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Solving strongly correlated electron models on a quantum computer

Dave Wecker, Matthew B. Hastings, Nathan Wiebe, Bryan K. Clark, Chetan Nayak, and Matthias Troyer
Phys. Rev. A 92, 062318 – Published 10 December 2015
Physics logo See Synopsis: Grounding the Hubbard Model

Abstract

One of the main applications of future quantum computers will be the simulation of quantum models. While the evolution of a quantum state under a Hamiltonian is straightforward (if sometimes expensive), using quantum computers to determine the ground-state phase diagram of a quantum model and the properties of its phases is more involved. Using the Hubbard model as a prototypical example, we here show all the steps necessary to determine its phase diagram and ground-state properties on a quantum computer. In particular, we discuss strategies for efficiently determining and preparing the ground state of the Hubbard model starting from various mean-field states with broken symmetry. We present an efficient procedure to prepare arbitrary Slater determinants as initial states and present the complete set of quantum circuits needed to evolve from these to the ground state of the Hubbard model. We show that, using efficient nesting of the various terms, each time step in the evolution can be performed with just O(N) gates and O(logN) circuit depth. We give explicit circuits to measure arbitrary local observables and static and dynamic correlation functions, in both the time and the frequency domains. We further present efficient nondestructive approaches to measurement that avoid the need to reprepare the ground state after each measurement and that quadratically reduce the measurement error.

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  • Received 1 July 2015

DOI:https://doi.org/10.1103/PhysRevA.92.062318

©2015 American Physical Society

Synopsis

Key Image

Grounding the Hubbard Model

Published 10 December 2015

Researchers propose a step-by-step quantum recipe to find the ground state of models of strongly interacting electrons.

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Authors & Affiliations

Dave Wecker1, Matthew B. Hastings2,1, Nathan Wiebe1, Bryan K. Clark2,3, Chetan Nayak2, and Matthias Troyer4

  • 1Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052, USA
  • 2Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA
  • 3Department of Physics, University of Illinois at Urbana-Champaign, Illinois 61801, USA
  • 4Theoretische Physik and Station Q Zurich, ETH Zurich, 8093 Zurich, Switzerland

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Issue

Vol. 92, Iss. 6 — December 2015

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