The variational quantum eigensolver (VQE) algorithm is particularly well suited for estimating the ground-state energies of molecular systems in the noisy intermediate-scale quantum era. However, the most popular unitary coupled-cluster ansatz requires a large number of qubits and gates that are constrained by short coherence time and hardware noise. In this study, we present schemes for estimating the ground-state energies of the molecules ${\mathrm{H}}_2$ and LiH using the VQE algorithm in a trapped-ion system with a high-dimensional method. It is shown that significantly fewer quantum gates are required to achieve the same result as the qubit-based model. High-dimensional quantum simulation can make more use of quantum resources. Utilizing the recently developed fixed-input-state method, the depth of the circuits can be further reduced. Only one and three single-qubit gates are required for the simulation of the ${\mathrm{H}}_2$ and LiH molecules, respectively. Finally, combined with the zero-noise extrapolation technique to mitigate the effects of noise, the accuracy of the results is significantly improved. These findings indicate that using a fixed input state in high-dimensional quantum simulations can enhance the performance of near-term quantum computing hardware.

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• Quantum algorithms
• Quantum circuits
• Quantum simulation