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Though there has been substantial progress in developing quantum algorithmsto study classical datasets, the cost of simply \textit{loading} classical datais an obstacle to quantum advantage. When the amplitude encoding is used,loading an arbitrary classical vector requires up to exponential circuit depthswith respect to the number of qubits. Here, we address this ``input problem''with two contributions. First, we introduce a circuit compilation method basedon tensor network (TN) theory. Our method -- AMLET (Automatic Multi-layerLoader Exploiting TNs) -- proceeds via careful construction of a specific TNtopology and can be tailored to arbitrary circuit depths. Second, we performnumerical 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 intoa quantum computer. The required circuit depths are often several orders ofmagnitude lower than the exponentially-scaling general loading algorithm wouldrequire. Besides introducing a more efficient loading algorithm, this workdemonstrates that many classical datasets are loadable in depths that are muchshorter than previously expected, which has positive implications for speedingup classical workloads on quantum computers.

Data is often loadable in short depth: Quantum circuits from tensor networks for finance, images, fluids, and proteins