Qubit
In quantum computing, a qubit () or quantum bit (sometimes qbit) is the basic unit of quantum information—the quantum version of the classical binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include: the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two states can be taken to be the vertical polarization and the horizontal polarization. In a classical system, a bit would have to be in one state or the other. However, quantum mechanics allows the qubit to be in a coherent superposition of both states/levels simultaneously, a property which is fundamental to quantum mechanics and quantum computing.
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.