  Before the advent of fault-tolerant quantum computers, variational quantum
algorithms (VQAs) play a crucial role in noisy intermediate-scale quantum
(NISQ) machines. Conventionally, the optimization of VQAs predominantly relies
on manually designed optimizers. However, learning to optimize (L2O)
demonstrates impressive performance by training small neural networks to
replace handcrafted optimizers. In our work, we propose L2O-$g^{\dagger}$, a
$\textit{quantum-aware}$ learned optimizer that leverages the Fubini-Study
metric tensor ($g^{\dagger}$) and long short-term memory networks. We
theoretically derive the update equation inspired by the lookahead optimizer
and incorporate the quantum geometry of the optimization landscape in the
learned optimizer to balance fast convergence and generalization. Empirically,
we conduct comprehensive experiments across a range of VQA problems. Our
results demonstrate that L2O-$g^{\dagger}$ not only outperforms the current
SOTA hand-designed optimizer without any hyperparameter tuning but also shows
strong out-of-distribution generalization compared to previous L2O optimizers.
We achieve this by training L2O-$g^{\dagger}$ on just a single generic PQC
instance. Our novel $\textit{quantum-aware}$ learned optimizer,
L2O-$g^{\dagger}$, presents an advancement in addressing the challenges of
VQAs, making it a valuable tool in the NISQ era.
