Universal Adiabatic Quantum Computation via the Space-Time Circuit-to-Hamiltonian Construction

Physical Review Letters

Volumn 114, Issue 14, 2015, Pages

  Gosset, David ^a   Terhal, Barbara M ^b   Vershynina, Anna ^b  

^a UNIVERSITY OF WATERLOO   (Canada)

^b RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CHAINS; EIGENVALUES AND EIGENFUNCTIONS; GROUND STATE; QUANTUM COMPUTERS;

ADIABATIC QUANTUM COMPUTATION; FUNCTION OF TIME; LARGE SYSTEM SIZE; LOCAL INTERACTIONS; SINGLE PARAMETER; TIME-INDEPENDENT HAMILTONIAN; TWO-DIMENSIONAL GRIDS; UNIVERSAL COMPUTATIONS;

HAMILTONIANS;

EID: 84937503431     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.114.140501     Document Type: Article

References (26)

1. E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser, arxiv:quant-ph/0001106.
2. D. Aharonov, W. van Dam, Z. Landau, S. Lloyd, J. Kempe, and O. Regev, in Proceedings of 45th FOCS (Society for Industrial and Applied Mathematics, Philadelphia, 2004).
3. R. Feynman, Opt. News 11, 11 (1985). ONEWDU 0098-907X 10.1364/ON.11.2.000011
4. A. Y. Kitaev, A. Shen, and M. Vyalyi, Classical and Quantum Computation, Graduate Studies in Mathematics Vol. 47 (American Mathematical Society, Providence, RI, 2002).
5. J. Kempe, A. Kitaev, and O. Regev, SIAM J. Comput. 35, 1070 (2006), earlier version in Proceedings of 24th FSTTCS (Society for Industrial and Applied Mathematics, Philadelphia, 2004). SMJCAT 0097-5397 10.1137/S0097539704445226
6. R. Oliveira and B. M. Terhal, Quantum Inf. Comput. 8, 900 (2010). QICUAW 1533-7146
7. N. Schuch and F. Verstraete, Nat. Phys. 5, 732 (2009). NPAHAX 1745-2473 10.1038/nphys1370
8. J. D. Biamonte and P. J. Love, Phys. Rev. A 78, 012352 (2008). PLRAAN 1050-2947 10.1103/PhysRevA.78.012352
9. Y. Cao, R. Babbush, J. Biamonte, and S. Kais, Phys. Rev. A 91, 012315 (2015). PLRAAN 1050-2947 10.1103/PhysRevA.91.012315
10. N. Margolus, in Complexity, Entropy, and the Physics of Information, SFI Studies in the Sciences of Complexity (Addison-Wesley, Reading, MA, 1990), pp. 273-287.
11. D. Janzing, Phys. Rev. A 75, 012307 (2007). PLRAAN 1050-2947 10.1103/PhysRevA.75.012307
12. A. Mizel, M. W. Mitchell, and M. L. Cohen, Phys. Rev. A 63, 040302 (2001). PLRAAN 1050-2947 10.1103/PhysRevA.63.040302
13. A. Mizel, arxiv:1403.7694.
14. A. Mizel, D. A. Lidar, and M. Mitchell, Phys. Rev. Lett. 99, 070502 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.99.070502
15. A. M. Childs, D. Gosset, and Z. Webb, in 41st International Colloquium on Automata, Languages, and Programming (Springer, Berlin Heidelberg, 2014), pp. 308-319.
16. N. P. Breuckmann and B. M. Terhal, J. Phys. A 47, 195304 (2014). JPAMB5 1751-8113 10.1088/1751-8113/47/19/195304
17. T. Koma and B. Nachtergaele, Lett. Math. Phys. 40, 1 (1997). LMPHDY 0377-9017 10.1023/A:1007351803403
18. F. C. Alcaraz, S. R. Salinas, and W. F. Wreszinski, Phys. Rev. Lett. 75, 930 (1995). PRLTAO 0031-9007 10.1103/PhysRevLett.75.930
19. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevLett.114.140501 contains technical supporting material, which includes Refs. [22-25].
20. T. Koshy, Catalan Numbers with Applications (Oxford University Press, USA, 2008).
21. A. M. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, and D. A. Spielman, in Proceedings of the Thirty-fifth Annual ACM Symposium on Theory of Computing (ACM, New York, 2003).
22. B. Sagan, The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions, Graduate Texts in Mathematics (Springer, New York, 2001).
23. S. Bravyi, arXiv:quant-ph/0602108.
24. R. P. Stanley, J. Am. Math. Soc. 1, 919 (1988). 0894-0347 10.1090/S0894-0347-1988-0941434-9
25. D. Romik, " The Surprising Mathematics of Longest Increasing Subsequences " (Cambridge University Press, Cambridge, England, 2015). Available for free download at https://www.math.ucdavis.edu/~romik/book.
26. B. F. Logan and L. A. Shepp, Adv. Math. 26, 206 (1977). ADMTA4 0001-8708 10.1016/0001-8708(77)90030-5