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Fidelity is symmetric in its arguments, i.e. F (ρ,σ) = F (σ,ρ). Note that this is not obvious from the original definition. F (ρ,σ) lies in [0,1], by the Cauchy–Schwarz inequality. F (ρ,σ) = 1 if and only if ρ = σ, since Ψ ρ = Ψ σ implies ρ = σ. So we can see that fidelity behaves almost like a metric.
This list contains quantum processors, also known as quantum processing units (QPUs).Some devices listed below have only been announced at press conferences so far, with no actual demonstrations or scientific publications characterizing the performance.
For N = 3 that is in the case of SU(3), the following situation arises. In SU(3) there are three labels, they are generally designated by (u,d,s) corresponding to up, down and strange quarks which follows the SU(3) algebra. They can also be designated generically as (1,2,3). For a two-particle system, we have the following six symmetry states:
The Cirac-Zoller CNOT gate was not experimentally demonstrated with two ions until 8 years later, in 2003, with a fidelity of 70-80%. [5] Around 1998, there was a collective effort to develop two-qubit gates independent of the motional state of individual ions, [ 6 ] [ 1 ] [ 7 ] one of which was the scheme proposed by Klaus Mølmer and Anders ...
Consider the real line with its usual Borel topology. Let denote the Dirac measure, a unit mass at the point in .The collection := {|} is not tight, since the compact subsets of are precisely the closed and bounded subsets, and any such set, since it is bounded, has -measure zero for large enough .
(x 2 + y 2)(x 2 − y 2) = z 2. Since x and y are coprime (this can be assumed because otherwise the factors could be cancelled), the greatest common divisor of x 2 + y 2 and x 2 − y 2 is either 2 (case A) or 1 (case B). The theorem is proven separately for these two cases.
obtained their generating function and studied their asymptotics at large n. Clearly, G n = G n (1). These numbers are strictly alternating G n (k) = (-1) n-1 |G n (k)| and involved in various expansions for the zeta-functions, Euler's constant and polygamma functions. A different generalization of the same kind was also proposed by Komatsu [31]
[1] [2] Examples of Real-time simulation settings include control systems in electronics and visualization of model results while examples for a many-query setting can include optimization problems and design exploration. In order to be applicable to real-world problems, often the requirements of a reduced order model are: [3] [4]