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Eigenvector Continuation with Subspace Learning

Dillon Frame, Rongzheng He, Ilse Ipsen, Daniel Lee, Dean Lee, and Ermal Rrapaj
Phys. Rev. Lett. 121, 032501 – Published 17 July 2018
Physics logo See Synopsis: Making Quantum Computations Behave
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Abstract

A common challenge faced in quantum physics is finding the extremal eigenvalues and eigenvectors of a Hamiltonian matrix in a vector space so large that linear algebra operations on general vectors are not possible. There are numerous efficient methods developed for this task, but they generally fail when some control parameter in the Hamiltonian matrix exceeds some threshold value. In this Letter we present a new technique called eigenvector continuation that can extend the reach of these methods. The key insight is that while an eigenvector resides in a linear space with enormous dimensions, the eigenvector trajectory generated by smooth changes of the Hamiltonian matrix is well approximated by a very low-dimensional manifold. We prove this statement using analytic function theory and propose an algorithm to solve for the extremal eigenvectors. We benchmark the method using several examples from quantum many-body theory.

  • Figure
  • Received 13 April 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.032501

© 2018 American Physical Society

Physics Subject Headings (PhySH)

Nuclear Physics

Synopsis

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Making Quantum Computations Behave

Published 17 July 2018

A new computational method tackles many-body quantum calculations that have defied a suite of existing approaches.

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Authors & Affiliations

Dillon Frame1,2, Rongzheng He1,2, Ilse Ipsen3, Daniel Lee4, Dean Lee1,2, and Ermal Rrapaj5

  • 1Facility for Rare Isotope Beams and Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
  • 2Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
  • 3Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695, USA
  • 4School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
  • 5Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1, Canada

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Issue

Vol. 121, Iss. 3 — 20 July 2018

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