# Context

Quantum probabilities are a formalism based on probability, logic and geometry – three ingredients used by most models of Information Access (IA). This led van Rijsbergen to suggest their use in IA [Rij04] because, unlike “standard” probabilities based on set theory, the “quantum” ones are based on vector spaces (Hilbert spaces) and are therefore more expressive.

This flexibility has begun to be exploited in order to tackle old and new challenges in IA, such as ad-hoc information retrieval (IR) [PF 10], contextual IR [Mel08], the problem of diversifying search results [ZA10], and summarization [PA 12]. In most of these studies, information objects are represented in a multi-dimensional, ie a set of vectors (probability density) or a subspace (event).

A crucial point for the success of quantum AI is to quickly find information objects. However, there is currently no effective technique for finding objects represented in Hilbert spaces directly, without first substantially reducing the number of objects considered with standard techniques. This limits the practical importance of such models and introduces a bias in the obtained results. It is necessary to design data structures and access methods adapted to the problem of quantum AI.

## Objectives

This is a six months long internship (starting March-October 2012) and will take place in the LIP6/CNRS laboratory in Paris, France. The monthly allowance is of 420 €.

The theoretical objective of the INDEQ project is to develop index structures for fast object retrieval, when objects are represented in Hilbert spaces. To achieve this goal, tree-based indices will be developed that estimate at each node what is the probability distribution of objects in each branch (given a quantum probability distribution).

The practical objective of this project is to design a solution to recommend information objects (e.g., movies) to a user, while avoiding exploring exhaustively all the candidate objects. To this end, the project aims at defining a new access method for selecting the object or objects that have the highest probability to match the user requesting a recommendation.

# Contact Information

Please email us if you are interested by this internship.

Benjamin Piwowarski – benjamin@bpiwowar.net

Hubert Naacke – hubert.naacke@lip6.fr

## Bibliography

[Mel08] Melucci, M. (2008). A basis for information retrieval in context. ACM Transactions On Information Systems, 26(3), 1–41.

[PF+10] Piwowarski, B., Frommholz, I., Lalmas, M., & van Rijsbergen, K. (2010). What can Quantum Theory bring to IR In J. Huang, N. Koudas, G. Jones, X. Wu, K. Collins-Thompson, & A. An (Eds.), CIKM’10: Proceedings of the nineteenth ACM conference on Conference on information and knowledge management.

[PA+12] Piwowarski, B., Amini, M.-R., & Lalmas, M. (2012). On using a Quantum Physics formalism for Multi-document Summarisation. Journal of the American Society for Information Science and Technology (accepted paper to be published).

[Rij04] van Rijsbergen, K. (2004). The Geometry of Information Retrieval. Cambridge University Press.

[ZA10] Zuccon, G., & Azzopardi, L. (2010). Using the Quantum Probability Ranking Principle to Rank Interdependent Documents. In C. Gurrin, Y. He, G. Kazai, U. Kruschwitz, S. Little, T. Roelleke, S. Rüger, et al. (Eds.), Advances in Information Retrieval (Vol. 5993, pp. 357–369). Springer.