Low-Depth Initial-State Preparation for Ground-State Energy Estimation of Two-Dimensional Strongly Correlated Systems

• URL: http://arxiv.org/abs/2609.15764v2
• Date: Tue, 15 Sep 2026 03:31:26 GMT
• Title: Low-Depth Initial-State Preparation for Ground-State Energy Estimation of Two-Dimensional Strongly Correlated Systems
• Abstract summary: Quantum algorithms for ground-state energy estimation require initial states with non-negligible fidelity to the ground state.<n>We design shallow circuits for the two-dimensional half-filled Hubbard model by first preparing an approximate Heisenberg ground state.<n>For a $10times10$ lattice, the estimated preparation cost is on the order of $105$ $T$ gates, including Clifford+$T$ synthesis, which is well within the megaquop regime.
• Score: 3.5375275309480094
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $4\times4$ lattice to lattices up to $10\times10$ 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 $4\times4$ 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 $10\times10$ 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.

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