Charge qubit
In quantum computing, a charge qubit is a qubit whose basis states are charge states (e.g. states which represent the presence or absence of excess Cooper pairs in the island). In superconducting quantum computing, a charge qubit is formed by a tiny superconducting island (also known as a Cooper-pair box) coupled by a Josephson junction to a superconducting reservoir (see figure). The state of the qubit is determined by the number of Cooper pairs which have tunneled across the junction. In contrast with the charge state of an atomic or molecular ion, the charge states of such an "island" involve a macroscopic number of conduction electrons of the island. The quantum superposition of charge states can be achieved by tuning the gate voltage U that controls the chemical potential of the island. The charge qubit is typically read-out by electrostatically coupling the island to an extremely sensitive electrometer such as the radio-frequency single-electron transistor.
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.