to benchmark the performance of the e-QEB-ADAPT-VQE. We demonstrate that the e-QEB-ADAPT-VQE can construct highly accurate ansätze that require at least an order of magnitude fewer

CNOT

s than standard fixed UCC ansätze, such as the UCCSD and the GUCCSD.

DOI: 10.48550/arxiv.2106.06296

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_2

to benchmark the performance of the e-QEB-ADAPT-VQE. We demonstrate that the e-QEB-ADAPT-VQE can construct highly accurate ansätze that require at least an order of magnitude fewer

CNOT

s than standard fixed UCC ansätze, such as the UCCSD and the GUCCSD.

{\mathrm{BeH}}_{2}

to benchmark the performance of the e-QEB-ADAPT-VQE. We demonstrate that the e-QEB-ADAPT-VQE can construct highly accurate ans\"atze that require at least an order of magnitude fewer cnot gates than standard fixed unitary coupled-cluster ans\"atze, such as the UCCSD and the GUCCSD. We also show that the e-QEB-ADAPT-VQE is more successful in constructing ans\"atze for excited molecular states than other ADAPT-VQE protocols.

_2

to benchmark the performance of the IQEB-VQE. We demonstrate that the e-IQEB-VQE can construct highly accurate ansatze that require at least an order of magnitude fewer

CNOT

s than standard fixed UCC ansatze, such as the UCCSD and the GUCCSD.

_2

, LiH, and linear H

_4

across bond lengths spanning weakly and strongly correlated regimes. The adaptive derivative-assembled problem-tailored (ADAPT) ansatz construction yields compact circuits suitable for near-term hardware. We also implement a modified version of the MORE-ADAPT-VQE algorithm for comparison with TEPID-ADAPT. We find that both algorithms accurately reproduce excited-state spectra and potential energy curves within chemical accuracy for all the molecules and geometries studied. However, TEPID-ADAPT has the advantage of utilizing only a single, physically motivated hyperparameter (temperature) that controls the energy scale at which excited states are targeted, while MORE-ADAPT utilizes multiple hyperparameters whose optimal values depend sensitively on the target problem. These results demonstrate that combining adaptive ansatz construction with density-matrix-based formulations provides an efficient framework for excited-state quantum chemistry on near-term devices.

\mathrm{H}_{2}, \mathrm{H}_{3}^{+}, \text{LiH}, \text{HF}, \text{OH}^{-}, \mathrm{H}_{2} \mathrm{O}, \text{BH}_{3}, \text{CH}_{4}

, and

\text{NH}_{3}

. The approach utilizes the Unitary Coupled Cluster for Single and Double excitations (UCCSD) ansatz along with the Bravyi-Kitaev transformation for fermionic-to-qubit encoding. Quantum simulation outputs are systematically benchmarked against Full Configuration Interaction (FCI), a numerically exact traditional approach, and Unrestricted Hartree-Fock (UHF). The results establish a robust consistency of the VQE-obtained molecular ground state energies against standard FCI and UHF benchmarks. This research provides a critical benchmark, confirming that VQE has the capability for high-precision molecular simulations and playing the role of a pivotal stepping stone toward revolutionizing applications in drug discovery and materials science.