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.
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.
Looking upon every encoding state of quantum information systems as a quantum information pattern, A kind of pattern-distance between different patterns as a measurement of comparability of quantum information patterns is defined, and two kinds of recognition algorithms based on pattern-distance for quantum information are proposed. They can respectively recognize quantum information with known objective pattern and unknown objective pattern. In the two algorithms, the phases and occurrence probabilities of different eigenpatterns of quantum information are sufficiently considered. Two examples demonstrate the feasibility and effectiveness of the two recognition methods. These algorithms point out a new and important path for applications of quantum information and pattern recognition.
Quantum Machine Learning (QML) represents a paradigm shift in computational approaches, offering the potential to surpass classical machine learning algorithms in complex data analysis. This paper investigates the application of QML to the identification of non-linear patterns, focusing on leveraging quantum states to uncover hidden correlations and anomalies within datasets. We propose a novel framework that utilizes quantum entanglement and superposition to enhance pattern recognition capabilities. The core mechanism centers on harnessing the inherent properties of quantum states to provide a fundamentally different approach to data analysis, specifically designed to address the challenges posed by non-linear data. This research explores the potential of quantum algorithms to improve pattern detection and anomaly detection, and investigates the influence of quantum characteristics on pattern recognition processes. The paper will detail the implementation of a quantum model for pattern recognition, discuss its performance compared to classical models, and explore the fundamental principles underpinning its effectiveness. We argue that this work introduces a new perspective on pattern recognition, offering the possibility of enhanced accuracy, robustness, and the ability to identify subtle patterns within complex datasets. The core claim posits that quantum machine learning can effectively identify and interpret non-linear patterns, offering significant advantages over conventional methods.
Summary form only given. In quantum cryptography, non-cloning properties of quantum states are exploited to achieve quantum security. At the same time, typically one optical mode is used, for instance that of a single-mode optical fiber, effectively reducing the problem to a one-dimensional system. Only recently have researchers begun to exploit higher dimensions for quantum cryptography [1]. High dimensional spaces appear naturally in imaging applications.We here experimentally investigate the question if it is possible to recognize an arbitrary pattern in a physical object using much fewer photons than the complexity of the pattern. Theoretically it has already been proposed to use a quantum computer for pattern recognition and that this can be achieved with very few photons [2]. To avoid using a quantum computer, we exploit a spatial light modulator, which can map a single incoming optical mode on thousands outgoing optical modes in a programmable way. In this way, a weak light pulse containing only a few or even a single photon can be distributed over the high number of pixels of a complex 2-dimensional image. The inverse is just as feasible: a known complex pattern can be mapped onto a single mode. We use this principle to analyze the light from a physical object when illuminated with, e.g., a plane wave. After reflection of or transmission through the object under investigation, the response can be projected onto a single mode. The signal in that mode can be analyzed with the standard repertoire of quantum optical measurements, determining, e.g., the field amplitude, the intensity or the number of photons.We use coherent pulses of light which have mean photon numbers much smaller than the thousands of modes of the complex image. We introduce the parameter S=K/n as the ratio of the number of modes, K, of the response field pattern and the number of photons, n, that is used for the illumination. This measurement is in the quantum domain if S>>1. We read out objects with S=4, well in the quantum regime. The method can be extended by preshaping the illumination light, with applications in authentication of physical objects [3,4].
This paper presents a novel algorithm for identifying and modeling complex quantum systems by leveraging the unique properties of quantum entanglement. Traditional structure recognition methods often struggle with the intricacies of quantum systems, necessitating a more sophisticated approach. We propose a quantum-enhanced self-organizing structure recognition system based on the principles of quantum entanglement, enabling the identification and modeling of intricate structural patterns. The core of our algorithm involves the construction of quantum systems with self-organized structures, utilizing entanglement as a fundamental mechanism for pattern recognition and structural analysis. This approach offers a fundamentally different perspective on structure identification compared to classical methods, potentially unlocking new insights into the behavior of complex quantum systems. This work explores the theoretical foundations and preliminary experimental validation of this innovative method.
Quantum hypothesis testing is one of the most fundamental problems in quantum information theory, with crucial implications in areas like quantum sensing, where it has been used to prove quantum advantage in a series of binary photonic protocols, e.g., for target detection or memory cell readout. In this work, we generalize this theoretical model to the multipartite setting of barcode decoding and pattern recognition. We start by defining a digital image as an array or grid of pixels, each pixel corresponding to an ensemble of quantum channels. Specializing each pixel to a black and white alphabet, we naturally define an optical model of a barcode. In this scenario, we show that the use of quantum entangled sources, combined with suitable measurements and data processing, greatly outperforms classical coherent-state strategies for the tasks of barcode data decoding and classification of black and white patterns. Moreover, introducing relevant bounds, we show that the problem of pattern recognition is significantly simpler than barcode decoding, as long as the minimum Hamming distance between images from different classes is large enough. Finally, we theoretically demonstrate the advantage of using quantum sensors for pattern recognition with the nearest-neighbor classifier, a supervised learning algorithm, and numerically verify this prediction for handwritten digit classification.
This paper presents a novel approach to pattern recognition centered around the application of quantum entanglement to significantly enhance the accuracy and speed of identifying subtle patterns. Traditional pattern recognition methods often struggle with complex datasets and require extensive computational resources. We propose a system that utilizes a quantum-inspired 'state vector' to capture intricate patterns, offering a potential paradigm shift in this field. The core mechanism involves establishing entanglement between quantum systems, which allows for a unique level of correlation and information processing, ultimately leading to improved pattern identification capabilities. This work explores the theoretical foundations and preliminary experimental validation of this approach, aiming to demonstrate substantial improvements over existing techniques.