Quantum image processing?

Abstract

This paper presents a number of problems concerning the practical (real) implementation of the techniques known as Quantum Image Processing. The most serious problem is the recovery of the outcomes after the quantum measurement, which will be demonstrated in this work that is equivalent to a noise measurement, and it is not considered in the literature on the subject. It is noteworthy that this is due to several factors: 1) a classical algorithm that uses Dirac's notation and then it is coded in MATLAB does not constitute a quantum algorithm, 2) the literature emphasizes the internal representation of the image but says nothing about the classical-to-quantum and quantum-to-classical interfaces and how these are affected by decoherence, 3) the literature does not mention how to implement in a practical way (at the laboratory) these proposals internal representations, 4) given that Quantum Image Processing works with generic qubits this requires measurements in all axes of the Bloch sphere, logically, and 5) among others. In return, the technique known as Quantum Boolean Image Processing is mentioned, which works with computational basis states (CBS), exclusively. This methodology allows us to avoid the problem of quantum measurement, which alters the results of the measured except in the case of CBS. Said so far is extended to quantum algorithms outside image processing too.Quantum computation and quantum information is the study of the information processing tasks that can be accomplished using quantum mechanical systems. Like many simple but profound ideas it was a long time before anybody thought of doing information processing using quantum mechanical systems [1].Quantum computation is the field that investigates the computational power and other properties of computers based on quantum-mechanical principles. An important objective is to find quantum algorithms that are significantly faster than any classical algorithm solving the same problem. The field started in the early 1980s with suggestions for analog quantum computers by Paul Benioff [2] and Richard Feynman [3,4], and reached more digital ground when in 1985 David Deutsch defined the universal quantum Turing machine [5]. The following years saw only sparse activity, notably the development of the first algorithms by Deutsch and Jozsa [6] and by Simon [7], and the development of quantum complexity theory by Bernstein and Vazirani [8]. However, interest in the field increased tremendously after Peter Shor's very surprising discovery of efficient quantum algorithms (or simulations on a quantum computer) for the problems of integer factorization and discrete logarithms in 1994 [9]. Quantum Information Processing (QuIn) -The main concepts related to Quantum InformationProcessing may be grouped in the next topics: quantum bit (qubit, which is the elemental quantum information unity), Bloch's Sphere (geometric environment for qubit representation), Hilbert's Space (which generalizes the notion of Euclidean space), Schrödinger's Equation (which is a partial d...

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