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Ground state preparation in (2+1)-dimensional pure Z2 lattice gauge theory via deterministic quantum imaginary time evolution

Minoru Sekiyama*

Lento Nagano†,‡

  • Department of Physics, Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

  • International Center for Elementary Particle Physics (ICEPP), The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

  • *Contact author: minorusekiyama@hep.phys.s.u-tokyo.ac.jp
  • †Contact author: lento.nagano@keio.jp
  • ‡Present address: Graduate School of Science and Technology, Keio University, Yokohama, Kanagawa 223-8522, Japan.
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Phys. Rev. D 114, 054506 – Published 21 September, 2026

DOI: https://doi.org/10.1103/k43t-x4p2

Abstract

In this paper, we apply the deterministic quantum imaginary time evolution (QITE) algorithm to obtain the ground state of a (2+1)-dimensional pure Z2 lattice gauge theory. We first construct the set of Pauli operators commuting with Gauss’s law constraints, generalizing a previous result. This makes the deterministic QITE gauge-invariant and reduces both the measurement and gate costs significantly without adding extra algorithm errors in the QITE. Then, the classical numerical simulation of the deterministic QITE using tensor networks is performed, and the results are compared with the density matrix renormalization group to evaluate the accuracy of the algorithm. Specifically, we investigate the coupling and system size dependence, and find that the deterministic QITE can achieve a relative error of less than 0.1% up to a 12-plaquette system and coupling values in a regime that we study. Furthermore, the error dependence on the number of time steps is studied and discussed.

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Phys. Rev. D 114, 054506– Published 21 September, 2026
  • Received 20 May 2026
  • Accepted 16 July 2026
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