Efficient state preparation for the Schwinger model with a theta term

Physical review. D/Physical review. D., vol. 111

Abstract

We present a comparison of different quantum state preparation algorithms and their overall efficiency for the Schwinger model with a theta term. While adiabatic state preparation is proved to be effective, in practice it leads to large gate counts to prepare the ground state. The quantum approximate optimization algorithm (QAOA) provides excellent results while keeping the counts small by design, at the cost of an expensive classical minimization process. We introduce a “blocked” modification of the Schwinger Hamiltonian to be used in the QAOA that further decreases the length of the algorithms as the size of the problem is increased. The rodeo algorithm (RA) provides a powerful tool to efficiently prepare any eigenstate of the Hamiltonian, as long as its overlap with the initial guess is large enough. We obtain the best results when combining the blocked QAOA ansatz and the RA, as this provides an excellent initial state with a relatively short algorithm without the need to perform any classical steps for large problem sizes.

Authors 7

1. Alexei Bazavov

   Michigan State University

   Affiliation as printed

   Michigan State University

2. Brandon Henke

   Michigan State University

   Affiliation as printed

   Michigan State University

3. Leon Hostetler

   Indiana University

   Affiliation as printed

   Indiana University

4. Dean Lee

   Facility for Rare Isotope Beams · Michigan State University

   Affiliation as printed

   Facility for Rare Isotope Beams

   Michigan State University

5. Huey-Wen Lin

   Michigan State University

   Affiliation as printed

   Michigan State University

6. Giovanni Pederiva corresponding

   Forschungszentrum Jülich

   Affiliation as printed

   Forschungszentrum Jülich

7. Andrea Shindler Aachen

   Lawrence Berkeley National Laboratory · RWTH Aachen University · University of California, Berkeley

   Affiliation as printed

   Lawrence Berkeley National Laboratory

   RWTH Aachen University

   University of California, Berkeley