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Bra-ket notation
... 1 gives us the completeness relation . Eigenvalue equation The bra-ket notation turns out useful even for the eigenvalue equation for observables. Consider an observable A ...
Wiki article - Anonymous (not verified) - 26/10/2015 - 17:56 - 0 comments
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Density matrix
... ρ is a positive semidefinite hermitian operator (its eigenvalue s are nonnegative) and the trace of ρ (the sum of its eigenvalues) ...
Wiki article - Anonymous (not verified) - 08/09/2020 - 13:08 - 0 comments
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Pure states
... (consisting of all density operators with at least one zero eigenvalue) is much larger than the set of extreme points (which have all but one eigenvalue zero). Caratheodory's Theorem guarantees that every point in a ...
Wiki article - Anonymous (not verified) - 26/10/2015 - 17:56 - 0 comments
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Observables and measurements
... spectrum from ( a , b ) ⊂ R . Each eigenvalue x is associated with a unique eigenstate $|\psi(x)\rang$ ... there could be several eigenstates corresponding to a given eigenvalue is mathematically a little bit more involving, but essentially the ...
Wiki article - Anonymous (not verified) - 26/10/2015 - 17:56 - 0 comments
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Quantum error correction and fault-tolerance
... procedure can be used to measure (non-fault-tolerantly) the eigenvalue of any (possibly multi-qubit) Pauli operator M : Produce an ... final state still tells us nothing about the data beyond the eigenvalue of M . If we perform a Hadamard transform and then measure ...
Wiki article - Anonymous (not verified) - 26/10/2015 - 17:56 - 0 comments
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Basic concepts in quantum computation
... of U is not altered along this network, but its eigenvalue e i ϕ is ``kicked back'' in front of the ... of ( − 1) f ( x ) which corresponds to the eigenvalue of the state of the auxiliary qubit under the action of the operator ...
Wiki article - Anonymous (not verified) - 04/01/2016 - 11:49 - 0 comments
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Mixed states
... characterized by the majorization relation between the eigenvalue sequences. Numerical measures of mixedness are functions on the ...
Wiki article - Anonymous (not verified) - 26/10/2015 - 17:56 - 0 comments
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Geometric (holonomic) gates
... ⟩ belonging to an eigen-space \cal{H}_0 with associated eigenvalue e.g., ɛ 0 = 0 . Due to the time ordering symbol the ... function ɛ 0 ( t ) varying the energy eigenvalue. The results would be unaltered apart from the insertion of a ...
Wiki article - Anonymous (not verified) - 26/10/2015 - 17:56 - 0 comments
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Grover's search algorithm
... observable, Ω , acting on H , with N distinct eigenvalue s whose values are all known. Each of the eigenstates of Ω ... is to identify this eigenstate |ω>, or equivalently the eigenvalue ω, that Uω acts specially upon. Steps of the algorithm The ...
Wiki article - Anonymous (not verified) - 03/11/2015 - 06:20 - 0 comments
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PhD Studentships in Theoretical Physics: theory of quantum information processing
... potential advisor References. [1] A variational eigenvalue solver on a photonic quantum processor Alberto Peruzzo, Jarrod ...
Position - Biamonte - 03/05/2020 - 19:10 - 0 comments