Adiabatic quantum algorithms as quantum phase transitions: First versus second order

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 74, Issue 6, 2006, Pages

  Schützhold, Ralf ^a   Schaller, Gernot ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; PHASE TRANSITIONS; PROBLEM SOLVING; QUADRATIC PROGRAMMING;

ADIABATIC QUANTUM ALGORITHMS; GROVER SEARCH ROUTINE; QUANTUM PHASE TRANSITIONS;

QUANTUM THEORY;

EID: 33846338404     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.74.060304     Document Type: Article

References (20)

1. P. W. Shor, SIAM J. Comput. SMJCAT 0097-5397 10.1137/S0097539795293172 26, 1484 (1997).
2. L. K. Grover, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79. 325 79, 325 (1997).
3. E. Farhi, Science SCIEAS 0036-8075 292, 472 (2001).
4. A. M. Childs, E. Farhi, and J. Preskill, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.012322 65, 012322 (2001);
5. M. S. Sarandy and D. A. Lidar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.250503 95, 250503 (2005).
6. M. Žnidarič, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.71.062305 71, 062305 (2005);
7. see also V. Kalapala and C. Moore, e-print cs.CC/0508037.
8. E. Farhi, J. Goldstone, S. Gutmann, and D. Nagaj, e-print quant-ph/0512159.
9. D. Aharonov, FOCS 2004: 45th Annual IEEE Symposium on Foundations of Computer Science, October 2004, Rome, Italy (IEEE Computer Society, Los Alamitos, CA, 2004), pp. 42-51;
10. D. Aharonov, e-print quant-ph/0405098.
11. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, England, 2000).
12. J. Roland and N. J. Cerf, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.042308 65, 042308 (2002).
13. J. Dziarmaga, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95. 245701 95, 245701 (2005).
14. R. Schützhold and G. Schaller (unpublished).
15. M. Žnidarič and M. Horvat, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.022329 73, 022329 (2006).
16. After completing our calculations, we learned that the final Hamiltonian 6 has already been discussed in M. C. Bañuls, R. Orús, J. I. Latorre, A. Pérez, and P. Ruiz-Femenía, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.022344 73, 022344 (2006).
17. A. M. Childs, E. Farhi, J. Goldstone, and S. Gutmann, Quantum Inf. Comput. QICUAW 1533-7146 2, 181 (2002).
18. Two complementary numerical approaches were used: (a) Direct integration of the Schrödinger equation with a fourth order Runge-Kutta integration scheme and an adaptively regulated time step and (b) determination of the spectral properties near the minimum gap (data not shown) with the aid of the implicitly restarted Arnoldi method [R. B. Lehoucq, ARPACK Users' Guide (SIAM, Philadelphia, 1998), also http://www.caam.rice.edu/software/ARPACK].
19. J. I. Latorre and R. Orús, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.062302 69, 062302 (2004);
20. R. Orús and J. I. Latorre, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.052308 69, 052308 (2004).