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

2025-09-22

AI Summary

Quantum machine learning faces significant challenges in modeling directly from quantum input data. Method: We propose the first quantum data re-uploading architecture specifically designed for quantum inputs, requiring only a single ancillary qubit. The architecture implements a discrete cascaded mapping via alternating entanglement, mid-circuit reset, single-qubit measurement, and repeated encoding—inspired by collision models of open quantum systems—to realize efficient, fully CPTP (completely positive trace-preserving) operations. Contribution/Results: We theoretically prove that this architecture can uniformly approximate any bounded continuous quantum function. It achieves both resource efficiency—using only a constant number of ancillary qubits—and strong expressive power. This work marks the first extension of the data re-uploading paradigm to quantum-native inputs, establishing a scalable, hardware-efficient modeling framework for processing quantum data natively.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Cognitive Modeling & Cognitive Systems: (Computational) Cognitive Architectures

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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. 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.

Problem

• Extending quantum data re-uploading to handle quantum state inputs
• Approximating continuous functions using quantum inputs with minimal resources
• Developing qubit-efficient quantum machine learning models for quantum data

Innovation

• Quantum data re-uploading with sequential qubit interactions
• Approximates functions using one ancilla and measurements
• Alternates entangling unitaries with mid-circuit resets