Bilaterally Symmetrical Transformation between Independent Operators and Rotations

Nikolay Raychev^*

Department of Computer Systems, Varna University of Management, Varna, Bulgaria.

DOI: 10.4236/jqis.2015.53010                

Abstract

This report describes an approach for representation of quantum operators through rotations and rotation through quantum operators. The approach of the proposed method transforms rotation in a kind of a unitary matrix that corresponds to the rotation. Operations with qubits are very similar to the rotation, but with an added phase coefficient. This fact is used to create a process for rotation between unitary matrices. This approach could be used to modifying the controls to apply in a different basis.

Keywords

Quantum Operators, Rotations, Phase Space, Quantum Circuit

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Deutsch, D. (1989) Quantum Computational Networks. Proceedings of the Royal Society London A, 425, 73. http://dx.doi.org/10.1098/rspa.1989.0099
[2]	DiVincenzo, D.P. (1995) Two-Bit Gates Are Universal for Quantum Computation. Physical Review A, 51, 1015. http://dx.doi.org/10.1103/PhysRevA.51.1015
[3]	Nielsen, M.A. and Chuang, I.L. (2000) Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, UK.
[4]	Loss, D. and DiVincenzo, D.P. (1998) Quantum Computation with Quantum Dots. Physical Review A, 57, 120. http://dx.doi.org/10.1103/PhysRevA.57.120
[5]	Petta, J.R., Johnson, A.C., Taylor, J.M., Laird, E.A., Yacoby, A., Lukin, M.D., Marcus, C.M., Hanson, M.P. and Gossard, A.C. (2005) Coherent Manipulation of Coupled Electron Spins in Semiconductor Quantum Dots. Science, 309, 2180-2184. http://dx.doi.org/10.1126/science.1116955
[6]	DiVincenzo, D.P., Bacon, D., Kempe, J., Burkard, G. and Whaley, K.B. (2000) Letters to Nature. Nature (London), 408, 339-342. http://dx.doi.org/10.1038/35042541
[7]	Zanardi, P. and Rasetti, M. (1997) Error Avoiding Quantum Codes. Modern Physics Letters B, 11, 1085; http://dx.doi.org/10.1142/S0217984997001304
[8]	Zanardi, P. and Rasetti, M. (1997) Noiseless Quantum Codes. Physical Review Letters, 79, 3306. http://dx.doi.org/10.1103/PhysRevLett.79.3306
[9]	Duan, L.-M. and Guo, G.-C. (1998) Reducing Decoherence in Quantum-Computer Memory with All Quantum Bits Coupling to the Same Environment. Physical Review A, 57, 737. http://dx.doi.org/10.1103/PhysRevA.57.737
[10]	Raychev, N. and Racheva, E. (2015) Interactive Environment for Implementation and Simulation of Quantum Algorithms. CompSysTech’15, Dublin, Ireland, 25-26 June.
[11]	Raychev, N. (2012) Dynamic Simulation of Quantum Stochastic Walk. Jubilee International Congress: Science Education in the Future (Technical University—Varna), 1, 116-124.
[12]	Raychev, N. (2012) Classical Simulation of Quantum Algorithms. Jubilee International Congress: Science Education in the Future (Technical University—Varna), 1, 110-116.
[13]	Raychev, N. (2015) Unitary Combinations of Formalized Classes in Qubit Space. International Journal of Scientific and Engineering Research, 6, 395-398. http://dx.doi.org/10.14299/ijser.2015.04.003
[14]	Raychev, N. (2015) Functional Composition of Quantum Functions. International Journal of Scientific and Engineering Research, 6, 413-415. http://dx.doi.org/10.14299/ijser.2015.04.004
[15]	Raychev, N. (2015) Logical Sets of Quantum Operators. International Journal of Scientific and Engineering Research, 6, 391-394. http://dx.doi.org/10.14299/ijser.2015.04.002