Low-Depth Initial-State Preparation for Ground-State Energy Estimation of Two-Dimensional Strongly Correlated Systems
Abstract
Quantum algorithms for ground-state energy estimation require initial states with non-negligible fidelity to the ground state. Guided by classical simulations, we design shallow circuits for the two-dimensional half-filled Hubbard model by first preparing an approximate Heisenberg ground state and then applying charge-fluctuation gates derived directly from the Schrieffer-Wolff (SW) generator. For the Heisenberg model, we demonstrate effective parameter transfer from a 4×4 lattice to lattices up to 10×10 without further optimization. We obtain promising lower bounds on the ground-state fidelity using tensor-network simulations, variational Monte Carlo reference states, and estimates of the ground-state energy and singlet gap. Exact 4×4 calculations show that the SW gates substantially improve the Hubbard ground-state fidelity of the embedded Heisenberg state. The successful Heisenberg parameter transfer supports the use of these small-lattice results to design shallow Hubbard circuits on larger lattices beyond the reach of classical simulations. For a 10×10 lattice, the estimated preparation cost is on the order of 105 T gates, including Clifford+T synthesis, which is well within the megaquop regime. These results offer a route to low-cost initial-state preparation for ground-starongly correlated systems.
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BibTeX
@misc{watanabe2026lowdepth,
title = {{Low-Depth Initial-State Preparation for Ground-State Energy Estimation of Two-Dimensional Strongly Correlated Systems}},
author = {Ryo Watanabe and Keisuke Fujii},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15764},
eprint = {2609.15764},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15764},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Low-Depth Initial-State Preparation for Ground-State Energy Estimation of Two-Dimensional Strongly Correlated Systems
AU - Ryo Watanabe
AU - Keisuke Fujii
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.15764
UR - https://arxiv.org/abs/2609.15764
AB - Quantum algorithms for ground-state energy estimation require initial states with non-negligible fidelity to the ground state. Guided by classical simulations, we design shallow circuits for the two-dimensional half-filled Hubbard model by first preparing an approximate Heisenberg ground state and then applying charge-fluctuation gates derived directly from the Schrieffer-Wolff (SW) generator. For the Heisenberg model, we demonstrate effective parameter transfer from a 4×4 lattice to lattices up to 10×10 without further optimization. We obtain promising lower bounds on the ground-state fidelity using tensor-network simulations, variational Monte Carlo reference states, and estimates of the ground-state energy and singlet gap. Exact 4×4 calculations show that the SW gates substantially improve the Hubbard ground-state fidelity of the embedded Heisenberg state. The successful Heisenberg parameter transfer supports the use of these small-lattice results to design shallow Hubbard circuits on larger lattices beyond the reach of classical simulations. For a 10×10 lattice, the estimated preparation cost is on the order of 10^5 T gates, including Clifford+T synthesis, which is well within the megaquop regime. These results offer a route to low-cost initial-state preparation for ground-starongly correlated systems.
ER -