  The tradeoff between trainability and expressibility is a central challenge
faced by today's variational quantum computing. Recent studies indicate that
resolving this dilemma necessitates designing specific parametrized quantum
circuits (PQC) tailored for specific problems, which urgently needs a general
and efficient method to assess the learnability of PQCs regarding a given
target. In this Letter, we demonstrate a simple and efficient metric for
learnability by comparing the fluctuations of the given training landscape with
standard learnable landscapes. This metric shows surprising effectiveness in
predicting learnability as it unifies the effects of insufficient
expressibility, barren plateaus, bad local minima, and overparametrization.
Importantly, it does not require actual training and can be estimated
efficiently on classical computers via Clifford sampling. We conduct extensive
numerical experiments to validate its effectiveness regarding both physical and
random Hamiltonians. We also prove a compact lower bound for the metric in
locally scrambled circuits as analytical guidance. Our findings enable
efficient predictions of learnability, allowing fast selection of suitable PQCs
for a given problem without training, which can improve the efficiency of
variational quantum computing especially when access to quantum devices is
limited.
