Re-uploading quantum data: a universal function approximator for quantum inputs
4 affiliations
- 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
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.
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BibTeX
@article{cha2026reuploading,
title = {{Re-uploading quantum data: a universal function approximator for quantum inputs}},
author = {Hyunho Cha and Daniel K. Park and Jungwoo Lee},
journal = {Quantum},
year = {2026},
month = oct,
doi = {10.22331/q-2026-10-29-2256},
url = {https://quantum-journal.org/papers/q-2026-10-29-2256/},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Re-uploading quantum data: a universal function approximator for quantum inputs
AU - Hyunho Cha
AU - Daniel K. Park
AU - Jungwoo Lee
PY - 2026
DA - 2026/10/29
JO - Quantum
DO - 10.22331/q-2026-10-29-2256
UR - https://quantum-journal.org/papers/q-2026-10-29-2256/
AB - 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.
SN - 2521-327X
ER -