Practical design and simulation of silicon-based quantum-dot qubits

Physical Review B - Condensed Matter and Materials Physics

Volumn 67, Issue 12, 2003, Pages 1213011-1213014

  Friesen, Mark ^a   Rugheimer, Paul ^a   Savage, Donald E ^a   Lagally, Max G ^a   Van der Weide, Daniel W ^b   Joynt, Robert ^a   Eriksson, Mark A ^a  

^a University of Wisconsin Madison   (United States)

^b UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GERMANIUM; SILICON;

ARTICLE; ELECTRON; ELECTRONICS; ENERGY; MATHEMATICAL COMPUTING; QUANTUM MECHANICS; QUANTUM THEORY; SIMULATION;

EID: 0042735693     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. P.W. Shor, in Proceedings of 35th Annual Symposium on Foundations of Computer Science, edited by S. Goldwasser (IEEE Computer Society Press, Los Alamitos, CA, 1994), pp. 124-134.
2. J. Preskill, Proc. R. Soc. London, Ser. A 454, 385 (1998).
3. 28Si to minimize the effect of nuclear (Ref. 24) spins. It is generally expected that decoherence times in confined structures like quantum dots will exceed the bulk values.
4. D. Loss and D.P. DiVincenzo, Phys. Rev. A 57, 120 (1998).
5. B.E. Kane, Nature (London) 393, 133 (1998).
6. R. Vrijen, E. Yablonovitch, K. Wang, H.W. Jiang, A. Balandin, V. Roychowdhury, T. Mor, and D. DiVincenzo, Phys. Rev. A 62, 012306 (2000).
7. D. Mozyrsky, V. Privman, and M.L. Glasser, Phys. Rev. Lett. 86, 5112 (2001).
8. J. Levy, Phys. Rev. A 64, 052306 (2001).
9. G. Burkard, D. Loss, and D.P. DiVincenzo, Phys. Rev. B 59, 2070 (1999).
10. X. Hu and S. Das Sarma, Phys. Rev. A 61, 062301 (2000).
11. The electrostatic and Hartree-Fock calculations were performed using finite-element software, FLEXPDE©. Image potentials arising from the nontrivial gate structure were calculated selfconsistently using a numerical Green's function technique.(Test charges were first introduced into the heterostructure. The direct contributions from the test charges were then subtracted from the solutions to obtain exact image potentials.) The quantummechanical problem was approximated as a single envelope (Ref. 16) function. A basis set of 18 single-electron HartreeFock wave functions was obtained in real space on an adaptive finite-element mesh. A basis of about 50 two-electron wave functions was then constructed in the configuration interaction approach. The Hamiltonian matrix was computed and diagonalized, giving an essentially exact result for the envelope function. For the four-qubit simulation [Fig. 1(b)], the wave functions of the outer two electrons were found to have an insignificant overlap with the two center electrons. Their couplings were, therefore, treated as purely Coulombic. It was not possible to calculate directly the tiny values of J corresponding to high potential barriers between the quantum dots. In this regime, we made use of the nearly exponential dependence of J on the gate voltage to obtain extrapolations.
12. D. Bacon, J. Kempe, D.A. Lidar, and K.B. Whaley, Phys. Rev. Lett. 85, 1758 (2000).
13. D.P. DiVincenzo, D. Bacon, J. Kempe, G. Burkard, and K.B. Whaley, Nature (London) 408, 339 (2000).
14. L.P. Kouwenhoven et al., in Mesoscopic Electron Transport, edited by L.L. Sohn, L.P. Kouwenhoven, and G. Schön (Kluwer Academic Publishers, Dordrecht, 1997), Vol. 345, pp. 105-214.
15. P. M. Mooney et al., Appl. Phys. Lett. 67, 2373 (1995).
16. ±, although a complete treatment of the interface physics is still lacking. Using the estimate given in Ref. 25 (α≃0.5 Å) we predict a valley splitting of ΔE >0.06 meV (0.7 K) for our heterostructure - more than 10 times our dilution fridge temperature. By optimizing the heterostructure to increase the electric field in the quantum well, it is possible to increase ΔE significantly. At low temperatures then, all electrons should be in the valley-split ground state, with no interference effects of the type discussed in Ref. 26.
17. The 104 estimate assumes two-qubit operations between any pair of qubits. In a linear qubit array with only nearest-neighbor couplings, a more restrictive threshold may be appropriate.
18. -4 relative error in its duration. Such accuracy is currently beyond the limits of commercial pulse generation technology.
19. Estimates are based on specifications for pulse amplitude jitter in PB-4 and PB-5 sub-MHz pulse generators from Berkeley Nucleonics Corporation (http://www.berkeleynucleonics.com).
20. Specifications from the Agilent Technologies 8133 and 81100 families of GHz pulse generators are listed as δV/V<0.01 (http://www.agilent.com).
21. M. Friesen, R. Joynt, and M. A. Eriksson, Appl. Phys. Lett. 81, 4619 (2002).
22. G. Feher and E.A. Gere, Phys. Rev. 114, 1245 (1959).
23. C. Tahan, M. Friesen, and R. Joynt, Phys. Rev. B 66, 035314 (2002).
24. J.P. Gordon and K.D. Bowers, Phys. Rev. Lett. 1, 368 (1958).
25. L.J. Sham and M. Nakayama, Phys. Rev. B 20, 734 (1979).
26. B. Koiller, X. Hu, and S. Das Sarma, Phys. Rev. Lett. 88, 027903 (2002).
27. J. Schliemann, D. Loss, and A.H. MacDonald, Phys. Rev. B 63, 085311 (2001).
28. X. Hu and S. Das Sarma, Phys. Rev. A 66, 012312 (2002).