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The fidelity between two quantum states and , expressed as density matrices, is commonly defined as: [1] [2] (,) = ().The square roots in this expression are well-defined because both and are positive semidefinite matrices, and the square root of a positive semidefinite matrix is defined via the spectral theorem.
The approach is based on the relation between the fidelity and the quantum Fisher information and that the fidelity can be computed based on semidefinite programming. For systems in thermal equibirum, the quantum Fisher information can be obtained from the dynamic susceptibility. [29]
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 ...
Manufacturer Name/codename designation Architecture Layout Fidelity (%) Qubits (physical) Release date Quantum volume Alpine Quantum Technologies PINE System [2]: Trapped ion
For example, low-fidelity data can be acquired by using a distributed simulation platform, such as X-Plane, and requiring novice participants to operate in scenarios that are approximations of the real-world context. The benefit of using low-fidelity data is that they are relatively inexpensive to acquire, so it is possible to elicit larger ...
For an electron, s is 1 ⁄ 2, and m s is either + 1 ⁄ 2 or − 1 ⁄ 2, often called "spin-up" and "spin-down", or α and β. [ 1 ] [ 2 ] The term magnetic in the name refers to the magnetic dipole moment associated with each type of angular momentum, so states having different magnetic quantum numbers shift in energy in a magnetic field ...
In 2 dimensions, the adiabatic exchange of particles is not necessarily possible. Instead, the eigenvalues of the exchange operator may be complex phase factors (in which case ^ is not Hermitian), see anyon for this case. The exchange operator is not well defined in a strictly 1-dimensional system, though there are constructions of 1 ...
The same approach has been used in chemical photography to capture an extremely wide dynamic range: A three-layer film with each underlying layer at one hundredth (10 −2) the sensitivity of the next higher one has, for example, been used to record nuclear-weapons tests. [56] Consumer-grade image file formats sometimes restrict dynamic range. [57]