Algorithmic cooling
A qubit (or quantum bit) is a unit of information that can be in a superposition of two states, denoted as formula_1 and formula_2. The general superposition can be written as formula_3where formula_4 and formula_5. If one measures the state of the qubit in the orthonormal basis composed of formula_1 and formula_2, one gets the result formula_1 with probability formula_9 and the result formula_2 with probability formula_11.
Cubic field
A cubic field is called a pure cubic field, if it can be obtained by adjoining the real cube root formula_2 of a cubefree positive integer "n" to the rational number field Q. Such fields are always complex cubic fields since each positive number has two complex non-real cube roots.A cyclic cubic field "K" is its own Galois closure with Galois group Gal("K"/Q) isomorphic to the cyclic group of order three. However, any other cubic field "K" is a non-galois extension of Q and has a field extension "N" of degree two as its Galois closure. The Galois group Gal("N"/Q) is isomorphic to the symmetric group "S" on three letters.