Towards structure-preserving quantum encodings
This work addresses the challenge of efficiently uploading classical data to quantum computers for machine learning, offering a foundational approach that could impact quantum computing researchers, though it is incremental as it builds on existing symmetry-based methods.
The authors tackled the problem of designing quantum encodings for machine learning by proposing category theory as a framework to preserve dataset and task structures, resulting in a method that enables precise mathematical questions for encoding design across various applications like geometric quantum learning and topological data analysis.
Harnessing the potential computational advantage of quantum computers for machine learning tasks relies on the uploading of classical data onto quantum computers through what are commonly referred to as quantum encodings. The choice of such encodings may vary substantially from one task to another, and there exist only a few cases where structure has provided insight into their design and implementation, such as symmetry in geometric quantum learning. Here, we propose the perspective that category theory offers a natural mathematical framework for analyzing encodings that respect structure inherent in datasets and learning tasks. We illustrate this with pedagogical examples, which include geometric quantum machine learning, quantum metric learning, topological data analysis, and more. Moreover, our perspective provides a language in which to ask meaningful and mathematically precise questions for the design of quantum encodings and circuits for quantum machine learning tasks.