Evaluating Sample-Based Krylov Quantum Diagonalization for Heisenberg Models with Applications to Materials Science

Entropy, vol. 28, pp. 367

Abstract

We evaluate the Sample-based Krylov Quantum Diagonalization (SKQD) algorithm on one- and two-dimensional Heisenberg models, including strongly correlated regimes in which the ground state is dense. Using problem-informed initial states and magnetization sector sweeps, we investigate SKQD for problems with non-sparse ground states, where energy accuracy and sampling efficiency are theoretically anticipated to degrade. Our studies reveal that SKQD reproduces ground-state energies and field-dependent magnetization across a range of anisotropies. Benchmarks against DMRG and exact diagonalization show consistent qualitative agreement, with accuracy improving systematically in more anisotropic regimes. We further demonstrate SKQD on quantum hardware by implementing 18- and 30-qubit Heisenberg chains, obtaining magnetization curves that match theoretical expectations. Simulations on the IBM Nighthawk processor for 64-qubit two-dimensional square lattice systems further indicate that the method remains effective beyond one-dimensional geometries.

Authors 7

1. Neel Misciasci

   Volkswagen Group (Germany) · Technical University of Munich

   Affiliation as printed

   CIT School, Technical University of Munich, 80333 Munich, Germany

   Volkswagen AG, Berliner Ring 2, 38440 Wolfsburg, Germany

2. Roman Fiřt corresponding

   Volkswagen Group (Germany)

   Affiliation as printed

   Volkswagen AG, Berliner Ring 2, 38440 Wolfsburg, Germany

3. Jonathan Edward Mueller

   Volkswagen Group (Germany)

   Affiliation as printed

   Volkswagen AG, Berliner Ring 2, 38440 Wolfsburg, Germany

4. Triet Friedhoff

   IBM (United States)

   Affiliation as printed

   IBM Quantum, IBM Chicago Office, Chicago, IL 60606, USA

5. Chinonso Onah Aachen Department of Physics

   Volkswagen Group (Germany) · RWTH Aachen University

   Affiliation as printed

   Department of Physics, RWTH Aachen University, 52062 Aachen, Germany

   Volkswagen AG, Berliner Ring 2, 38440 Wolfsburg, Germany

6. Aaron Lee Schulze

   Volkswagen Group (Germany) · Universität Ulm

   Affiliation as printed

   Department of Physics, University of Ulm, Albert–Einstein–Allee 11, 89081 Ulm, Germany

   Volkswagen AG, Berliner Ring 2, 38440 Wolfsburg, Germany

7. Sarah Mostame corresponding

   IBM (United States) · IBM Research - Thomas J. Watson Research Center

   Affiliation as printed

   IBM Quantum, IBM T.J. Watson Research Center, Yorktown Heights, NY 10598, USA