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Find link is a tool written by Edward Betts.Longer titles found: Antiunitary operator (view)
searching for Unitary operator 53 found (146 total)
alternate case: unitary operator
Square root of a matrix
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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 theSqueeze operator (871 words) [view diff] exact match in snippet view article find links to article
operators inside the exponential are the ladder operators. It is a unitary operator and therefore obeys S(ζ)S†(ζ)=S†(ζ)S(ζ)=1^{\displaystyle S(\zeta )S^{\daggerAmplitude amplification (1,568 words) [view diff] exact match in snippet view article find links to article
when measured is sin2(θ){\displaystyle \sin ^{2}(\theta )}. Define a unitary operator Q(ψ,P):=−SψSP{\displaystyle Q(\psi ,P):=-S_{\psi }S_{P}\,\!}, whereLinear optical quantum computing (3,795 words) [view diff] exact match in snippet view article find links to article
special case where the reflecting rate is 1, so that the corresponding unitary operator is a rotation matrix given by R(θ)=[cosθ−sinθsinθcosθ]{\displaystylePositive-definite function on a group (838 words) [view diff] exact match in snippet view article find links to article
representation is a unital homomorphism Φ: G → L(H) where Φ(s) is a unitary operator for all s. For such Φ, Φ(s−1) = Φ(s)*. Positive-definite functionsQuantum operation (2,748 words) [view diff] exact match in snippet view article find links to article
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 systemComplexification (Lie group) (7,023 words) [view diff] exact match in snippet view article
of operators with polar decomposition g = u • exp iX, where u is a unitary operator in the compact group and X is a skew-adjoint operator in its Lie algebraKLM protocol (2,930 words) [view diff] exact match in snippet view article find links to article
special case where the reflecting rate is 1, so that the corresponding unitary operator is a rotation matrix given by R(θ)=[cosθ−sinθsinθcosθ]{\displaystyleKK-theory (1,081 words) [view diff] exact match in snippet view article find links to article
B, such that there is an even unitary operator from the 0-end of the homotopy to the first cycle, and a unitary operator from the 1-end of the homotopyQuantum clock model (917 words) [view diff] exact match in snippet view article find links to article
ZN{\displaystyle \mathbb {Z} _{N}} symmetry, which is generated by the unitary operator UX=∏jXj{\displaystyle U_{X}=\prod _{j}X_{j}} where the product is overUniformly bounded representation (3,361 words) [view diff] exact match in snippet view article find links to article
this gives a criterion for an invertible operator to be similar to a unitary operator: the operator norms of all the positive and negative powers must beQuantum amplifier (1,747 words) [view diff] exact match in snippet view article find links to article
phase-invariant amplifiers may be described as follows. Assume that the unitary operator U^ {\displaystyle ~{\hat {U}}~} amplifies in such a way that the inputQuasinormal operator (551 words) [view diff] exact match in snippet view article find links to article
\,} In general, a partial isometry may not be extendable to a unitary operator and therefore a quasinormal operator need not be normal. For exampleQuaternionic representation (685 words) [view diff] exact match in snippet view article find links to article
is a unitary representation and the quaternionic structure j is a unitary operator, then V admits an invariant complex symplectic form ω, and hence isBQP (3,343 words) [view diff] exact match in snippet view article find links to article
into gj=I⊗g~j{\displaystyle g_{j}=I\otimes {\tilde {g}}_{j}} for some unitary operator g~j{\displaystyle {\tilde {g}}_{j}} acting on two qubits, which withoutGelfand–Naimark–Segal construction (2,008 words) [view diff] exact match in snippet view article find links to article
Then π, π' are unitarily equivalent *-representations i.e. there is a unitary operator U from H to H′ such that π'(a) = Uπ(a)U* for all a in A. The operatorChoi–Jamiołkowski isomorphism (3,044 words) [view diff] exact match in snippet view article find links to article
transposition. However, this issue can be avoided by expressing any unitary operator as a product of two symmetric unitary operators. Therefore, for anyFoldy–Wouthuysen transformation (3,111 words) [view diff] exact match in snippet view article find links to article
unitary transformation on a fermion wave function of the form: where the unitary operator is the 4 × 4 matrix: Above, p^i≡pi|p|{\displaystyle {\hat {p}}^{i}\equivAbelian von Neumann algebra (1,521 words) [view diff] exact match in snippet view article find links to article
spatially isomorphic (or unitarily isomorphic) if and only if there is a unitary operator U: H → K such that UAU∗=B.{\displaystyle UAU^{*}=B.} In particularWeak measurement (2,786 words) [view diff] exact match in snippet view article find links to article
weakly correlates the system and ancilla (specifically, the interaction unitary operator need only to be expanded to first or second order in perturbation theory)Generalized Clifford algebra (1,525 words) [view diff] exact match in snippet view article find links to article
Sciences de Toulouse. 12 (1): B65–B99. Schwinger, J. (April 1960). "Unitary operator bases". Proc Natl Acad Sci U S A. 46 (4): 570–9. Bibcode:1960PNAS.Hadamard test (705 words) [view diff] exact match in snippet view article find links to article
+\left|1\right\rangle \right)\otimes \left|\psi \right\rangle }. We then apply the unitary operator on |ψ⟩{\displaystyle \left|\psi \right\rangle } conditioned on theLindbladian (3,483 words) [view diff] exact match in snippet view article find links to article
Also note that U(t,t0){\displaystyle U(t,t_{0})}is the total unitary operator of the entire system. It is straightforward to confirm that the LiouvillePi (16,888 words) [view diff] exact match in snippet view article find links to article
above is the most canonical definition, however, giving the unique unitary operator on L2 that is also an algebra homomorphism of L1 to L∞. The HeisenbergRotating-wave approximation (2,083 words) [view diff] exact match in snippet view article find links to article
an overall phase of eiω0t/2{\displaystyle e^{i\omega _{0}t/2}} on a unitary operator does not affect the underlying physics, so in the further usages ofFourier inversion theorem (3,305 words) [view diff] exact match in snippet view article find links to article
f\in L^{2}(\mathbb {R} ^{n})} shows that the Fourier transform is a unitary operator on L2(Rn){\displaystyle L^{2}(\mathbb {R} ^{n})}. The inverse FourierOscillator representation (19,823 words) [view diff] exact match in snippet view article find links to article
S{\displaystyle {\mathcal {S}}} onto itself. By density it extends to a unitary operator on L2(R), as asserted by Plancherel's theorem. Suppose U(s) and V(t)Polar factorization theorem (1,177 words) [view diff] exact match in snippet view article find links to article
divergence-free. polar decomposition – Representation of invertible matrices as unitary operator multiplying a Hermitian operator Brenier, Yann (1991). "Polar factorizationSpectral triple (1,944 words) [view diff] exact match in snippet view article find links to article
fundamental one is the polar decomposition D = F|D| of D into a self adjoint unitary operator F (the 'phase' of D) and a densely defined positive operator |D| (theProjective representation (4,133 words) [view diff] exact match in snippet view article find links to article
vectors are considered equivalent if they are proportional.] Thus, a unitary operator that is a multiple of the identity actually acts as the identity onHeisenberg group (5,254 words) [view diff] exact match in snippet view article find links to article
L^{2}(K)}. Indeed, the continuous characters separate points so any unitary operator of L2(K){\displaystyle L^{2}(K)} that commutes with them is an L∞{\displaystyleHeisenberg group (5,254 words) [view diff] exact match in snippet view article find links to article
L^{2}(K)}. Indeed, the continuous characters separate points so any unitary operator of L2(K){\displaystyle L^{2}(K)} that commutes with them is an L∞{\displaystyleKeldysh formalism (2,279 words) [view diff] exact match in snippet view article find links to article
{O}}(t)=U^{\dagger }(t,0){\mathcal {O}}(0)U(t,0)}. The time-evolution unitary operator U(t2,t1){\displaystyle U(t_{2},t_{1})} is the time-ordered exponentialMeasurement in quantum mechanics (8,136 words) [view diff] exact match in snippet view article find links to article
Expressing time evolution for a duration t{\displaystyle t} by the unitary operator U=e−iHt/ℏ{\displaystyle U=e^{-iHt/\hbar }}, the state for the systemCorepresentations of unitary and antiunitary groups (1,405 words) [view diff] exact match in snippet view article find links to article
S of a Hamiltonian is represented in quantum mechanics either by a unitary operator, S = U, or an antiunitary one, S = UK where U is unitary, and K denotesWave function (13,111 words) [view diff] exact match in snippet view article find links to article
to Quantum Mechanics (3rd ed.). The Fourier transform viewed as a unitary operator on the space L2 has eigenvalues ±1, ±i. The eigenvectors are "HermiteUnitary transformation (quantum mechanics) (2,225 words) [view diff] exact match in snippet view article
terms of a time-dependent Hamiltonian H(t){\displaystyle H(t)} and unitary operator U(t){\displaystyle U(t)}. Under this change, the Hamiltonian transformsQuantum computational chemistry (3,240 words) [view diff] exact match in snippet view article find links to article
The goal of qubitization is to embed this Hamiltonian into a larger, unitary operator, which is a type of operator in quantum mechanics that preserves theRepresentation of a Lie group (5,119 words) [view diff] exact match in snippet view article find links to article
of the Hilbert space are then described by unitary operators, but a unitary operator that is a multiple of the identity does not change the physical stateSIC-POVM (3,264 words) [view diff] exact match in snippet view article find links to article
q)=S^{p}T^{q}} which generates the Heisenberg-Weyl group. This is a unitary operator since W(p,q)W†(p,q)=SpTqT−qS−p=Id{\displaystyle {\begin{aligned}W(pSuperconducting quantum computing (8,182 words) [view diff] exact match in snippet view article find links to article
operators is sufficient for satisfying universality as every single qubit unitary operator U{\displaystyle U} may be presented as U=RX(θ1)RY(θ2)RX(θ3){\displaystyleCritical three-state Potts model (1,611 words) [view diff] exact match in snippet view article find links to article
Z3{\displaystyle \mathbb {Z} _{3}} subgroup of this symmetry is generated by the unitary operator ∏jXj{\displaystyle \prod _{j}X_{j}}. In one dimension, the model hasSemisimple representation (3,621 words) [view diff] exact match in snippet view article find links to article
=\langle v,w\rangle }, which is to say π(g){\displaystyle \pi (g)} is a unitary operator and so π{\displaystyle \pi } is a unitary representation. Hence, everyPeriodic table of topological invariants (1,832 words) [view diff] exact match in snippet view article find links to article
symmetry, and chiral (or sublattice) symmetry. Chiral symmetry is a unitary operator S{\displaystyle S}, that acts on ci{\displaystyle c_{i}}, as a unitaryIntegrated quantum photonics (4,185 words) [view diff] exact match in snippet view article find links to article
Bertani P (July 1994). "Experimental realization of any discrete unitary operator". Physical Review Letters. 73 (1): 58–61. Bibcode:1994PhRvL..73...58RSingular integral operators of convolution type (11,821 words) [view diff] exact match in snippet view article find links to article
at ∞ to 1, and the upper halfplane onto the unit disk. Define the unitary operator from L2(T) onto L2(R) by Uf(x)=π−1/2(x+i)−1f(C(x)).{\displaystyle Uf(x)=\piQuantum random circuits (1,366 words) [view diff] exact match in snippet view article find links to article
U(t;0)=U_{t}U_{t-1}\cdots U_{3}U_{2}U_{1}} where for each step, the unitary operator is represented by a tensor product of local unitary gates uτ,x{\displaystyleErgodic flow (5,016 words) [view diff] exact match in snippet view article find links to article
under ceiling functions. Let R be the Fourier transform on L2(R,m), a unitary operator such that Rλ(t)R∗ = Vt where λ(t) is translation by t and Vt is multiplicationBeltrami equation (10,241 words) [view diff] exact match in snippet view article find links to article
{\widehat {Tf}}(z)={{\overline {z}} \over z}{\widehat {f}}(z).} It is a unitary operator and if f is a tempered distribution on C with partial derivatives inNeumann–Poincaré operator (10,376 words) [view diff] exact match in snippet view article find links to article
formally self-adjoint. Let H0 be the Hilbert space completion. Define a unitary operator V from H0 onto A2(Ω) by V(ψ)=U(D(φ)+S(ψ))|Ω,{\displaystyle \displaystyleLight front quantization (12,481 words) [view diff] exact match in snippet view article find links to article
rotation with the inverse of the corresponding dynamical rotation is a unitary operator that (1) preserves the S{\displaystyle S}-matrix and (2) changes theDifferential forms on a Riemann surface (10,756 words) [view diff] exact match in snippet view article find links to article
\oplus } ker ∆. Identifying H2(T2) with L2(T2) = H0(T2) using the unitary operator I + Δ, the first statement reduces to proving that the operator T =Product operator formalism (4,936 words) [view diff] exact match in snippet view article find links to article
Uf(A)U†=f(UAU†){\displaystyle Uf(A)U^{\dagger }=f(UAU^{\dagger })} for unitary operator U{\displaystyle U}, operator A{\displaystyle A} and function f{\displaystyle