Dephasing of Quantum Bits by a Quasi-Static Mesoscopic Environment

Loss D., DiVincenzo D. (1998). Phys. Rev. A 57:120

Imamoglu A., Awschalom D.D., Burkard G., DiVincenzo D.P., Loss D., Sherwin M., Small A. (1999). Phys. Rev. Lett. 83:4204

Merkulov I.A., Efros A.L., Rosen M. (2002). Phys. Rev. B 65:205309

Khaetskii A.V., Loss D., Glazman L. (2002). Phys. Rev. Lett. 88:186802, URL http://publish.aps.org/abstract/prl/v88/p186802.

Taylor J.M., Marcus C.M., Lukin M.D. (2003). Phys. Rev. Lett. 90:206803

Johnson A.C., Petta J., Taylor J.M., Lukin M.D., Marcus C.M., Hanson M.P., Gossard A.C. (2005). Nature 435:925

F. H. L. Koppens, J. A. Folk, J. M. Elzerman, R. Hanson, L. H. Willems van , I. T. Vink, H.-P. Tranitz, W. Wegscheider, L. P. Kouwenhoven, and L. M. K. Vandersypen, Science p. 1113719 (2005), URL http://www.sciencemag.org/cgi/content/abstract/1113719v2.

Petta J.R., Johnson A.C., Taylor J.M., Laird E., Yacoby A., Lukin M.D., Marcus C.M. (2005). Science 309:2180

de Sousa R., Das Sarma S. (2003). Phys. Rev. B 67:033301

Coish W.A., Loss D. (2004). Phys. Rev. B 70:195340

Elzerman J.M., Hanson R., van Beveren L.H.W., Witkamp B., Vandersypen L.M.K., Kouwenhoven L.P. (2004). Nature 430:431

Fujisawa T., Tokura Y., Hirayama Y. (2001). Phys. Rev. B. (Rapid Comm.) 63:081304

Golovach V.N., Khaetskii A., Loss D. (2004). Phys. Rev. Lett. 93:016601

Hanson R., Witkamp B., Vandersypen L.M.K., van Beveren L.H.W., Elzerman J.M., Kouwenhoven L.P. (2003). Phys. Rev. Lett. 91:196802

Vion D., Aassime A., Cottet A., Joyez P., Pothier H., Urbina C., Esteve D., Devorett M. (2002). Science 296:886

Pashkin A., Yamamoto T., Astafiev O., Nakamura Y., Averin D., Tsai J. (2003). Nature 421:823

Chiorescu I., Nakamura Y., Harmans C., Mooij J. (2003). Science 299:1869

Martinis J., Nam S., Aumentado J., Urbina C. (2002). Phys. Rev. Lett. 89:117901

Simmonds R., Lang K.M., Hite D.A., Nam S., Pappas D.P., Martinis J.M. (2004). Phys. Rev. Lett. 93:077003

Makhlin Y., Shnirman A. (2004). Phys. Rev. Lett. 92:178301

Falci G., D’Arrigo A., Mastellone A., Paladino E. (2005). Phys. Rev. Lett. 94:167002

Taylor J.M., Imamoglu A., Lukin M.D. (2003). Phys. Rev. Lett. 91:246802

Weissman M.B. (1988). Rev. Mod. Phys. 60:537

D. Klauser, W. A. Coish, and D. Loss, e-print: cond-mat/0510177 (2005).

Coish W.A., Loss D. (2005). Phys. Rev. B 72:125337

X. Hu and S. D. Sarma, e-print: cond-mat/0507725 (2005).

Zurek W.H. (1981). Phys. Rev. D 24:1516

Prokof’ev N.V., Stamp P.C.E. (2000). Reports Prog Phys 63:669

Rose G., Smirnov A.Y. (2001). J. Phys.: Cond. Mat. 13:11027

Zanardi P., Rasetti M. (1997). Phys. Rev. Lett. 79:3306

Viola L., Lloyd S. (1998). Phys. Rev. A 58:2733

The breakdown of the two-level approximation in superconductor-based qubit designs has already been explored in great detail (Burkard et al. Phys. Rev B. 69, 064503 (2004)) and we instead focus on other sources of error due to local spins, charge traps, etc.

Feynman R.P., Vernon F.L. (1963). Ann. Phys. 24:118

Magnus W. (1954). Commun. Pure Appl. Math 7:649

Cottet A., et al. (2001). Macroscopic Quantum Coherence and Quantum Computing. Kluwer/Plenum, New York, p. 111

G. Giedke, J. M. Taylor, D. D’Alessandro, M. D. Lukin, and A. Imamoglu, e-print: quantph/ 0508144 (2005).

J. M. Taylor, J. Petta, A. C. Johnson, A. Yacoby, C. M. Marcus, and M. D. Lukin, (in preparation) (2006).

de Sousa R., Das Sarma S. (2003). Phys. Rev. B 68:115322

W. Yao, R.-B. Liu, and L. J. Sham, e-print: cond-mat/0508441 (2005).

Deng C., Hu X. (2005). Phys. Rev. B 72:165333

Paget D. (1982). Phys. Rev. B 25:4444

G. Teklemariam, E. M. Fortunato, C. C. Lopez, J. Emerson, J. P. Paz, T. F. Havel, and D. G. Cory, e-print: quant-ph/0303115 (2003).

For an arbitrary, quasi-static bath (i.e., not necessary a spin-bath) with a density matrix that is diagonal in the eigenbasis of \(\hat{A}_z\), \(\Phi_{\rm FID} = e^{-i \delta t} \int_{-\infty}^{\infty} d \Lambda \rho(\Lambda) e^{-i \Lambda t}\), demonstrating that Φ FID is exactly the inverse Fourier transform of the bath degree of freedom in this case.

By assuming the bath density matrix is diagonal in the \(\hat{A}_z\) eigenbasis, the result derived (Eqn. 40) in fact is generally true for any bath that is non-singular (ρ sym (ω ≥ Ω) not singular) and satisfies u ≥ 0, not just a spin-bath. However, the spin-bath provides a natural case for \([\hat{H}_B,\hat{A}_z] \simeq 0\), as mentioned in the text.

Well-separated singularities in ρsym can be treated as additional stationary phase integral terms, and for each, corresponding oscillations at the resonance with different time-scales u j will emerge.

Paget D., Lampel G., Sapoval B., Safarov V. (1977). Phys. Rev. B 15:5780

Waugh J., Huber L., Haeberlen U. (1968). Phys. Rev. Lett. 20:180

Kautz R., Martinis J. (1990). Phys. Rev. B 42:9903

Galperin Y.M., Gurevich V.L. (1991). Phys. Rev. B 43:12900

Caldeira A.O., Leggett A.J. (1983). Ann. Phys. 149:347

Chattah A.K., lvarez G.A., Levstein P.R., Cucchietti F.M., Pastawski H.M., Raya J., Hirschinger J. (2003). J. Chem. Phys. 119:7943

Danieli E.P., Pastawski H.M., Álvarez G.A. (2005). Chem. Phys. Lett. 402:88

Facchi P., Tasaki S., Pascazio S., Nakazato H., Tokuse A., Lidar D. (2005). Phys. Rev. A 71:022302

Imamolgu A., Knill E., Tian L., Zoller P. (2003). Phys. Rev. Lett. 91:017402

Arecchi F.T., Courtens E., Gilmore R., Thomas H. (1972). Phys. Rev. A 6:2211, URL http://80-link.aps.org.ezp1.harvard.edu/abstract/PRA/v6/p2211.