  Though there has been substantial progress in developing quantum algorithms
to study classical datasets, the cost of simply \textit{loading} classical data
is an obstacle to quantum advantage. When the amplitude encoding is used,
loading an arbitrary classical vector requires up to exponential circuit depths
with respect to the number of qubits. Here, we address this ``input problem''
with two contributions. First, we introduce a circuit compilation method based
on tensor network (TN) theory. Our method -- AMLET (Automatic Multi-layer
Loader Exploiting TNs) -- proceeds via careful construction of a specific TN
topology and can be tailored to arbitrary circuit depths. Second, we perform
numerical experiments on real-world classical data from four distinct areas:
finance, images, fluid mechanics, and proteins. To the best of our knowledge,
this is the broadest numerical analysis to date of loading classical data into
a quantum computer. The required circuit depths are often several orders of
magnitude lower than the exponentially-scaling general loading algorithm would
require. Besides introducing a more efficient loading algorithm, this work
demonstrates that many classical datasets are loadable in depths that are much
shorter than previously expected, which has positive implications for speeding
up classical workloads on quantum computers.
