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In quantum computing, Grover's algorithm, also known as the quantum search algorithm, is a quantum algorithm for unstructured search that finds with high probability the unique input to a black box function that produces a particular output value, using just () evaluations of the function, where is the size of the function's domain.
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 ...
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]
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]
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.
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.
The quantum algorithm solving Simon's problem, usually called Simon's algorithm, served as the inspiration for Shor's algorithm. [1] Both problems are special cases of the abelian hidden subgroup problem , which is now known to have efficient quantum algorithms.
For example, the outcome of the measurement of a qubit reveals the result of a binary classification task. While many proposals of quantum machine learning algorithms are still purely theoretical and require a full-scale universal quantum computer to be tested, others have been implemented on small-scale or special purpose quantum devices.