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arXiv:2012.00921 · Nature

Accurately computing the electronic properties of a quantum ring

C. Neill, T. McCourt, X. Mi, Z. Jiang, Murphy Yuezhen Niu, W. Mruczkiewicz, I. Aleiner, F. Arute, K. Arya, J. Atalaya, R. Babbush, J. C. Bardin, R. Barends, A. Bengtsson, A. Bourassa, M. Broughton, B. B. Buckley, David A. Buell, B. Burkett, N. Bushnell, J. Campero, Z. Chen, B. Chiaro, R. Collins, W. Courtney, S. Demura, A. R. Derk, A. Dunsworth, D. Eppens, C. Erickson, Edward Farhi, Austin G. Fowler, B. Foxen, C. Gidney, M. Giustina, Jonathan A. Gross, Matthew P. Harrigan, S. D. Harrington, J. Hilton, A. Ho, S. Hong, T. Huang, W. J. Huggins, Sergei V. Isakov, M. Jacob-Mitos, E. Jeffrey, Cody Jones, D. Kafri, K. Kechedzhi, J. Kelly, S. Kim, P. V. Klimov, A. N. Korotkov, F. Kostritsa, David Landhuis, P. Laptev, E. Lucero, O. Martin, J. R. McClean, M. McEwen, A. Megrant, K. C. Miao, Masoud Mohseni, J. Mutus, O. Naaman, M. Neeley, M. Newman, T. E. O’Brien, A. Opremcak, E. Ostby, B. Pató, A. Petukhov, C. Quintana, N. Redd, N. C. Rubin, D. Sank, K. J. Satzinger, V. Shvarts, D. Strain, M. Szalay, M. D. Trevithick, B. Villalonga, T. C. White, Z. Yao, P. Yeh, A. Zalcman, H. Neven, S. Boixo, L. B. Ioffe, P. Roushan, Y. Chen, V. Smelyanskiy

Published Jun 23, 2021• 70 citations
arXivHTMLPDF
DOI
10.1038/s41586-021-03576-2

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In this article, we discuss how a kind of hybrid computation, which employs symbolic, numeric, classic, and quantum algorithms, allows us to conduct Hartree-Fock electronic structure computation of molecules. In the proposed algorithm, we replace the Hartree-Fock equations with a set of equations composed of multivariate polynomials. We transform those polynomials to the corresponding Gr\"obner bases, and then we investigate the corresponding quotient ring, wherein the orbital energies, the LCAO coefficients, or the atomic coordinates are represented by the variables in the ring. In this quotient ring, the variables generate the transformation matrices that represent the multiplication with the monomial bases, and the eigenvalues of those matrices compose the roots of the equation. The quantum phase estimation (QPE) algorithm enables us to record those roots in the quantum states, which would be used in the input data for more advanced and more accurate quantum computations.
We consider few-electron concentric double quantum rings with parabolic confining potential and compare the ground-state energies calculated by exact diagonalization of the Hamiltonian, accurate quantum Monte Carlo, and local spin-density functional approaches. Electronic localization in one of the rings and the formation of rotating Wigner molecules is shown, respectively, from the one-body and the two-body density operators. As the confinement strength of the outer ring is finely increased, the circularly symmetric electron density exhibits a radial crossover from this ring to the inner one without altering the angular character of the system.