Quantum theory (QT) is being applied to domains such as artificial intelligence, human language, cognition, information retrieval, biology, political science, economics, organizations, and social interaction. After highly successful meetings at Stanford (QI-2007) and Oxford (QI-2008), QI-2009 brought together researchers interested in advancing and applying the methods and structures of QT to these and other domains outside of quantum physics:-Advancement of theory and experimentation for applying quantum theory to non-quantum domains -Use of quantum algorithms to address, or to more efficiently solve, problems in non-quantum domains (including contrasts between classical vs. quantum methods) -Practical applications to quantum domains, such as implementation of AI, or information retrieval (IR) techniquesThe proceedings include 21 long papers and 3 position papers. Each paper was thoroughly reviewed by at least two members of the international Program Committee. The proceedings highlight the cross-disciplinary nature of quantum interaction with papers covering topics such as computation, cognition, decision theory, information retrieval, information systems, social interaction, computational linguistics and finance. In addition, we were honored to receive a keynote presentation by Dagmar Bruss (Institute for Theoretical Physics, University of Düsseldorf). We gratefully acknowledge the support of Earl Research and Kirsty Kitto for helping prepare these proceedings.