Whereas in a classical computer the bit is the unit of information, in a quantum device called a quantum computer-which is a special type of quantum automaton- this is replaced by a corresponding concept called qubit.
In order to have any practical use such a qubit must also meet several conditions, such as: it has to be measurable, undergo controlled unitary transformations, have a long coherence time, be capable of initialization,
and so on. Scalability to a quantum state space
of
column vectors
with the inner product
is also such a condition, where
denotes the transpose conjugate of
. Then a unit vector
in
denotes a quantum state. As an example, in a superconducting flux qubit an electric current can be imagined to circulate simultaneously in a stable (or coherent) loop both clockwise and counterclockwise. A qubit in such a superposition is in a highly symmetrical quantum state. Superconducting qubits involve large numbers of particles (Cooper pairs) as the superconducting current involves many billions of such coherent electron pairs. In such a many-particle superconducting loop, spontaneous symmetry breaking
tends to determine the qubit to end up in a definite state, by `breaking up the superposition'. On the other hand, an ion suspended in a magnetic trap or a single electron in a quantum dot on a chip
do not exhibit this phenomenon. In August 2005, a group
of physicists at the National Institute of Standards and Technology (NIST) suceeded in preparing single-ion qubits with a coherence time longer than 10 seconds.
Furthermore, one can define as follows a more complex concept than the qudit by allowing for entanglement of quantum states.
Quantum computers could then perform calculations by manipulating qubits within a quantum register. However, the requirement for long coherence times may be a major obstacle to building quantum computers [1].
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