Elementary Quantum Gate Realizations for Multiple-Control Toffoli Gates

A new method for determining elementary quantum gate realizations for multiple-control Toffoli (MCT) gates is presented. The realization for each MCT gate is formed as a composition of realizations of smaller MCT gates. A marking algorithm which is more effective than the traditional moving rule is used to optimize the final circuit. The main improvement is that the resulting circuits make significantly better use of ancillary lines than has been achieved in earlier approaches. Initial results are also presented for circuits with nearest-neighbour communication. These results show that the overall approach is not as effective for that problem indicating that research on direct synthesis of nearest-neighbour quantum circuits should be considered. While, the results presented are for the NCV quantum gate library (i.e. for quantum circuits composed of NOT gates, controlled-NOT gates, and controlled-V=V+ gates), the approach can be applied to other libraries of elementary quantum gates.

[1]  Igor L. Markov,et al.  Fast equivalence-checking for quantum circuits , 2009, 2010 IEEE/ACM International Symposium on Nanoscale Architectures.

[2]  Susmita Sur-Kolay,et al.  Nearest Neighbour based Synthesis of Quantum Boolean Circuits , 2007, Eng. Lett..

[3]  Robert Wille,et al.  Equivalence Checking of Reversible Circuits , 2009, ISMVL.

[4]  Tsutomu Sasao,et al.  Progress in Applications of Boolean Functions , 2010, Progress in Applications of Boolean Functions.

[5]  D. Michael Miller,et al.  Mapping a Multiple-control Toffoli Gate Cascade to an Elementary Quantum Gate Circuit , 2012, J. Multiple Valued Log. Soft Comput..

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

[7]  Mozammel H. A. Khan,et al.  Cost Reduction in Nearest Neighbour Based Synthesis of Quantum Boolean Circuits , 2008, Eng. Lett..

[8]  Robert Wille,et al.  Synthesis of quantum circuits for linear nearest neighbor architectures , 2011, Quantum Inf. Process..

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

[10]  D. M. Miller,et al.  Lowering the Quantum Gate Cost of Reversible Circuits , 2010, 2010 53rd IEEE International Midwest Symposium on Circuits and Systems.

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

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

[13]  Robert Wille,et al.  RevLib: An Online Resource for Reversible Functions and Reversible Circuits , 2008, 38th International Symposium on Multiple Valued Logic (ismvl 2008).

[14]  Masaki Nakanishi,et al.  An Efficient Method to Convert Arbitrary Quantum Circuits to Ones on a Linear Nearest Neighbor Architecture , 2009, 2009 Third International Conference on Quantum, Nano and Micro Technologies.

[15]  A. Chakrabarti,et al.  Rules for Synthesizing Quantum Boolean Circuits Using Minimized Nearest-Neighbour Templates , 2007, 15th International Conference on Advanced Computing and Communications (ADCOM 2007).

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