Quantum annealing with trigger Hamiltonians: Application to 2-satisfiability and nonstoquastic problems

Vrinda Mehta, Fengping Jin, Hans De Raedt, and Kristel Michielsen
Phys. Rev. A 104, 032421 – Published 27 September 2021

Abstract

We study the performance of quantum annealing for two sets of problems, namely, 2-satisfiability (2-SAT) problems represented by Ising-type Hamiltonians and nonstoquastic problems which are obtained by adding extra couplings to the 2-SAT problem Hamiltonians. In addition, we add to the transverse Ising-type Hamiltonian used for quantum annealing a third term, the trigger Hamiltonian with ferromagnetic or antiferromagnetic couplings, which vanishes at the beginning and end of the annealing process. We also analyze some problem instances using the energy spectrum, average energy or overlap of the state during the evolution with the instantaneous low-lying eigenstates of the Hamiltonian, and identify some nonadiabatic mechanisms which can enhance the performance of quantum annealing.

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  • Received 10 June 2021
  • Accepted 2 September 2021

DOI:https://doi.org/10.1103/PhysRevA.104.032421

©2021 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Vrinda Mehta1,2, Fengping Jin1, Hans De Raedt1,3, and Kristel Michielsen1,2,4,*

  • 1Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52425 Jülich, Germany
  • 2RWTH Aachen University, D-52056 Aachen, Germany
  • 3Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, NL-9747 AG Groningen, The Netherlands
  • 4JARA-CSD, Jülich-Aachen Research Alliance, 52425 Jülich, Germany

  • *k.michielsen@fz-juelich.de

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Issue

Vol. 104, Iss. 3 — September 2021

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