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.
Qutrit
The qubit's orthonormal basis states formula_6 span the two-dimensional complex Hilbert space formula_7, corresponding to spin-up and spin-down of a spin-1/2 particle. Qutrits require a Hilbert space of higher dimension, namely the three-dimensional formula_8 spanned by the qutrit's basis formula_9
, which can be realized by a three-level quantum system. Note, however, that not all three-level quantum systems are qutrits.