Find link

language:

Find link is a tool written by Edward Betts.

searching for Unitary matrix 38 found (143 total)

Clifford gates (934 words) [view diff] exact match in snippet view article find links to article

{1}/{\sqrt {2}}} in the unitary matrix representation, removing the phase gate S disallows i {\displaystyle i} in the unitary matrix, and removing the CNOT

Continuous-time quantum walk (1,022 words) [view diff] exact match in snippet view article find links to article

quantum walk on a given (simple) graph that is dictated by a time-varying unitary matrix that relies on the Hamiltonian of the quantum system and the adjacency

Hamiltonian cycle polynomial (2,247 words) [view diff] exact match in snippet view article find links to article

to polynomial-time calculate the Hamiltonian cycle polynomial of any unitary matrix U {\displaystyle U} (i.e. such that U T U = I {\displaystyle U^{T}U=I}

Euler's rotation theorem (4,498 words) [view diff] exact match in snippet view article find links to article

{1}{\alpha _{m}}}\right)} and it follows that the eigenvalues of a unitary matrix are on the unit circle in the complex plane: α k ∗ = 1 α k ⟺ α k ∗ α

Schur–Horn theorem (2,888 words) [view diff] exact match in snippet view article find links to article

1 , {\displaystyle U\Lambda U^{-1},} where U {\displaystyle U} is a unitary matrix. Then a i i = ∑ j = 1 n λ j | u i j | 2 , i = 1 , 2 , … , n . {\displaystyle

Mach–Zehnder interferometer (2,410 words) [view diff] exact match in snippet view article find links to article

|\alpha |^{2}+|\beta |^{2}=1} . Both beam splitters are modelled as the unitary matrix B = 1 2 ( 1 i i 1 ) {\displaystyle B={\frac {1}{\sqrt

Chirality (physics) (3,265 words) [view diff] exact match in snippet view article

Lagrangian is unchanged under a rotation of qL by any 2×2 unitary matrix L, and qR by any 2×2 unitary matrix R. This symmetry of the Lagrangian is called flavor

Boson sampling (7,102 words) [view diff] exact match in snippet view article find links to article

Specifically, suppose the linear interferometer is described by an N×N unitary matrix U , {\displaystyle U,} which performs a linear transformation of the

Local hidden-variable theory (1,177 words) [view diff] exact match in snippet view article find links to article

U ⊗ U , {\displaystyle U\otimes U,} where U {\displaystyle U} is a unitary matrix. For two qubits, they are noisy singlets given as ϱ = p | ψ − ⟩ ⟨ ψ

Linear optical quantum computing (3,868 words) [view diff] exact match in snippet view article find links to article

computation has been proven. Up to N × N {\displaystyle N\times N} unitary matrix operations ( U ( N ) {\displaystyle U(N)} ) can be realized by only

Schrödinger–HJW theorem (1,097 words) [view diff] exact match in snippet view article find links to article

transformation acting on the auxiliary space, namely, there exists a unitary matrix U A {\displaystyle U_{A}} such that | Ψ S A 1 ⟩ = ( I ⊗ U A ) | Ψ S

Polynomial matrix spectral factorization (3,321 words) [view diff] exact match in snippet view article find links to article

at the orbit of L {\displaystyle L} under right multiplication by a unitary matrix, V = L U {\displaystyle V=LU} . To obtain the lower triangular decomposition

Quantum machine learning (10,306 words) [view diff] exact match in snippet view article find links to article

associative memories (in their simplest realization) store patterns in a unitary matrix U acting on the Hilbert space of n qubits. Retrieval is realized by

Dilation (operator theory) (678 words) [view diff] exact match in snippet view article

\theta \\\ \sin \theta &-\cos \theta \end{bmatrix}}.} which is just the unitary matrix describing rotation by θ. For this reason, the Julia operator V(T) is

Quantum mechanics (12,063 words) [view diff] exact match in snippet view article find links to article

|\alpha |^{2}+|\beta |^{2}=1} . Both beam splitters are modelled as the unitary matrix B = 1 2 ( 1 i i 1 ) {\displaystyle B={\frac {1}{\sqrt

Sign function (2,787 words) [view diff] exact match in snippet view article find links to article

{Q}}{\boldsymbol {P}}} where Q {\displaystyle {\boldsymbol {Q}}} is a unitary matrix and P {\displaystyle {\boldsymbol {P}}} is a self-adjoint, or Hermitian

List of numerical analysis topics (8,344 words) [view diff] exact match in snippet view article find links to article

triangular matrix Singular value decomposition — unitary matrix times diagonal matrix times unitary matrix Matrix splitting — expressing a given matrix as

Naimark's dilation theorem (1,489 words) [view diff] exact match in snippet view article find links to article

N ] {\displaystyle U={\begin{bmatrix}M\\N\end{bmatrix}}} is a n × n unitary matrix, the projection-valued measure whose elements are projections onto the

KLM protocol (3,048 words) [view diff] exact match in snippet view article find links to article

elements support a complete set of operators on any single qubit. The unitary matrix associated with a beam splitter B θ , ϕ {\displaystyle \mathbf {B} _{\theta

Elitzur–Vaidman bomb tester (3,737 words) [view diff] exact match in snippet view article find links to article

the qubit if a bomb is present R ϵ {\textstyle R_{\epsilon }} is the unitary matrix ( cos ⁡ ϵ − sin ⁡ ϵ sin ⁡ ϵ cos ⁡ ϵ ) {\textstyle {\begin{pmatrix}\cos

Standard Model (7,169 words) [view diff] exact match in snippet view article find links to article

U=e^{-ig_{s}\lambda ^{a}\phi ^{a}(x)}} is 3 × 3 {\displaystyle 3\times 3} unitary matrix with determinant 1, making it a member of the group SU(3), and ϕ a (

Chiral model (3,206 words) [view diff] exact match in snippet view article find links to article

be conveniently written using 2×2 matrix notation by introducing the unitary matrix U = 1 F ( σ 1 2 + i π ⋅ τ ) , {\displaystyle U={\frac {1}{F}}\left(\sigma

John Archibald Wheeler (6,013 words) [view diff] exact match in snippet view article find links to article

Structure", Wheeler introduced the S-matrix—short for scattering matrix—"a unitary matrix of coefficients connecting the asymptotic behavior of an arbitrary particular

Hermitian symmetric space (7,418 words) [view diff] exact match in snippet view article find links to article

matrices. Type IIIn: for every complex symmetric n × n matrix M there is a unitary matrix U such that UMUt is diagonal. This is proved by a classical argument

Restricted representation (3,061 words) [view diff] exact match in snippet view article find links to article

f_{2}\geq \cdots \geq f_{N}} where the fi are integers. In fact if a unitary matrix U has eigenvalues zi, then the character of the corresponding irreducible

Principal component analysis (14,281 words) [view diff] exact match in snippet view article find links to article

definite matrix and thus is guaranteed to be diagonalisable by some unitary matrix. In practical implementations, especially with high dimensional data

Fidelity of quantum states (4,035 words) [view diff] exact match in snippet view article find links to article

=\operatorname {tr} \left({\sqrt {\rho }}{\sqrt {\sigma }}U\right),} where the unitary matrix U {\displaystyle U} is defined as U = ( ∑ k | μ k ⟩ ⟨ u k | ) ( ∑ j

Classical group (7,823 words) [view diff] exact match in snippet view article find links to article

physicists call g † {\displaystyle g^{\dagger }} . As a comparison, a Unitary matrix U(n) is defined as U ( n ) = { g | g ∗ g = I } . {\displaystyle \mathrm

Joel Lee Brenner (2,061 words) [view diff] case mismatch in snippet view article find links to article

S2CID 120118613. J. L. Brenner; F. T. Smith (1962). "On a Property of a Unitary Matrix". SIAM Review. 4 (4): 395. Bibcode:1962SIAMR...4..395B. doi:10.1137/1004094

Quantum artificial life (1,906 words) [view diff] exact match in snippet view article find links to article

biodiversity within the artificial environment. The M operation is a unitary matrix which can be described as: M = ( cos ⁡ ( θ ) s i n ( θ ) s i n ( θ )

Periodic table of topological invariants (1,940 words) [view diff] exact match in snippet view article find links to article

the complex conjugation operator and U T {\displaystyle U_{T}} is a unitary matrix. Either T 2 = 1 {\displaystyle T^{2}=1} or T 2 = − 1 {\displaystyle

Perron–Frobenius theorem (8,235 words) [view diff] exact match in snippet view article find links to article

μ=ρ(A)eiφ is eigenvalue for B), then B = eiφ D AD−1 for some diagonal unitary matrix D (i.e. diagonal elements of D equals to eiΘl, non-diagonal are zero)

Invariant convex cone (3,569 words) [view diff] exact match in snippet view article find links to article

factorization states that for any complex symmetric matrix M, there is a unitary matrix U such that UMUt is diagonal. IfS is a semigroup properly containing

Gaussian network model (4,574 words) [view diff] exact match in snippet view article find links to article

by diagonalization of the Kirchhoff matrix, Γ = UΛUT. Here, U is a unitary matrix, UT = U−1, of the eigenvectors ui of Γ and Λ is the diagonal matrix

List of Italian inventions and discoveries (25,900 words) [view diff] exact match in snippet view article find links to article

oscillated considerably in temperature over geological ages. CKM Matrix: a unitary matrix containing information about the strength of the flavour-changing weak

Intrinsic bond orbitals (2,927 words) [view diff] exact match in snippet view article find links to article

′ {\displaystyle |i'\rangle =\sum _{i}^{occ}|i\rangle U_{ii'}} The unitary matrix U i i ′ {\displaystyle U_{ii'}} , which produces the localized IBOs

Oscillator representation (21,523 words) [view diff] exact match in snippet view article find links to article

the symplectic group has a complex counterpart. Indeed, if C is the unitary matrix C = 1 2 ( I i I I − i I ) {\displaystyle {C={1 \over {\sqrt

Igor L. Markov (2,624 words) [view diff] exact match in snippet view article find links to article

{\displaystyle n} -qubit quantum circuit that (a) implements a given unitary matrix using no more than ( 23 / 48 ) × 4 n − ( 3 / 2 ) × 2 n + 4 / 3 {\displaystyle