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Voltage stabilizers are additives capable of inhibiting electrical treeing; a degradation mechanism for insulation materials subjected to strong divergent electric fields.
Lecture 18: Geometric Application of Stabilizer 18 Stabilizer 18.1 Review A group action is when a group G acts on a set S by G×S → S. and sends (g, s) 7 →gs. The orbit of an element in s is all the elements it gets mapped to, O. s = {gs ∈ S : g ∈ G}, and the stabilizer is. Stab. G (s) := {g ∈ G : gs = s}≤ G, 18.2 Counting Formula
The stabilizer subtheory is built around the Clifford group, whose elements will be referred to as Clifford unitaries. To define these, we first introduce the Weyl operators (also called generalized Pauli operators). Consider a d-dimensional quantum system, and define the computational basis {|0i , . . . , |d − 1i} in its Hilbert space H.
Stabilizer codes are an important class of quantum codes whose construction is analogous to classical linear codes. Let Pn be the real valued group of matrices fI;X;iY;Zg as the basis. Note that this is a group, because it is closed under multiplication and contains inverses.
We say that a unitary U stabilizes a pure state |Ψ if U|Ψ = |Ψ . In other words, if |Ψ is an eigenstate of U with eigenvalue +1. Crucially, global phase matters here! If U|Ψ = –|Ψ , then U does not stabilize |Ψ . | as do their inverses U-1 and V-1. Also, the identity matrix, I, stabilizes everything.
Two stabilization mechanisms are possible: close approach. Thermal energy provides kinetic energy to the colloidal particles which collide with energy (kT). The charges on the particle surface provide an energy barrier to be overcome in order to have aggregation.
If x is a point of X, the elements of Gwhich leave x fixed form a subgroup of G called the stabilizer Gx of x. In Example (i) the stabilizer of each real number is the trivial subgroup {O} of 7l...
