Quantum Simulation of the Majorana Equation and Unphysical Operations

Physical Review X

Volumn 1, Issue 2, 2011, Pages

  Casanova, J ^a   Sabin C ^b   Leon J ^b   Egusquiza, I L ^a   Gerritsma, R ^c,d   Roos, C F ^c,d   Garcia Ripoll, J J ^b   Solano, E ^a,e  

^a UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

^b INSTITUTO DE FÍSICA FUNDAMENTAL   (Spain)

^c ERICH SCHMID INSTITUTE OF MATERIALS SCIENCE   (Austria)

^d UNIVERSITY OF INNSBRUCK   (Austria)

^e BASQUE FOUNDATION FOR SCIENCE   (Spain)

Author keywords

Optics; Quantum Physics

Indexed keywords

CHARGE CONJUGATION; COMPLEX CONJUGATIONS; EXOTIC PARTICLES; GENERAL METHOD; MAJORANA; MATHEMATICAL OPERATIONS; NON-HAMILTONIAN; QUANTUM PHYSICS; QUANTUM SIMULATIONS; QUANTUM SIMULATORS; RELATIVISTIC WAVE EQUATIONS; THE STANDARD MODEL; TIME REVERSAL; TRAPPED ION;

OPTICS; QUANTUM CHEMISTRY;

HIGH ENERGY PHYSICS;

EID: 84865103370     PISSN: None     EISSN: 21603308     Source Type: Journal    
DOI: 10.1103/PhysRevX.1.021018     Document Type: Article

References (27)

1. R. Feynman, Simulating Physics with Computers, Int. J. Theor. Phys. 21, 467 (1982).
2. S. Lloyd, Universal Quantum Simulators, Science 273, 1073 (1996).
3. I. Buluta and F. Nori, Quantum Simulators, Science 326, 108 (2009).
4. H. Friedenauer, H. Schmitz, J. Glueckert, D. Porras, and T. Schatz, Simulating a Quantum Magnet with Trapped Ions, Nature Phys. 4, 757 (2008).
5. K. Kim, M.-S. Chang, S. Korenblit, R. Islam, E. E. Edwards, J. K. Freericks, G.-D. Lin, L.-M. Duan, and C. Monroe, Quantum Simulation of Frustrated Ising Spins with Trapped Ions, Nature (London) 465, 590 (2010).
6. B. P. Lanyon, J.D. Whitfield, G. G. Gillet, M. E. Goggin, M. P. Almeida, I. Kassal, J. D. Biamonte, M. Mohseni, B. J. Powell, M. Barbieri, A. Aspuru-Guzik, and A. G. White, Towards Quantum Chemistry on a Quantum Computer, Nature Chem. 2, 106 (2010).
7. M. Greiner, O. Mandel, T. Esslinger, T.W. Hansch, and I. Bloch, Quantum Phase Transition from a Superfluid to a Mott Insulator in a Gas of Ultracold Atoms, Nature (London) 415, 39 (2002).
8. J. Casanova, A. Mezzacapo, L. Lamata, and E. Solano, Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions, arXiv:1110.3730.
9. O. Lahav, A. Itah, A. Blumkin, C. Gordon, S. Rinott, A. Zayats, and J. Steinhauer, Realization of a Sonic Black Hole Analog in a Bose-Einstein Condensate, Phys. Rev. Lett. 105, 240401 (2010).
10. J. Casanova, L. Lamata, I. L. Egusquiza, R. Gerritsma, C. F. Roos, J. J. Garcia-Ripoll, and E. Solano, Quantum Simulation of Quantum Field Theories in Trapped Ions, arXiv:1107.5233 [Phys. Rev. Lett. (to be published)].
11. S. P. Jordan, K. S. M. Lee, and J. Preskill, Quantum Algorithms for Quantum Field Theories, arXiv:1111.3633.
12. L. Lamata, J. Leon, T. Schatz, and E. Solano, Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion, Phys. Rev. Lett. 98, 253005 (2007).
13. R. Gerritsma, G. Kirchmair, F. Zahringer, E. Solano, R. Blatt, and C. F. Roos, Quantum Simulation of the Dirac Equation, Nature (London) 463, 68 (2010).
14. J. Casanova, J. J. Garcia-Ripoll, R. Gerritsma, C. F. Roos, and E. Solano, Klein Tunneling and Dirac Potentials in Trapped Ions, Phys. Rev. A 82, 020101(R) (2010).
15. R. Gerritsma, B. P. Lanyon, G. Kirchmair, F. Zahringer, C. Hempel, J. Casanova, J. J. Garcia-Ripoll, E. Solano, R. Blatt, and C. F. Roos, Quantum Simulation of the Klein Paradox with Trapped Ions, Phys. Rev. Lett. 106, 060503 (2011).
16. L. Lamata, J. Casanova, R. Gerritsma, C. F. Roos, J. J. Garcia-Ripoll, and E. Solano, Relativistic Quantum Mechanics with Trapped Ions, New J. Phys. 13, 095003 (2011).
17. E. Majorana, Teoria Simmetrica dell'Elettrone e del Positrone, Nuovo Cimento 14, 171 (1937).
18. B. Thaller, The Dirac Equation (Springer-Verlag, Berlin, 1992).
19. A. Zee, Quantum Field Theory in a Nutshell (Princeton University Press, Princeton, 2003).
20. A. Aste, A Direct Road to Majorana Fields, Symmetry 2, 1776 (2010).
21. C. Giunti and C.W. Kim, Fundamentals of Neutrino Physics and Astrophysics (Oxford University Press, Oxford, 2007).
22. A.Y. Kitaev, Unpaired Majorana Fermions in Quantum Wires, Phys. Usp. 44, 131 (2001).
23. A. Mezzacapo, J. Casanova, L. Lamata, and E. Solano, Topological Qubits with Majorana Fermions in Trapped Ions, arXiv:1111.5603.
24. F. Wilczek, Majorana Returns, Nature Phys. 5, 614 (2009).
25. Since the early times of quantum mechanics, several mappings that turn complex wave functions onto real ones have been proposed, generating different kinds of wave equations. In this sense, it is possible to turn the Majorana equation into a Klein-Gordon-type (see [20]), or into a Dirac equation; see J. Serpe, Two-Component Wave Equations, Phys. Rev. 76, 1538 (1949).
26. R. F. Streater and A. S. Wightman, PCT, Spin and Statistics and All That (Princeton University Press, Princeton, 2000).
27. Majorana equations in 2 1 and 3 1 dimensions are transformed into 3 1 and 7 1 Dirac equations.