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The Geometry Of Quantum Learning
, 2003
"... Concept learning provides a natural framework in which to place the problems solved by the quantum algorithms of BernsteinVazirani and Grover. By combining the tools used in these algorithmsquantum fast transforms and amplitude amplificationwith a novel (in this context) toola solution met ..."
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Concept learning provides a natural framework in which to place the problems solved by the quantum algorithms of BernsteinVazirani and Grover. By combining the tools used in these algorithmsquantum fast transforms and amplitude amplificationwith a novel (in this context) toola solution method for geometrical optimization problems we derive a general technique for quantum concept learning. We name this technique "Amplified Impatient Learning" and apply it to construct quantum algorithms solving two new problems: BATTLESHIP and MAJORITY, more e#ciently than is possible classically.
quantph/0309059 THE GEOMETRY OF QUANTUM LEARNING
, 2003
"... Concept learning provides a natural framework in which to place the problems solved by the quantum algorithms of BernsteinVazirani and Grover. By combining the tools used in these algorithms—quantum fast transforms and amplitude amplification—with a novel (in this context) tool—a solution method fo ..."
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Concept learning provides a natural framework in which to place the problems solved by the quantum algorithms of BernsteinVazirani and Grover. By combining the tools used in these algorithms—quantum fast transforms and amplitude amplification—with a novel (in this context) tool—a solution method for geometrical optimization problems— we derive a general technique for quantum concept learning. We name this technique “Amplified Impatient Learning ” and apply it to construct quantum algorithms solving two new problems: BATTLESHIP and MAJORITY, more efficiently than is possible classically.
Towards Realising Secure and Efficient Image and Video Processing Applications on Quantum Computers
, 2013
"... entropy ..."
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Quantum approach to Image processing
"... Quantum computing is a new trend in computationtheory and a quantum mechanical system has several useful properties like Entanglement. In this paper tried to explain some method and algortithm for image processing that works in a quantum computer and how to profits from advantages of quantum system, ..."
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Quantum computing is a new trend in computationtheory and a quantum mechanical system has several useful properties like Entanglement. In this paper tried to explain some method and algortithm for image processing that works in a quantum computer and how to profits from advantages of quantum system, and then illustrate several computational experiment in this direction. 1.
Quantum Image Representation Through TwoDimensional Quantum States and Normalized Amplitude
"... ar ..."
Quantum Software Reusability
, 2003
"... The design of efficient quantum circuits is an important issue in quantum computing. It is in general a formidable task to find a highly optimized quantum circuit for a given unitary matrix. We propose a quantum circuit design method that has the following unique feature: It allows to construct effi ..."
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The design of efficient quantum circuits is an important issue in quantum computing. It is in general a formidable task to find a highly optimized quantum circuit for a given unitary matrix. We propose a quantum circuit design method that has the following unique feature: It allows to construct efficient quantum circuits in a systematic way by reusing and combining a set of highly optimized quantum circuits. Specifically, the method realizes a quantum circuit for a given unitary matrix by implementing a linear combination of representing matrices of a group, which have known fast quantum circuits. We motivate and illustrate this method by deriving extremely efficient quantum circuits for the discrete Hartley transform and for the fractional Fourier transforms. The sound mathematical basis of this design method allows to give meaningful and natural interpretations of the resulting circuits. We demonstrate this aspect by giving a natural interpretation of known teleportation circuits.
Quantum Algorithms and Complexity for Numerical Problems
, 2011
"... Quantum computing has attracted a lot of attention in different research fields, such as mathematics, physics and computer science. Quantum algorithms can solve certain problems significantly faster than classical algorithms. There are many numerical problems, especially those arising from quantum ..."
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Quantum computing has attracted a lot of attention in different research fields, such as mathematics, physics and computer science. Quantum algorithms can solve certain problems significantly faster than classical algorithms. There are many numerical problems, especially those arising from quantum systems, which are notoriously difficult to solve using classical computers, since the computational time required often scales exponentially with the size of the problem. However, quantum computers have the potential to solve these problems efficiently, which is also one of the founding ideas of the field of quantum computing. In this thesis, we explore five different computational problems, designing innovative quantum algorithms and studying their computational complexity. First, we design an adiabatic quantum algorithm for the counting problem, i.e., approximating the proportion α, of the marked items in a given database. As the quantum system undergoes a designed cyclic adiabatic evolution, it acquires a Berry phase 2piα. By estimating the Berry phase, we can approximate α, and solve the problem. For an error bound ε, the algorithm can solve the problem with cost of order ε−3/2, which is not as good
Contributions to InformationBased Complexity and to Quantum Computing
, 2013
"... Multivariate continuous problems are widely encountered in physics, chemistry, finance and in computational sciences. Unfortunately, interesting real world multivariate continuous problems can almost never be solved analytically. As a result, they are typically solved numerically and therefore appr ..."
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Multivariate continuous problems are widely encountered in physics, chemistry, finance and in computational sciences. Unfortunately, interesting real world multivariate continuous problems can almost never be solved analytically. As a result, they are typically solved numerically and therefore approximately. In this thesis we deal with the approximate solution of multivariate problems. The complexity of such problems in the classical setting has been extensively studied in the literature. On the other hand the quantum computational model presents a promising alternative for dealing with multivariate problems. The idea of using quantum mechanics to simulate quantum physics was initially proposed by Feynman in 1982. Its potential was demonstrated by Shor’s integer factorization algorithm, which exponentially improves the cost of the best classical algorithm known. In the first part of this thesis we study the tractability of multivariate problems in the worst and average case settings using the real number model with oracles. We derive necessary and sufficient conditions for weak tractability for linear multivariate tensor product problems in those settings.