Caracterização Matemática e Visualização da Esfera de Bloch: Ferramentas para Computação Quântica

Authors

  • L.M. Carvalho
  • C. Lavor
  • V.S. Motta

DOI:

https://doi.org/10.5540/tema.2007.08.03.0351

Abstract

Faremos uma descrição matemática da esfera de Bloch, discutiremos propriedades dessa representação e apresentaremos algumas visualizações de 1 qbit.

References

[1] W.E. Baylis, R. Cabrera, C. Rangan, Control and representation of n-qubit quantum systems, arxiv.org, quant-ph/0606019, June 2006.

B.A. Bernevig, H.-D. Chen, Geometry of the three-qubit state, entanglement and division algebras, J. Ph. A: Math. and Gen.l, 36 (2003), 8325–8339.

K. Dietz, Generalized Bloch spheres for m-qubit states, Journal of Physics A: Mathematical and General, 3 (2006), 1433–1447.

R.P. Feynman, F.L. Vernon, R.W. Hellwarth, Geometrical representation of the Schr¨oedinger equation for solving the MASER problem, Journal of Applied Physics, 28, No. 1 (1957), 49–52.

T. Havel, C. Doran, A Bloch-sphere-type model for two qubits in the geometric algebra of a 6-D Euclidean vector space, Proceedings of SPIE, 5436 (2004), 93–106.

M. Hirvensalo, “Quantum Computing”, Springer, New York, 2001.

K. Kato, M. Oto, H. Imai, K. Imai, Voronoi diagrams for pure 1-qubit quantum states, arxiv.org, Quantum Physics, quant-ph/0604101, April 2006.

G. Kimura, A. Kossakowski, The Bloch-vector space for n-level systems: the spherical-coordinate point of view, Open Systems & Information Dynamics,12, No. 3 (2005), 207–229.

A. Y. Kitaev, A. Shen, M. Vyalyi, “Classical and Quantum Computing”, volume 47 of Graduate Studies in Mathematics, AMS, 2002.

P. Kurzynski, A. Grudka, Graphical representation of generalized quantum measurements, arxiv.org, Quantum Physics, quant-ph/0604189, April 2006.

A. Maitra, P. Parashar, Hadamard type operations for qubits, arxiv.org, Quantum Physics, quant-ph/0505068, May 2005.

R. Mosseri, Two and three qubits geometry and Hopf fibrations, arxiv.org, Quantum Physics, quant-ph/0310053, 2003.

M. A. Nielsen, I. L. Chuang, “Quantum Computation and Quantum Information”, Cambridge University Press, Cambridge, 2000.

R. Portugal, C. Lavor, L. M. Carvalho, N. Maculan, “Uma Introdução à Computação Quˆantica”, Notas em Matemática Aplicada, Vol. 8, SBMAC, S˜ao Carlos, 2004.

J. Preskill, “Quantum Information and Computation”, Lecture Notes, California Institute of Technology, unpublished 1998.

J. Zhang, J. Vala, S. Sastry, K.B. Whaley, Geometric theory of nonlocal twoqubit operations, Phys. Rev. A, 67, No. 4 (2003), 042313.

Published

2007-06-01

How to Cite

Carvalho, L., Lavor, C., & Motta, V. (2007). Caracterização Matemática e Visualização da Esfera de Bloch: Ferramentas para Computação Quântica. Trends in Computational and Applied Mathematics, 8(3), 351–360. https://doi.org/10.5540/tema.2007.08.03.0351

Issue

Section

Original Article