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This research advances deterministic quantum imaginary time evolution by constructing gauge-invariant Pauli operators that significantly reduce measurement and gate costs in lattice gauge theory simulations. The study validates the algorithm's accuracy against density matrix renormalization group methods, achieving sub-0.1% relative error even as system size increases to twelve plaquettes. These findings are critical for developing efficient quantum algorithms capable of solving complex problems in high-energy physics without prohibitive resource overheads.
Ground state preparation in $(2+1)$-dimensional pure $\mathbb{Z}_2$ lattice gauge theory via deterministic quantum imaginary time evolution
arXiv:2604.17874v3 Announce Type: replace-cross 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 $\mathbb{Z}_2$ 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 (DMRG) 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 twelve-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.
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 $\mathbb{Z}_2$ 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 (DMRG) 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 twelve-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.
arXiv:2604.17874 [hep-lat]
(or arXiv:2604.17874v3 [hep-lat] for this version)
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