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Quantum Counting
The Quantum counting algorithm is a quantum algorithm for efficiently counting the number of solutions for a given search problem. The algorithm is based on the quantum phase estimation algorithm and on Grover's search algorithm. Counting problems are common in diverse fields such as statistical estimation, statistical physics, networking, etc. As for quantum computing, the ability to perform quantum counting efficiently is needed in order to use Grover's search algorithm (because running Grover's search algorithm requires knowing how many solutions exist). Moreover, this algorithm solves the quantum existence problem (namely, deciding whether ''any'' solution exists) as a special case. The algorithm was devised by Gilles Brassard, Peter Høyer and Alain Tapp in 1998. The problem Consider a finite set \^n of size N=2^n and a set B of "solutions" (that is a subset of \^n ). Define: : \begin f : \left\^n \to \ \\ f(x) = \begin 1 & x \in B \\ 0 & x \notin B \end \end In othe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Algorithm
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. 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 or instruction can be performed on a classical computer. Similarly, a quantum algorithm is a step-by-step procedure, where each of the steps can be performed on a quantum computer. Although all classical algorithms can also be performed on a quantum computer, the term quantum algorithm is generally reserved for algorithms that seem inherently quantum, or use some essential feature of quantum computation such as quantum superposition or quantum entanglement. Problems that are undecidable using classical computers remain undecidable using quantum computers. What makes quantum algorithms interesting is that they might be able to solve some problems fa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotation Matrix
In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation (mathematics), rotation in Euclidean space. For example, using the convention below, the matrix :R = \begin \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end rotates points in the plane counterclockwise through an angle about the origin of a two-dimensional Cartesian coordinate system. To perform the rotation on a plane point with standard coordinates , it should be written as a column vector, and matrix multiplication, multiplied by the matrix : : R\mathbf = \begin \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end \begin x \\ y \end = \begin x\cos\theta-y\sin\theta \\ x\sin\theta+y\cos\theta \end. If and are the coordinates of the endpoint of a vector with the length ''r'' and the angle \phi with respect to the -axis, so that x = r \cos \phi and y = r \sin \phi, then the above equations become the List of trigonometric identities#Angle sum and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamiltonian Cycle
In the mathematics, mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path (graph theory), path in an undirected or directed graph that visits each vertex (graph theory), vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a cycle (graph theory), cycle that visits each vertex exactly once. A Hamiltonian path that starts and ends at adjacent vertices can be completed by adding one more edge to form a Hamiltonian cycle, and removing any edge from a Hamiltonian cycle produces a Hamiltonian path. The computational problems of determining whether such paths and cycles exist in graphs are NP-complete; see Hamiltonian path problem for details. Hamiltonian paths and cycles are named after William Rowan Hamilton, who invented the icosian game, now also known as ''Hamilton's puzzle'', which involves finding a Hamiltonian cycle in the edge graph of the dodecahedron. Hamilton solved this problem using the icosian calculus, an algebraic structur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
