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The book is suitable as an introduction to quantum computing for computer scientists, mathematicians, and physicists, requiring of them only a background in linear algebra and the theory of complex numbers, [2] [3] although reviewer Donald L. Vestal suggests that additional background in the theory of computation, abstract algebra, and information theory would also be helpful. [4]
In quantum computing, a quantum algorithm is an algorithm that runs on a realistic model of quantum computation, the most commonly used model being the quantum circuit model of computation. [ 1 ] [ 2 ] A classical (or non-quantum) algorithm is a finite sequence of instructions, or a step-by-step procedure for solving a problem, where each step ...
Quantum circuit algorithms can be implemented on integrated circuits, conducted with instrumentation, or written in a programming language for use with a quantum computer or a quantum processor. With quantum processor based systems, quantum programming languages help express quantum algorithms using high-level constructs. [1]
The hidden subgroup problem is especially important in the theory of quantum computing for the following reasons.. Shor's algorithm for factoring and for finding discrete logarithms (as well as several of its extensions) relies on the ability of quantum computers to solve the HSP for finite abelian groups.
Hamiltonian simulation (also referred to as quantum simulation) is a problem in quantum information science that attempts to find the computational complexity and quantum algorithms needed for simulating quantum systems. Hamiltonian simulation is a problem that demands algorithms which implement the evolution of a quantum state efficiently.
HHL algorithm; Quantum annealing; Quantum artificial life; Quantum counting algorithm; Quantum Fourier transform; Quantum optimization algorithms; Quantum phase estimation algorithm; Quantum singular value transformation; Quantum sort; Quantum walk; Quantum walk search
For combinatorial optimization, the quantum approximate optimization algorithm (QAOA) [6] briefly had a better approximation ratio than any known polynomial time classical algorithm (for a certain problem), [7] until a more effective classical algorithm was proposed. [8] The relative speed-up of the quantum algorithm is an open research question.
In the context of quantum computing, the quantum walk search is a quantum algorithm for finding a marked node in a graph. [ 1 ] The concept of a quantum walk is inspired by classical random walks , in which a walker moves randomly through a graph or lattice .