A quantum information retrieval approach to memory

We review our models of quantum associative memories that represent the “quantization” of fully coupled neural networks like the Hopfield model. The idea is to replace the classical irreversible attractor dynamics driven by an Ising model with pattern-dependent weights by the reversible rotation of an input quantum state onto an output quantum state consisting of a linear superpo- sition with probability amplitudes peaked on the stored pattern closest to the input in Hamming distance, resulting in a high probability of measuring a memory pattern very similar to the input. The unitary operator implementing this transformation can be formulated as a sequence of one- qubit and two-qubit elementary quantum gates and is thus the exponential of an ordered quantum Ising model with sequential operations and with pattern-dependent interactions, exactly as in the classical case. Probabilistic quantum memories, that make use of postselection of the measurement result of control qubits, overcom...

Experiments in cognitive science and decision theory show that the ways in which people combine concepts and make decisions cannot be described by classical logic and probability theory. This has serious implications for applied disciplines such as information retrieval, artificial intelligence and robotics. Inspired by a mathematical formalism that generalizes quantum mechanics the authors have constructed a contextual framework for both concept representation and decision making, together with quantum models that are in strong alignment with experimental data. The results can be interpreted by assuming the existence in human thought of a double-layered structure, a 'classical logical thought' and a 'quantum conceptual thought', the latter being responsible of the above paradoxes and nonclassical effects. The presence of a quantum structure in cognition is relevant, for it shows that quantum mechanics provides not only a useful modeling tool for experimental data but also supplies a structural model for human and artificial thought processes. This approach has strong connections with theories formalizing meaning, such as semantic analysis, and has also a deep impact on computer science, information retrieval and artificial intelligence. More specifically, the links with information retrieval are discussed in this paper.

The emerging research area of a quantum-inspired computing has been applied to various¯eld such as computational intelligence, and showed its superior abilities. However, most existing researches are focused on theoretical simulations, and have not been implemented in systems under practical environment. For human-robot communication, associative memory becomes essential for multi-modal communication. However, it always su®ers from low memory capacity and recall reliability. In this paper, we propose a quantum-inspired bidirectional associative memory with fuzzy inference. We show that fuzzy inference satis¯es basic postulates of quantum mechanics, but also learning algorithm for weight matrix in associative memory. In addition, we construct a communication system with robot partner using proposed model. This is the¯rst successful attempt to overcome conventional problems in associative memory model with a robot application.

Theoretical Computer Science, 2018

In recent years, the mathematical structure of quantum theory has been successfully employed in different areas beyond physics, such as biology, economics, psychology and computer science. This special issue aims precisely at setting a landmark with respect to the benefits in applying and cross-fertilizing quantum approaches in computer science, therefore opening the quantum approach to the general community of computer, information, and data scientists. In particular, we aim at presenting articles of a theoretical nature, that are on the one hand useful to illustrate the potential of using quantum structures in areas such as natural language processing and semantics, and on the other hand to propose applications of the genuine quantum features such as contextuality, interference, emergence, and others, to tackle important challenges in modern computer science such as the multi-modal nature of data, the user interaction context and the theoretically-sound fusion of data coming from different sources. Historically, the application of quantum structures to computer science took off in 2004. Indeed, the book of C.J. "Keith" van Rijsbergen, renowned scientist in Information Retrieval (IR), entitled 'The Geometry of Information Retrieval' [1], appeared that year and in fact introduced the mathematical lattice and algebra structure of the quantum formalism to the domain of IR, in conjunction with probability and abstract vectors spaces, which have always been the backbone of IR models. Since the 1970s, C.J. van Rijsbergen did extensive work on non-classical logics, building on the research work of Suppes [2-4] and Hardegree [5,6], which naturally led him into the work by John von Neumann on non-classical logic for quantum mechanics [7], and the exploration of these logics in Hilbert spaces, emphasizing the work of Gleason and his famous theorem [8]. In 2003, van Rijsbergen wrote his book on the geometry of IR, which includes an extensive annotated bibliography [1]. In the same year, independently from van Rijsbergen, and inspired directly by the vector space structure of Hilbert spaces, Diederik Aerts and Marek Czachor published the article entitled 'Quantum aspects of semantic analysis and symbolic artificial intelligence' [9], where they showed that semantic space models, with their use of real vector spaces, possess striking similarities with the complex Hilbert spaces used in quantum theory. Diederik Aerts worked extensively, as a physicist, on quantum logic and probability in the foundations of quantum theory, during the eighties [10,11]. His hidden-measurement interpretation of quantum probability [11] lead him to propose, in 1995, a quantum model for human decision making [12] and in 2002, in collaboration with Liane Gabora, a quantum model for the mechanism of formation of concept combinations in human languages [13]. The similarity of this work, formulated in a complex Hilbert space, with the work that models terms and documents by vectors in a 'semantic vector space', more particularly in Latent Semantic Analysis [14,15], gave rise to the comparison between quantum theory and semantic spaces, in the aforementioned article [9]. Also in the same year, Dominic Widdows developed the first explicit geometric model with his quantum logic of word meanings and concrete explorations into the lattice structure of vector subspaces, published in his book entitled 'Geometry and Meaning' [16]. Dominic Widdows worked as a mathematician in the domain of computational linguistics and was also inspired by quantum logic and its intimate relationship with geometry when he investigated how this could be applied in linguistics. In the approach to IR that he developed, he replaced the negation relation with the orthogonality relation, as it appears in quantum logic, working out simple examples using search engines, demonstrating their superiority with respect to standard search engines founded on Boolean operations [17,18]. After these initial steps, a proper research domain on quantum structures in computer science came into being (developing in parallel with the use of quantum structures in psychology, referred to as 'quantum cognition') and certainly the initiative of Peter Bruza to begin, starting from 2007, a yearly conference called 'Quantum Interaction' has played an important role in the flourishing of the domain. The initiative of Massimo Melucci to bring together some of the major