The Bravyi-Kitaev transformation for quantum computation of electronic structure

Journal of Chemical Physics

Volumn 137, Issue 22, 2012, Pages

  Seeley, Jacob T ^a   Richard, Martin J ^a   Love, Peter J ^a  

^a HAVERFORD COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALTERNATIVE METHODS; CONDENSED MATTER; E-PRINTS; FERMIONIC SYSTEMS; JORDAN-WIGNER TRANSFORMATION; MOLECULAR HYDROGEN; QUANTUM CHEMICAL; QUANTUM CIRCUIT; QUANTUM SIMULATIONS; SIMULATION COST; TIME STEP;

ELECTRONIC STRUCTURE; HAMILTONIANS; LATTICE CONSTANTS; MOLECULAR PHYSICS; QUANTUM COMPUTERS; QUANTUM OPTICS;

QUANTUM CHEMISTRY;

EID: 84871228749     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4768229     Document Type: Article

References (33)

1. R. P. Feynman, Opt. Photonics News 11, 11 (1985). 10.1364/ON.11.2.000011
2. S. Lloyd, Science 273, 1073 (1996). 10.1126/science.273.5278.1073
3. A. Aspuru-Guzik, A. D. Dutoi, P. J. Love, and M. Head-Gordon, Science 309, 1704 (2005). 10.1126/science.1113479
4. D. A. Lidar and H. Wang, Phys. Rev. E 59, 2429 (1999). 10.1103/PhysRevE.59.2429
5. I. Kassal, S. P. Jordan, P. J. Love, M. Mohseni, and A. Aspuru-Guzik, Proc. Natl. Acad. Sci. U.S.A. 105, 18681 (2008). 10.1073/pnas.0808245105
6. G. Ortiz, J. Gubernatis, E. Knill, and R. Laflamme, Phys. Rev. A 64, 022319 (2001). 10.1103/PhysRevA.64.022319
7. I. Kassal and A. Aspuru-Guzik, J. Chem. Phys. 131, 4102 (2009). 10.1063/1.3266959
8. D. S. Abrams and S. Lloyd, Phys. Rev. Lett. 79, 2586 (1997). 10.1103/PhysRevLett.79.2586
9. R. Somma, G. Ortiz, J. E. Gubernatis, E. Knill, and R. Laflamme, Phys. Rev. A 65, 42323 (2002). 10.1103/PhysRevA.65.042323
10. P. Jordan and E. Wigner, Z. Phys. 47, 631 (1928). 10.1007/BF01331938
11. J. D. Whitfield, J. Biamonte, and A. Aspuru-Guzik, Mol. Phys. 109, 735 (2011). 10.1080/00268976.2011.552441
12. F. Verstraete and J. I. Cirac, J. Stat. Mech.: Theory Exp. 09, 012 (2005). 10.1088/1742-5468/2005/09/P09012
13. S. Bravyi and A. Kitaev, Ann. Phys. 298, 210 (2002); 10.1006/aphy.2002. 6254
14. e-print arXiv:quant-ph/0003137v2.
15. R. C. Ball, Phys. Rev. Lett. 95, 176407 (2005). 10.1103/PhysRevLett.95. 176407
16. B. P. Lanyon, J. D. Whitfield, G. G. Gillett, 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, Nat. Chem. 2, 106 (2010). 10.1038/nchem.483
17. A. Aspuru-Guzik and P. Walther, Nat. Phys. 8, 285 (2012). 10.1038/nphys2253
18. J. Du, N. Xu, X. Peng, P. Wang, S. Wu, and D. Lu, Phys. Rev. Lett. 104, 030502 (2010). 10.1103/PhysRevLett.104.030502
19. B. P. Lanyon, C. Hempel, D. Nigg, M. Müller, R. Gerritsma, F. Zähringer, P. Schindler, J. T. Barreiro, M. Rambach, G. Kirchmair, M. Hennrich, P. Zoller, R. Blatt, and C. F. Roos, Science 334, 57 (2011). 10.1126/science.1208001
20. R. Blatt and C. F. Roos, Nat. Phys. 8, 277 (2012). 10.1038/nphys2252
21. L. Veis and J. Pittner, J. Chem. Phys. 133, 4106 (2010). 10.1063/1.3503767
22. L. Veis, J. Višňák, T. Fleig, S. Knecht, T. Saue, L. Visscher, and J. Pittner, Phys. Rev. A 85, 030304 (2012). 10.1103/PhysRevA.85. 030304
23. P. J. Love, " Back to the future: A roadmap for quantum simulation from vintage quantum chemistry.," Adv. Chem. Phys. (to be published), e-print arXiv:1208.5524.
24. N. C. Jones, J. D. Whitfield, P. L. McMahon, M.-H. Yung, R. V. Meter, A. Aspuru-Guzik, and Y. Yamamoto, " Simulating chemistry efficiently on fault-tolerant quantum computers.," e-print arXiv:1204.0567v1 (unpublished).
25. P. Zanardi, Phys. Rev. A 65, 042101 (2002). 10.1103/PhysRevA.65.042101
26. H. F. Trotter, Proc. Am. Math. Soc. 10, 545 (1959). 10.1090/S0002-9939- 1959-0108732-6
27. M. Suzuki, Phys. Lett. A 165, 387 (1992). 10.1016/0375-9601(92)90335-J
28. N. Hatano, and M. Suzuki, in Quantum Annealing and Other Optimization Methods, Lecture Notes in Physics Vol. 679, edited by, A. Das, and, B. K. Chakrabarti, (Springer, 2005), pp. 36-68.
29. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
30. R. McWeeny, Methods of Molecular Quantum Mechanics (Academic, 1992).
31. A. Szabo and N. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory (Dover, 1996).
32. A. Dutta, U. Divakaran, D. Sen, B. K. Chakrabarti, T. F. Rosenbaum, and G. Aeppli, " Transverse field spin models: From statistical physics to quantum information.," e-print arXiv:1012.0653v1 (unpublished).
33. R. P. Muller, " Python quantum chemistry (pyquante) program. " (2007); online at http://pyquante.sourceforge.net/.