Modelling of Quantum Qubit Behaviour for Future Quantum Computers

Andrey N. Chibisov; Mary A. Chibisova

doi:10.14529/jsfi180308

Authors

Andrey N. Chibisov Computing Center, Far Eastern Branch, Russian Academy of Sciences
Mary A. Chibisova Computing Center, Far Eastern Branch, Russian Academy of Sciences

DOI:

https://doi.org/10.14529/jsfi180308

Abstract

This work deals with quantum qubit modelling based on a silicon material with embedded phosphorus atoms because a future quantum computer can be built on the basis of this qubit. The building of atomic models of bulk crystalline silicon and silicene, as well as calculation of their total energies, were performed using the Quantum ESPRESSO software package, using highperformance computing (HPC). For silicon and phosphorus atoms the generalized gradient approximation (GGA) was used in terms of the spin-orbit non-collinear interaction by means of the Quantum ESPRESSO package. The equilibrium orientations of the phosphorus qubit spins and localization of the wave functions in the 2D and bulk crystalline silicon phases were theoretically investigated by means of quantum-mechanical calculations. The existence of an exchange interaction between qubits has been confirmed, which leads to a change in the wave function’s localization and spin orientation, and in the case of silicene, this interaction was stronger.

References

Bergou, J.A., Hillery, M.: Introduction to the Theory of Quantum Information Processing. Springer New York (2013), DOI: 10.1007/978-1-4614-7092-2

Broome, M.A., Gorman, S.K., House, M.G., Hile, S.J., et al.: Two-electron spin correlations in precision placed donors in silicon. Nature Communications 9(1) (mar 2018), DOI: 10.1038/s41467-018-02982-x

Dzade, N.Y., Obodo, K.O., Adjokatse, S.K., Ashu, A.C., Amankwah, E., Atiso, C.D., Bello, A.A., Igumbor, E., Nzabarinda, S.B., Obodo, J.T., Ogbuu, A.O., Femi, O.E., Udeigwe, J.O., Waghmare, U.V.: Silicene and transition metal based materials: prediction of a twodimensional piezomagnet. Journal of Physics: Condensed Matter 22(37), 375502 (aug 2010), DOI: 10.1088/0953-8984/22/37/375502

Giannozzi, P., Baroni, S., Bonini, N., Calandra, M., et al.: QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. Journal

of Physics: Condensed Matter 21(39), 395502 (sep 2009), DOI: 10.1088/0953-8984/21/39/395502

Gorman, S.K., Broome, M.A., Baker, W.J., Simmons, M.Y.: Impact of nuclear spin dynamics on electron transport through donors. Physical Review B 92(12) (sep 2015), DOI: 10.1103/physrevb.92.125413

Kane, B.E.: A silicon-based nuclear spin quantum computer. Nature 393(6681), 133–137 (may 1998), DOI: 10.1038/30156

Morello, A., Pla, J.J., Zwanenburg, F.A., Chan, K.W., Tan, K.Y., Huebl, H., M¨ott¨onen, M., Nugroho, C.D., Yang, C., van Donkelaar, J.A., Alves, A.D.C., Jamieson, D.N., Escott,

C.C., Hollenberg, L.C.L., Clark, R.G., Dzurak, A.S.: Single-shot readout of an electron spin in silicon. Nature 467(7316), 687–691 (sep 2010), DOI: 10.1038/nature09392

Oberbeck, L., Hallam, T., Curson, N.J., Simmons, M.Y., Clark, R.G.: STM investigation of epitaxial si growth for the fabrication of a si-based quantum computer. Applied Surface Science 212-213, 319–324 (may 2003), DOI: 10.1016/s0169-4332(03)00370-2

Pla, J.J., Tan, K.Y., Dehollain, J.P., Lim, W.H., Morton, J.J.L., Jamieson, D.N., Dzurak, A.S., Morello, A.: A single-atom electron spin qubit in silicon. Nature 489(7417), 541–545 (sep 2012), DOI: 10.1038/nature11449

Veldhorst, M., Yang, C.H., Hwang, J.C.C., Huang, W., Dehollain, J.P., Muhonen, J.T., Simmons, S., Laucht, A., Hudson, F.E., Itoh, K.M., Morello, A., Dzurak, A.S.: A two-qubit logic gate in silicon. Nature 526(7573), 410–414 (oct 2015), DOI: 10.1038/nature15263