The QuBit
The QuBit
Computers use switching states of transistors that can assume the classical state 0 or 1 to store information or perform computing operations. In a quantum computer, the smallest unit of information is called a QuBit. Unlike the bit, which assumes either one or the other state (0 or 1), a QuBit Q consists of an arbitrary superposition of these two states:
\Ket{Q}=\alpha\Ket{0}+\beta\Ket{1}α and β are (in general) complex numbers indicating the fraction for 0 and 1, respectively. The state 0 resp. 1 and the state Q are represented as vectors on the surface of a Bloch sphere [1]:
Excursus: Vector representation and braket notation
\Bra{0}=\begin{bmatrix} 1 & 0 \end{bmatrix}; \Bra{1}=\begin{bmatrix} 0 & 1 \end{bmatrix}
The values for α and β are normalized so that their square results in the value 1:
|\alpha|^{2} + |\beta|^{2}=1In this case, |α|2 and |β|2 indicate the probabilities of which state the QuBit is currently in. A permissible state for a QuBit is shown in the next figure, where the probability of encountering 0 or 1 is 50% to 50% [1]:
This state is abbreviated as |+〉.
Measurement of a QuBit state
Once the state of a QuBit is determined by a measurement, it transitions to one of the two classical states 0 or 1 with probability |α|2 or |β|2, respectively.
Sources
[1] M. Ellerhoff. Mit Quanten Rechnen. ISBN 978-3-658-31221-3