Re-uploading quantum data: A universal function approximator for quantum inputs
This work provides a qubit-efficient and expressive approach for designing quantum machine learning models that operate directly on quantum data, addressing a specific bottleneck in the field.
The authors tackled the problem of extending quantum data re-uploading to quantum inputs, which was underexplored due to the inaccessibility of quantum state information in classical form, and they proposed an architecture that approximates any bounded continuous function using only one ancilla qubit and single-qubit measurements.
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. 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 qubit-efficient and expressive approach to designing quantum machine learning models that operate directly on quantum data.