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Strategies for solving the Fermi-Hubbard model on near-term quantum computers

Chris Cade, Lana Mineh, Ashley Montanaro, and Stasja Stanisic
Phys. Rev. B 102, 235122 – Published 10 December 2020
Physics logo See synopsis: Gaining a Quantum Advantage Sooner than Expected

Abstract

The Fermi-Hubbard model is of fundamental importance in condensed-matter physics, yet is extremely challenging to solve numerically. Finding the ground state of the Hubbard model using variational methods has been predicted to be one of the first applications of near-term quantum computers. Here we carry out a detailed analysis and optimization of the complexity of variational quantum algorithms for finding the ground state of the Hubbard model, including costs associated with mapping to a real-world hardware platform. The depth complexities we find are substantially lower than previous work. We performed extensive numerical experiments for systems with up to 12 sites. The results suggest that the variational ansätze we used—an efficient variant of the Hamiltonian variational ansatz and a generalization thereof—will be able to find the ground state of the Hubbard model with high fidelity in relatively low quantum circuit depths. Our experiments include the effect of realistic measurements and depolarizing noise. If our numerical results on small lattice sizes are representative of the somewhat larger lattices accessible to near-term quantum hardware, they suggest that optimizing over quantum circuits with a gate depth less than a thousand could be sufficient to solve instances of the Hubbard model beyond the capacity of classical exact diagonalization.

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  • Received 21 February 2020
  • Accepted 20 October 2020

DOI:https://doi.org/10.1103/PhysRevB.102.235122

©2020 American Physical Society

Physics Subject Headings (PhySH)

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

synopsis

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Gaining a Quantum Advantage Sooner than Expected

Published 10 December 2020

For an important quantum many-body problem, a hybrid quantum-classical algorithm could outperform purely classical approaches using surprisingly few quantum resources.  

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Authors & Affiliations

Chris Cade1,*, Lana Mineh1,2,3, Ashley Montanaro1,2, and Stasja Stanisic1

  • 1Phasecraft Ltd, Bristol BS1 5DD, United Kingdom
  • 2School of Mathematics, University of Bristol, Bristol BS8 1UG, United Kingdom
  • 3Quantum Engineering Centre for Doctoral Training, University of Bristol, Bristol BS8 1FD, United Kingdom

  • *Present address: QuSoft and CWI, Amsterdam, Netherlands.

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Issue

Vol. 102, Iss. 23 — 15 December 2020

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