• Open Access

Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer

Thomas E. Baker and David Poulin
Phys. Rev. Research 2, 043238 – Published 16 November 2020

Abstract

One of the potential applications of a quantum computer is solving quantum chemical systems. It is known that one of the fastest ways to obtain somewhat accurate solutions classically is to use approximations of density functional theory. We demonstrate a general method for obtaining the exact functional as a machine learned model from a sufficiently powerful quantum computer. Only existing assumptions for the current feasibility of solutions on the quantum computer are used. Several known algorithms including quantum phase estimation, quantum amplitude estimation, and quantum gradient methods are used to train a machine learned model. One advantage of this combination of algorithms is that the quantum wavefunction does not need to be completely re-prepared at each step, lowering a sizable prefactor. Using the assumptions for solutions of the ground-state algorithms on a quantum computer, we demonstrate that finding the Kohn-Sham potential is not necessarily more difficult than the ground-state density. Once constructed, a classical user can use the resulting machine learned functional to solve for the ground state of a system self-consistently, provided the machine learned approximation is accurate enough for the input system. It is also demonstrated how the classical user can access commonly used time- and temperature-dependent approximations from the ground-state model. Minor modifications to the algorithm can learn other types of functional theories including exact time and temperature dependence. Several other algorithms—including quantum machine learning—are demonstrated to be impractical in the general case for this problem.

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  • Received 12 August 2020
  • Accepted 12 October 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.043238

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Thomas E. Baker1 and David Poulin1,2,3

  • 1Institut quantique & Département de physique, Université de Sherbrooke, Sherbrooke, Québec J1K 2R1 Canada
  • 2Quantum Architecture and Computation Group, Microsoft Research, Redmond, Washington 98052, USA
  • 3Canadian Institute for Advanced Research, Toronto, Ontario, M5G 1Z8 Canada

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Issue

Vol. 2, Iss. 4 — November - December 2020

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