Speaker
Description
Data encoding plays a central role in Quantum Machine Learning, determining the class of functions that a quantum model can represent. While Fourier-based analyses have provided valuable insights into angle-encoded models, the representational biases induced by commonly used quantum image encodings remain poorly understood.
In this work, we investigate the functional structure induced by common embeddings used in Quantum Computer Vision through the lens of spectral and functional analysis. Building on recent advances in the characterization of parameterized quantum models, we develop a framework that enables the systematic study of image-oriented encoding strategies, including regular qubit-efficient and image-specific approaches. This perspective allows us to analyze the structural constraints, inductive biases, and representational capabilities imposed by different embeddings independently of downstream optimization procedures.
Using a combination of analytical and empirical techniques, we compare several representative quantum image encodings, including established approaches such as FRQI and Hamiltonian image encoding, together with qubit-efficient embedding strategies. To characterize their induced function spaces, we introduce quantitative descriptors that capture aspects such as the effective dimensionality, controllability, and geometric structure of the accessible representations. Our analysis reveals substantial differences in the effective accessibility and organization of these function spaces, uncovering missing spectral components, geometric constraints, controllability hierarchies, and expressive bottlenecks associated with different encoding strategies.
These results provide new insight into the foundations of Quantum Computer Vision and establish functional analysis as a practical framework for understanding, comparing and designing quantum learning architectures for high-dimensional visual data.
| Topic | Encoding and processing of data in quantum systems |
|---|---|
| Additional Topic | Theoretical foundations of quantum learning |