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Bulletin of the Russian Academy of Sciences Physics

Applying Quantum Means to a Photon Contextual Query Using Bell Tests

S. N. Andrianov, Natalia S. Andrianova, Farid Mansurovich Ablayev, А. А. Калачев, Ю. Ю. Кочнева, A. V. Shkalikov

Published Dec 1, 2021• 0 citations
Publisher

Abstract

Abstract The possibilities of generating a contextual query using the quantum Hyperspace Analogue to Language (HAL) model are analyzed. An approach to establishing a semantic connection between words in texts is developed using the generally accepted basic formula for Bell’s parameter as a parameter of connection. A modification of the approach that allows determination of hyponymic isotopy and thus establish a semantic connection between the concepts is proposed. Prospects for using the quantum states of light to implement this approach are discussed.

DOI
10.3103/s1062873821120030

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Abstract The possibilities of generating a contextual query using the quantum Hyperspace Analogue to Language (HAL) model are analyzed. An approach to establishing a semantic connection between words in texts is developed using the generally accepted basic formula for Bell’s parameter as a parameter of connection. A modification of the approach that allows determination of hyponymic isotopy and thus establish a semantic connection between the concepts is proposed. Prospects for using the quantum states of light to implement this approach are discussed.
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Quantum-inspired algorithms represent an important direction in modern software information technologies that use heuristic methods and approaches of quantum science. This work presents a quantum approach for document search, retrieval, and ranking based on the Bell-like test, which is well-known in quantum physics. We propose quantum probability theory in the hyperspace analog to language (HAL) framework exploiting a Hilbert space for word and document vector specification. The quantum approach allows for accounting for specific user preferences in different contexts. To verify the algorithm proposed, we use a dataset of synthetic advertising text documents from travel agencies generated by the OpenAI GPT-4 model. We show that the "entanglement" in two-word document search and retrieval can be recognized as the frequent occurrence of two words in incompatible query contexts. We have found that the user preferences and word ordering in the query play a significant role in relatively small sizes of the HAL window. The comparison with the cosine similarity metrics demonstrates the key advantages of our approach based on the user-enforced contextual and semantic relationships between words and not just their superficial occurrence in texts. Our approach to retrieving and ranking documents allows for the creation of new information search engines that require no resource-intensive deep machine learning algorithms.
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A lexeme can be represented as a vector in a Hilbert space. Each element of the vector represents the weight of a semantic relation with a second vector: the context of a second lexeme. Two query operators are defined in a way that they attribute the value +1 to the component of the state that corresponds to the word meaning we are interested in, and -1 in the orthogonal direction. Entangled states have been used to detect semantic relationships in Information Retrieval (IR). In particular, since the first operator corresponds to negation and the conditional gate corresponds to an implication in classical logic, they can represent two basic semantic relationships : hyponymy (e.g. genus-species) and antonymy (e.g. masculine-feminine). In fact, according to Semantics, if A and B are antonymic terms, then A is an hyponym of (i.e. implies) not-B as in the Gremias semiotic square. We underline how the relations of a given semantic universe, and the corresponding result of our operators, depends only on the considered text. Among others, this analogy suggests the application of quantum-based models to language and IR.
Tests are essential in Information Retrieval (IR), in order to evaluate the effectiveness of a query. Tests intended to exhibit the sense of words in con-text were undertaken and linked with Quantum Mechanics (QM). Poll tests were undertaken on heterogeneous media such as music and polysemy in foreign languages. Interference effects are shown in the results. Bell inequality was used leading to a significant spread in the results of the poll tests but without violating the classical limit. Then an automatic pertinence measure tool on texts has been developed using the HAL algorithm using an orthonormal vector decomposition model. In this case the spread in the values can lead to the violation of the Bell inequality even beyond Cirel'son bound.