Informally, a set of universal quantum gates is any set of gates to which any operation possible on a quantum computer can be reduced, that is, any other unitary operation can be expressed as a finite sequence of gates from the set. Technically, this is impossible since the number of possible quantum gates is uncountable, whereas the number of finite sequences from a finite set is countable. To solve this problem, we only require that any quantum operation can be approximated by a sequence of gates from this finite set. Moreover, for the specific case of single qubit unitaries the Solovay–Kitaev theorem guarantees that this can be done efficiently.
One simple set of two-qubit universal quantum gates is the Hadamard gate, the gate, and the controlled NOT gate.
A single-gate set of universal quantum gates can also be formulated using the three-qubit Deutsch gate, which performs the transformation
The universal classical logic gate, the Toffoli gate, is reducible to the Deutsch gate, thus showing that all classical logic operations can be performed on a universal quantum computer.
Read more about this topic: Quantum Gate
Famous quotes containing the words universal, quantum and/or gates:
“The philosopher is like a man fasting in the midst of universal intoxication. He alone perceives the illusion of which all creatures are the willing playthings; he is less duped than his neighbor by his own nature. He judges more sanely, he sees things as they are. It is in this that his liberty consists—in the ability to see clearly and soberly, in the power of mental record.”
—Henri-Frédéric Amiel (1821–1881)
“A personality is an indefinite quantum of traits which is subject to constant flux, change, and growth from the birth of the individual in the world to his death. A character, on the other hand, is a fixed and definite quantum of traits which, though it may be interpreted with slight differences from age to age and actor to actor, is nevertheless in its essentials forever fixed.”
—Hubert C. Heffner (1901–1985)
“The gates of Hell are open night and day;
Smooth the descent, and easy is the way:
But, to return, and view the cheerful skies;
In this, the task and mighty labour lies.”
—Virgil [Publius Vergilius Maro] (70–19 B.C.)