On Quantum Context-Free Grammars
Merina Aruja, Lisa Mathew, Jayakrishna Vijayakumar
TL;DR
This paper establishes necessary and sufficient unitary conditions for the well-formedness of quantum context-free grammars, addressing the probability normalization issue in quantum grammar derivations.
Contribution
It introduces a formal set of conditions ensuring the proper probabilistic interpretation of quantum context-free grammars, advancing theoretical understanding.
Findings
Derived conditions guarantee well-formedness of QCFGs
Ensures probabilities of derived words do not exceed one
Provides a foundation for future quantum language processing
Abstract
Quantum computing is a relatively new field of computing, which utilises the fundamental concepts of quantum mechanics to process data. The seminal paper of Moore et al. [2000] introduced quantum grammars wherein a set of amplitudes was attached to each production. However they did not study the final probability of the derived word. Aruja et al. [2025] considered conditions for the well-formedness of quantum context-free grammars (QCFGs), in order to ensure that the probabilty of the derived word does not exceed one. In this paper we propose certain necessary and sufficient conditions (also known as unitary conditions) for well-formedness of QCFGs
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Taxonomy
TopicsDNA and Biological Computing · Quantum Computing Algorithms and Architecture · Machine Learning and Algorithms