  We study a hardware-efficient variational quantum algorithm ansatz tailored
for the trapped-ion quantum simulator, HEA-TI. We leverage programmable
single-qubit rotations and global spin-spin interactions among all ions,
reducing the dependence on resource-intensive two-qubit gates in conventional
gate-based methods. We apply HEA-TI to state engineering of cluster states and
analyze the scaling of required quantum resources. We also apply HEA-TI to
solve the ground state problem of chemical molecules $\mathrm{H_{2}}$,
$\mathrm{LiH}$ and $\mathrm{F_{2}}$. We numerically analyze the quantum
computing resources required to achieve chemical accuracy and examine the
performance under realistic experimental noise and statistical fluctuation. The
efficiency of this ansatz is shown to be comparable to other commonly used
variational ansatzes like UCCSD, with the advantage of substantially easier
implementation in the trapped-ion quantum simulator. This approach showcases
the hardware-efficient ansatz as a powerful tool for the application of the
near-term quantum computer.
