF '05.

[16]  Andrzej Jajszczyk Nonblocking, repackable, and rearrangeable Clos networks: fifty years of the theory evolution , 2003, IEEE Commun. Mag..

[17]  Alexis De Vos,et al.  Multiple-Valued Reversible Logic Circuits , 2009, J. Multiple Valued Log. Soft Comput..

[18]  D. M. Miller,et al.  Upper bound on number of products in AND-OR-XOR expansion of logic functions , 1995 .

[19]  Alexis De Vos,et al.  Scaling a Unitary Matrix , 2014, Open Syst. Inf. Dyn..

[20]  Frank K. Hwang,et al.  Control Algorithms for Rearrangeable Clos Networks , 1983, IEEE Trans. Commun..

[21]  Tsutomu Sasao,et al.  Representations of Discrete Functions , 2011 .

[22]  Thomas C. Bartee Digital Computer Fundamentals , 1971 .

[23]  Robert Wille,et al.  Embedding of Large Boolean Functions for Reversible Logic , 2014, ACM J. Emerg. Technol. Comput. Syst..

[24]  M. Wolf,et al.  Sinkhorn normal form for unitary matrices , 2014, 1408.5728.

[25]  N. Higham Computing the polar decomposition with applications , 1986 .

[26]  D. Bouwmeester,et al.  The Physics of Quantum Information , 2000 .

[27]  A. Hurwitz,et al.  über die Erzeugung der Invarianten durch Integration , 1963 .

[28]  Stefan Frehse,et al.  RevKit: An Open Source Toolkit for the Design of Reversible Circuits , 2011, RC.

[29]  Hartmut Fuhr,et al.  On biunimodular vectors for unitary matrices , 2015, 1506.06738.

[30]  Alexis De Vos,et al.  Synthesis of reversible logic for nanoelectronic circuits , 2007, Int. J. Circuit Theory Appl..

[31]  Rolf Drechsler,et al.  Upper bounds for reversible circuits based on Young subgroups , 2014, Inf. Process. Lett..

[32]  Alexis De Vos,et al.  Young subgroups for reversible computers , 2008, Adv. Math. Commun..

[33]  Andrew R. Jones,et al.  A Combinatorial Approach to the Double Cosets of the Symmetric Group with respect to Young Subgroups , 1996, Eur. J. Comb..

[34]  David Deutsch,et al.  Machines, logic and quantum physics , 2000, Bull. Symb. Log..

[35]  Gregor von Bochmann,et al.  Quick Birkhoff-von Neumann Decomposition Algorithm for Agile All-Photonic Network Cores , 2006, 2006 IEEE International Conference on Communications.