Unitary Operator

(redirected from Unitary operation)
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Unitary Operator

 

an extension of the notation of a rotation of Euclidean space to the infinite-dimensional case. More precisely, a unitary operator is a rotation of a Hilbert space about the origin. In analytic terms, an operator U that maps the Hilbert space H onto itself is said to be unitary if (f, g) = (Uf,Ug) for any two vectors f, g in H. A unitary operator preserves lengths of vectors and angles between vectors and is a linear operator. A unitary operator U has a unitary inverse U–1 such that U–1 = U*, where U* is the adjoint of U.

An example of a unitary operator is the Fourier-Plancherel operator, which associates to each function f(x), – ∞ < x < ∞, with square integrable absolute value the function

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
Then [U.sub.L] is used as a unitary operation; the feature vectors of identifying palmprint and the palmprint from database are loaded in the quantum entanglement state, that is, to transform formula (20) into the following quantum state:
A unitary operation is used in formula 22) after computing the matching function [f.sub.c] between the two palmprints which are shown by the following equation:
This technical (syntactic) tool, which originates in early transformational-generative grammar but is fully developed in recent versions of the Chomskyan Minimalist Program, might be interpreted as an operation that creates objects within objects, a single unitary operation combining structure building and movement.
Granulation is a widely applied unitary operation, especially in the pharmaceutical and chemical industries, with operators sharing the common goal of controlling particle size to meet granulate performance goals.
Since the set of unitary operations is continuous, it is clear that a discrete set of gates is not sufficient to implement an arbitrary unitary operation.
Now, it can be shown that the discrete set of quantum gates formed by the normalizer group, plus the Toffoli gate is universal for quantum computation; that is an arbitrary unitary operation on d qubits can be approximated to an arbitrary accuracy using a circuit composed only from these gates.
Hence, Mohasco functioned as part of a single unitary operation with Carpet.
Once the results from Alice and Bob are published, Charlie measures his qubit 3 before telling Alice and Bob the unitary operation I = |0><0| + |1><1|, [[sigma].sub.x] = |0><1| + |1><0|, [[sigma].sub.z] = |0><0| - |1><1|, i[[sigma].sub.y] = |0><1| - |1><0| to transfer their qubit 0 and qubit 6, which leads to successful swapping as follows:
In our protocol, only the controller knows the initial GHZ state and EPR pairs, so the legitimate users a reunable to know how to use the unitary operation to transfer their qubit state correctly.
The process incorporates sustainability in all the steps that are critical for extraction: choice of the solvent or technologies, utilization of by-products, reduction of unitary operations, and limitation of chemical alteration of botanical extracts.
He also taught courses in thermodynamics and unitary operations and processes.
In Campbell Sales, New York again sought to compel a combined report between a non-New York taxpayer and a New York taxpayer on the grounds of stock ownership, unitary operations, and substantial intercorporate transactions.