Unitary operator information

functional analysis, a unitary operator is a surjective bounded operator on a Hilbert space that preserves the inner product. Unitary operators are usually taken...

Semi-orthogonal matrix Quantum logic gate Special Unitary group SU(n) Symplectic matrix Unitary group U(n) Unitary operator Li, Chi-Kwong; Poon, Edward (2002). "Additive...

are the same space, a unitary transformation is an automorphism of that Hilbert space, and then it is also called a unitary operator. A closely related notion...

mathematics, a unitary representation of a group G is a linear representation π of G on a complex Hilbert space V such that π(g) is a unitary operator for every...

of normal operators are unitary operators: N* = N−1 Hermitian operators (i.e., selfadjoint operators: N* = N; also, anti-selfadjoint operators: N* = −N)...

shift operator acting on two-sided sequences is a unitary operator on ℓ 2 ( Z ) . {\displaystyle \ell _{2}(\mathbb {Z} ).} The shift operator acting...

decomposition of antiunitary operators contrasts with the spectral decomposition of unitary operators. In particular, a unitary operator on a complex Hilbert...

Unitary equivalence may refer to: Unitary equivalence of bounded operators in Hilbert space; see self-adjoint operator Unitary equivalence of a unitary...

mechanics, such as state vectors, probability amplitudes, unitary operators, and Hermitian operators, emerge naturally from the classical Maxwell's equations...

morphism Unitary operator Unitary transformation Unitary representation Unitarity (physics) E-unitary inverse semigroup Unitary authority Unitary state Unital...

are unitary operators: N* = N−1 Hermitian operators (i.e., self-adjoint operators): N* = N skew-Hermitian operators: N* = −N positive operators: N =...

unique). The unitary operator U is not unique. Rather it is possible to determine a "natural" unitary operator as follows: AP+ is a unitary operator from the...

limiting argument. Furthermore, F : L2(Rn) → L2(Rn) is a unitary operator. For an operator to be unitary it is sufficient to show that it is bijective and preserves...

performed by classical circuits. Quantum gates are unitary operators, and are described as unitary matrices relative to some orthonormal basis. Usually...

t units of time on the state of an isolated system S is given by a unitary operator Ut on the Hilbert space H associated to S. This means that if the system...

vectors are considered equivalent if they are proportional.] Thus, a unitary operator that is a multiple of the identity actually acts as the identity on...

constant-coefficient differential operator is unitarily equivalent to a multiplication operator. Indeed, the unitary operator that implements this equivalence...

an eigenstate of the annihilation (lowering) operator. The displacement operator is a unitary operator, and therefore obeys D ^ ( α ) D ^ † ( α ) = D...

into the group of unitary operators. If G is a compact Lie group, every finite-dimensional representation is equivalent to a unitary one. Each representation...

\qquad z=r\,e^{i\theta }} where the operators inside the exponential are the ladder operators. It is a unitary operator and therefore obeys S ( ζ ) S † (...

set Stone's theorem on one-parameter unitary groups Holomorphic functional calculus Spectral theory Compact operator Laplace transform Fredholm theory Liouville–Neumann...

claim. A hyponormal compact operator (in particular, a subnormal operator) is normal. The spectrum of a unitary operator U lies on the unit circle in...