Pattern Recognition in Quantum Computation

Federico Holik, Giuseppe Sergioli, Héctor Freytes +1 more

We present a generalization of the problem of pattern recognition to arbitrary probabilistic models. This version deals with the problem of recognizing an individual pattern among a family of different species or classes of objects which obey probabilistic laws which do not comply with Kolmogorov's axioms. We show that such a scenario accommodates many important examples, and in particular, we provide a rigorous definition of the classical and the quantum pattern recognition problems, respectively. Our framework allows for the introduction of non-trivial correlations (as entanglement or discord) between the different species involved, opening the door to a new way of harnessing these physical resources for solving pattern recognition problems. Finally, we present some examples and discuss the computational complexity of the quantum pattern recognition problem, showing that the most important quantum computation algorithms can be described as non-Kolmogorovian pattern recognition problems.

Davide Pastorello

Carlo A. Trugenberger

Konstantinos P. Prousalis, Nikos Konofaos

A dot matrix approach for sequence alignment is combined with a known quantum multi-pattern recognition method in order to improve the problem of sequence alignment. This dot matrix technique allows the application of some quantum computing principles on the pattern recognition problems like those used in the Grover's algorithm. When the recognized patterns exceed the limit of the 1/3 of the overall patterns, the multi-pattern recognition is accomplished simultaneously with the probability of 100%. The contribution concerns the way that the adopted quantum pattern recognition algorithm is applied speeding up the sequence alignment process. An example application demonstrates the effectiveness of the proposed method. String alignments isn't an essential task only in bioinformatics, but also in calculating the edit distance cost between strings in a natural language or in financial data.

Wei He

Music, as a form of art characterized by its complexity and diversity, holds significant cultural and emotional value for humanity. Piano music, being a prominent representative, demands efficient and precise recognition and analysis of its intricate harmonic, melodic, and rhythmic patterns. Traditional computational approaches often face limitations in handling such intricate patterns. However, quantum computing, emerging as a novel computational paradigm, presents new avenues for addressing these challenges. This paper aims to explore the potentials and methodologies of quantum computing in the realm of music, particularly focusing on the intricate pattern recognition of piano music. We introduce the fundamental principles and advantages of quantum computing. Subsequently, we delve into the application of quantum algorithms in piano music analysis, specifically addressing the recognition of harmonic structures and rhythmic patterns. Finally, we envision the future trends and challenges of quantum computing technology in the realm of music. Through this research endeavor, we aim to gain deeper insights into the potential of quantum computing in the field of music and offer novel ideas and methodologies for future investigations.

Péter Wittek