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arXiv:quant-ph/9703010

Quantum Computations and Images Recognition

Alexander Yu. Vlasov

Published Mar 7, 1997• 44 citations
arXivHTMLPDF

Abstract

The using of quantum parallelism is often connected with consideration of quantum system with huge dimension of space of states. The n-qubit register can be described by complex vector with 2^n components (it belongs to n'th tensor power of qubit spaces). For example, for algorithm of factorization of numbers by quantum computer n can be about a few hundreds for some realistic applications for cryptography. The applications described further are used some other properties of quantum systems and they do not demand such huge number of states. The term "images recognition" is used here for some broad class of problems. For example, we have a set of some objects V_i and function of "likelihood": F(V,W) < F(V,V) = 1 If we have some "noisy" or "distorted" image W, we can say that recognition of W is V_i, if F(W,V_i) is near 1 for some V_i.

DOI
10.48550/arxiv.quant-ph/9703010

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The using of quantum parallelism is often connected with consideration of quantum system with huge dimension of space of states. The n-qubit register can be described by complex vector with 2^n components (it belongs to n'th tensor power of qubit spaces). For example, for algorithm of factorization of numbers by quantum computer n can be about a few hundreds for some realistic applications for cryptography. The applications described further are used some other properties of quantum systems and they do not demand such huge number of states. The term "images recognition" is used here for some broad class of problems. For example, we have a set of some objects V_i and function of "likelihood": F(V,W) < F(V,V) = 1 If we have some "noisy" or "distorted" image W, we can say that recognition of W is V_i, if F(W,V_i) is near 1 for some V_i.
A real quantum computer theoretically can perform a large number of parallel processing at the same time by superposition states and unitary transformations in a Hilbert space. We show that arbitrary unitary transformation can be operated in a framework of classic physics such as optics. We also show that, using the optics, the same processing as what quantum computing logic does can be implemented and that image recognition can be done by that logic. Although our system currently does not utilize entanglement physics like a quantum computer using electronic spin system, we can construct a high dimensional Hilbert space (e.g. one thousand dimension). We consider that our system may be another approach to realize quantum computing paradigm.
Quantum Image Processing has exploded in recent years with dozens of papers trying to take advantage of quantum parallelism in order to offer a better alternative to how current computers are dealing with digital images. The vast majority of these papers define or make use of quantum representations based on very large superposition states spanning as many terms as there are pixels in the image they try to represent. While such a representation may apparently offer an advantage in terms of space (number of qubits used) and speed of processing (due to quantum parallelism), it also harbors a fundamental flaw: only one pixel can be recovered from the quantum representation of the entire image, and even that one is obtained non-deterministically through a measurement operation applied on the superposition state. We investigate in detail this measurement bottleneck problem by looking at the number of copies of the quantum representation that are necessary in order to recover various fractions of the original image. The results clearly show that any potential advantage a quantum representation might bring with respect to a classical one is paid for dearly with the huge amount of resources (space and time) required by a quantum approach to image processing.
This article presents the most common image recognition algorithms implemented for a quantum neural network, consider them and draw a conclusion which algorithm is preferable to use in this or that case. Currently, there is a rapid increase in interest in quantum algorithms for pattern recognition, since the first quantum computers have already appeared. This is because the use of quantum algorithms since the advent of quantum computers has allowed an exponential increase in the speed of solving NP-complete problems. Paper decide the some problems of finding and creation of approaches for the functioning of quantum calculation processes and prototypes of quantum devices in the framework of quantum image processing. A method for storing and processing image components in quantum systems is proposed, which potentially will give a significant step toward in efficiency in comparison with existing classical ones and provide a solution to a number of complex problems.
Quantum image processing uses quantum computing, which implements the concepts of entanglement and superposition to increase efficiency, scalability, and revolutionary promise in demanding image processing ap plications. In this research paper, a comprehensive frame work for quantum image processing (QIP) is presented, which includes innovative quantum algorithms for pattern recognition, image improvement, and representation. The system presents advanced quantum encoding models for effective image data manipulation and storage. In addition, it discusses the quantum image-based algorithms that give better results than classical techniques in terms of speed and accuracy for image enhancement tasks such as edge recognition, contrast adjustment, and noise reduction. Researchers have developed quantum-based feature ex traction and classification methods for pattern recognition, which demonstrate enhanced scalability and accuracy for complex visual data. It has various applications in satellite data processing, secure visual data transmission, and medical imaging highlighted by simulations and theoretical analysis that confirm the proposed approaches.
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The goal of machine learning (ML) is to develop models that automatically learn from the past without being explicitly programmed. ML has numerous applications, such as pattern recognition, forecasting upcoming trends, and judgement. It can handle massive amounts of huge vectors and tensors representing multidimensional data. To handle these processes on traditional computers, enormous time and computational resources are required. Unlike traditional computers, which use binary bits to compute, quantum computers (Q.C.) use qubits, which can simultaneously hold 0 and 1 combinations through superposition and entanglement. This makes Q.Cs an excellent choice for implementing ML algorithms because they are skilled at handling and post-processing large tensors. Although many of the models used for ML on quantum computers are based on concepts from their classical computing counterparts, the use of quantum computers has made them the better of the two. This paper assess the speed and complexity benefits of using quantum computers and gives a general overview of the state of knowledge regarding the use of ML on Q.C.