Quantum Computers
Theory and Algorithms
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Open AccessSelf-testing of a single quantum system from theory to experiment
Self-testing allows one to characterise quantum systems under minimal assumptions. However, existing schemes rely on quantum nonlocality and cannot be applied to systems that are not entangled. Here, we introd...
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Open AccessRecent progress in quantum photonic chips for quantum communication and internet
Recent years have witnessed significant progress in quantum communication and quantum internet with the emerging quantum photonic chips, whose characteristics of scalability, stability, and low cost, flourish ...
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Open AccessAn improved parameterization procedure for NDDO-descendant semi-empirical methods
MNDO-based semi-empirical methods in quantum chemistry have found widespread application in the modelling of large and complex systems. A method for the analytic evaluation of first and second derivatives of m...
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Binary Degrees of Freedom and Qubits
In this chapter, we review the notations used in quantum mechanics and discuss some fundamental ideas of quantum mechanics within the context of quantum computers. The underlying principles of quantum mechanic...
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Shor’s Algorithm
The Shor algorithm is widely regarded as the first non-trivial quantum algorithm that shows a potential of an ‘exponential’ speeding-up over its equivalent classical algorithms.
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Solving Linear Equations
Historically, some of the most ancient mathematical problems are directly related to the solutions of linear equations. As a matter of fact, a long time ago, the Chinese mentioned their techniques for solving ...
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Efficiency of a Quantum Computer
To understand why the workings of a quantum computer is radically different from a classical computer—a difference that makes it far more powerful than any possible classical computer—some of the results obtai...
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Introduction
Quantum mechanics describes and explains the workings of nature—and is by far the most successful theory of science. Although quantum mechanics has qualitatively changed our view of nature, a satisfactory unde...
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Deutsch Algorithm
Deutsch algorithm illustrates, using a very special example, that a quantum computer, in principle, is more efficient than a classical computer.
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Deutsch–Jozsa Algorithm
The Deutsch–Jozsa algorithm generalizes the Deutsch algorithm to the case of n-degrees of freedom. The derivation of the more complex quantum Fourier transform algorithm can be adapted to yield the result.
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Simon’s Algorithm
At the outset of quantum algorithms in the early nineties, there were not many practical algorithms that show significant advantage of a quantum computer to a classical computer.
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Quantum-Classical Hybrid Algorithms
At the moment, quantum computers are extremely noisy. Yet, one would still like to harness the advantage of existing quantum computational device if possible. The conviction comes from our understanding of qua...
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Binary Numbers, Vectors, Matrices and Tensor Products
In this part of the book, we briefly reviewed the general mathematical framework behind gates, bits and qubits. These topics form a recurring theme, and they are employed in all the derivations of this book.
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Principles of Quantum Mechanics
The principles and formalism of quantum mechanics are reviewed as these provide the basis for quantum computers and quantum algorithms. This chapter is based on the Copenhagen interpretation of quantum mecha...
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Phase Estimation and quantum Fourier Transform (qFT)
Phase estimation and the quantum Fourier transform (qFT) are the inverse of each other. From a pedagogical point of view, to start the discussion with phase estimation provides greater clarity. The reason bein...
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Grover’s Algorithm
Grover’s algorithm and for factorizing (large) primes are the two masterpieces of quantum computing.
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Quantum Error Correction
Fault-tolerant quantum computation essentially relies on quantum error-correcting codes. By repeated measurements of the error and the application of the corresponding correction operations, encoded states c...
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Book
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Classical Gates and Algorithms
An algorithm is defined to be a well-defined finite set of instructions that are carried out systematically in a given number of steps for solving a well-defined problem. An algorithm, in particular, can have ...
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Quantum Superposition and Entanglement
Two properties of Hilbert space that are pivotal in making quantum algorithms faster than classical algorithms are superposition and entanglement, in Sects. 5.1 and 5.7. A few special , discussed below, concre...
