The ChurchTuring Thesis 

There are various equivalent formulations of the ChurchTuring thesis. A common one is that every effective computation can be carried out by a Turing machine. 

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Simon’s Algorithm 

The reason why we looked at the particular ?blackbox? problems from the previous couple of lectures is because they give examples in which quantum algorithms give some advantage over classical algorithms. 

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The Schmidt Decomposition And Purifications 

Density operators and the partial trace are just the beginning of a wide array of tools useful for the study of composite quantum systems, which are at the heart of quantum computation and quantum information. 

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Schmidt Decomposition 

Consider two Hilbert spaces and with dimensions and respectively. We may construct the tensor product space and write a general state as 

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Quantum Computing An Introduction 

He suggested in 1982 that quantum computers might have fundamentally more powerful computational abilities than conventional ones (basing his conjecture on the extreme difficulty encountered in computing the result of quantum mechanical processes 

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Quantum Circuit Models 

A classical circuit implements a multioutput boolean function , given as primitive a
finite collection of gates each of which implements a boolean function on k bits for some small k. The
picture of the circuit 

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Quantum Circuit Complexity 

We study a complexity model of quantum circuits analogous to the standard Boolean Circuit model. 

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Quantum Circuit Model 

To explain the quantum circuit model of computation.To explain Deutsch’s algorithm.
To explain an alternate model of quantum computation based upon measurement. 

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Quantum Computing 

Strange as it sounds, the computer of tomorrow could be built around a cup of coffee. The caffeine molecule is just one of the possible building blocks of a 'quantum computer', a new type of computer that promises to provide mind boggling performance that can break secret codes in a matter of seconds. 

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Introduction To Quantum Computing 

Basic facts about quantum computing, Grover’s search,The hidden subgroup problem,etc.., 

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Quantum Computing  Lecture Notes 

The following lecture notes are based on the book Quantum Computation and Quantum Information by Michael A. Nielsen and Isaac L. Chuang. They are for a mathbased quantum computing course that I teach here at the University of Washington to computer science graduate
students (with advanced undergraduates admitted upon request) 

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Quantum algorithms 

This book started with the world's oldest and most widely used algorithms (the ones for adding
and multiplying numbers) and an ancient hard problem (FACTORING). 

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Main features 

The main drawback of the search with the minimal A(x) (see Deterministic Finite Automaton) is the size of the automaton 

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Defining the Quantum Computer 

The Turing machine, developed by Alan Turing in the 1930s, is a theoretical device that consists of tape of unlimited length that is divided into little squares. Each square can either hold a symbol (1 or 0) or be left blank. 

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