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

Physical Review A, vol. 104

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.

Authors 4

1. Vrinda Mehta Aachen

   Forschungszentrum Jülich · Jülich Supercomputing Centre · RWTH Aachen University

   Affiliation as printed

   Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52425 Jülich, Germany

   RWTH Aachen University, D-52056 Aachen, Germany

2. Fengping Jin

   Forschungszentrum Jülich · Jülich Supercomputing Centre

   Affiliation as printed

   Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52425 Jülich, Germany

3. Hans A. De Raedt

   University of Groningen · Forschungszentrum Jülich · Jülich Supercomputing Centre · Zernike Institute for Advanced Materials

   Affiliation as printed

   Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52425 Jülich, Germany

   Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4, NL-9747 AG Groningen, The Netherlands

4. Kristel F. L. Michielsen Aachen

   Forschungszentrum Jülich · Jülich Aachen Research Alliance · Jülich Supercomputing Centre · RWTH Aachen University

   Affiliation as printed

   Institute for Advanced Simulation, Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52425 Jülich, Germany

   JARA-CSD, Jülich-Aachen Research Alliance, 52425 Jülich, Germany

   RWTH Aachen University, D-52056 Aachen, Germany