Quantinuum, a UK-based quantum computing company, has developed a new modeling framework for structured concepts using quantum theory. The team, including Sean Tull, Razin A. Shaikh, Sara Sabrina Zemljiˇc, and Stephen Clark, used category theory to formalize their framework. The model can learn concepts from data, both classically and quantum-inspired. The researchers used string diagrams to describe quantum processes, which they claim helps clarify their approach. The model builds on Gårdenfors’ framework of conceptual spaces, where cognition is modeled geometrically. The team used a hybrid classical-quantum network to perform concept classification.
Conceptual Spaces and Quantum Concepts: A New Modelling Framework
This article introduces a new modeling framework for structured concepts, using a category-theoretic generalization of conceptual spaces. The authors demonstrate how these conceptual representations can be learned automatically from data, using two different instantiations: one classical and one quantum. The work contributes a thorough category-theoretic formalization of the framework, which the authors argue helps clarify some of the most important features of their approach.
Building on Gärdenfors’ Conceptual Spaces
The authors build on Gärdenfors’ classical framework of conceptual spaces, where cognition is modelled geometrically through the use of convex spaces. These spaces are then factorised in terms of simpler spaces called domains. The authors show how concepts from the domains of shape, colour, size, and position can be learned from images of simple shapes. In the classical implementation, concepts are represented as Gaussians, while in the quantum one, they are represented as quantum effects.
Classical and Quantum Implementations
In the classical case, the authors develop a new model inspired by the β-VAE model of concepts, but designed to be more closely connected with language. This allows the names of concepts to form part of the graphical model. In the quantum case, concepts are learned by a hybrid classical-quantum network trained to perform concept classification. The classical image processing is carried out by a convolutional neural network, while the quantum representations are produced by a parameterised quantum circuit.
Quantum Models of Concepts
The authors also consider whether their quantum models of concepts can be considered conceptual spaces in the Gärdenfors sense. They argue that the formalism of quantum theory provides an alternative mathematical structure to the convex structure of conceptual spaces. This structure has features well-suited to modeling concepts, such as entanglement for capturing correlations and partial orders for capturing conceptual hierarchies.
Future Work
The authors acknowledge that further work is needed to demonstrate that the framework can be applied to data from a psychology lab and to agents acting in virtual environments. They also clarify that they are not claiming the existence of quantum processes in the brain but rather that some cognitive processes can be effectively modeled at an abstract level using quantum formalism.
“From Conceptual Spaces to Quantum Concepts: Formalising and Learning Structured Conceptual Models“.
