Re-uploading quantum data: a universal function approximator for quantum inputs

Hyunho Cha; Daniel K. Park; Jungwoo Lee

doi:10.22331/q-2026-10-29-2256

Re-uploading quantum data: a universal function approximator for quantum inputs

Hyunho Cha¹, Daniel K. Park^2,3,4, and Jungwoo Lee¹

¹NextQuantum and Department of Electrical and Computer Engineering, Seoul National University, Seoul 08826, Republic of Korea
²Department of Statistics and Data Science, Yonsei University, Seoul 03722, Republic of Korea
³Department of Applied Statistics, Yonsei University, Seoul 03722, Republic of Korea
⁴Department of Quantum Information, Yonsei University, Incheon 21983, Republic of Korea

Published:	2026-10-29, volume 10, page 2256
Editor:	Diego García-Martín
Eprint:	arXiv:2509.18530v7
Doi:	https://doi.org/10.22331/q-2026-10-29-2256
Citation:	Quantum 10, 2256 (2026).

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Abstract

Quantum data re-uploading has proved powerful for classical inputs, where repeatedly encoding features into a small circuit yields universal function approximation. Extending this idea to quantum inputs remains underexplored, as the information contained in a quantum state is not directly accessible in classical form. We propose and analyze a quantum data re-uploading architecture in which a qubit interacts sequentially with fresh copies of an arbitrary input state. The circuit can approximate any bounded continuous function using only one ancilla qubit and single-qubit measurements, provided that sufficiently many copies of the input state and, in general, sufficiently many layers are available. By alternating entangling unitaries with mid-circuit resets of the input register, the architecture realizes a discrete cascade of completely positive and trace-preserving maps, analogous to collision models in open quantum system dynamics. Our framework provides a space-efficient and expressive approach to designing quantum machine learning models that operate directly on quantum data.

Popular summary

In quantum computing, scientists often want to process quantum information via machine learning models, just as classical computers learn from classical data. A clever technique called "data re-uploading" has proven powerful for handling classical inputs. In this paper, we extend this concept to a new frontier by exploring what happens when the input data itself is a quantum state. We prove that re-uploading quantum data allows quantum circuits to learn any function. This offers a hardware-efficient blueprint for building quantum machine learning systems capable of analyzing quantum data.

► BibTeX data

@article{Cha2026reuploadingquantum,
  doi = {10.22331/q-2026-10-29-2256},
  url = {https://doi.org/10.22331/q-2026-10-29-2256},
  title = {Re-uploading quantum data: a universal function approximator for quantum inputs},
  author = {Cha, Hyunho and Park, Daniel K. and Lee, Jungwoo},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {2256},
  month = oct,
  year = {2026}
}

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