Volume 518 - The 42nd International Symposium on Lattice Field Theory (LATTICE2025) - Parallel Session Quantum computing and quantum information
Ground state energy of a two-dimensional pure Z2 lattice gauge theory via sample-based Krylov quantum diagonalization
L. Nagano*, Y. Iiyama, T. Hayata, K. Terashi, Y. Kawashima, W. Kirby, M. Motta, V.R. Pascuzzi and A. Mezzacapo
*: corresponding author
Full text: Not available
Abstract
We study the application of sample-based Krylov quantum diagonalization (SKQD) to a two-dimensional pure $\mathbb{Z}_2$ lattice gauge theory.
SKQD samples configurations
from states obtained via time-evolution quantum circuits, projects the Hamiltonian into the subspace spanned by the sampled configurations, and solves an eigenvalue problem to estimate the ground-state energy.
We consider a model defined on a triangular lattice, which allows for an efficient construction of time-evolution circuits on the IBM Quantum Heron processor. We also propose a configuration recovery method based on Gauss's law and a conditional restricted Boltzmann machine (CRBM), to mitigate the effects of noise.
We simulate a lattice of 108 links using the superconducting quantum processor $\texttt{ibm}\_\texttt{kawasaki}$, which allows us to obtain the ground-state energy within a few percent of tensor network results.
We also compare configuration recovery with and without the CRBM, and observe that the CRBM improves the accuracy at each iteration.
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