https://doi.org/10.1140/epjqt/s40507-026-00473-3
Research
Fast quantum amplitude encoding of typical classical data
1
Institute of Software Technology, German Aerospace Center (DLR), Sankt Augustin, Germany
2
University of Cologne, Cologne, Germany
3
Microwaves and Radar Institute, German Aerospace Center (DLR), Oberpfaffenhofen, Germany
a
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Received:
7
April
2025
Accepted:
25
January
2026
Published online:
5
February
2026
Abstract
We present an improved version of a quantum amplitude encoding scheme that encodes the N entries of a unit classical vector 
into the amplitudes of a quantum state. Our approach has a quadratic speed-up with respect to the original one. We also describe several generalizations, including to complex entries of the input vector and a parameter M that determines the parallelization. The number of qubits required for the state preparation scales as 
. The runtime, which depends on the data density ρ and on the parallelization paramater M, scales as 
, which in the most parallel version (
) is always less or equal than 
.
By analysing the data density, we prove that the average runtime is 
for input vectors that are uniformly sampled on the N-sphere. We present numerical evidence that this favourable runtime behaviour also holds for real-world data, such as radar satellite images. This is promising as it allows for an input-to-output advantage of the quantum Fourier transform.
Key words: State preparation / Amplitude encoding / Satellite data
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjqt/s40507-026-00473-3.
© The Author(s) 2026
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