Set of universal logic gates

Having demonstrated, by construction, that each of the computational elements required of a conventional digital computer for its own computation - namely, (1) digital bit-stream signals, (2) wires, (3) redirection circuits, (4) an internal system clock, (5) a (potentially infinite) memory, and (6) a set of universal logic gates... 

In classical computation, any logical operation can be done from combinations of the logic gate nand (NOT-AND). The similar is true in quantum computing any quantum operation can be implemented using a set of universal logic gates. Such a set is composed of the Hadamard (H), controlled NOT (CNOT), phase (S) and jr/8 (T). 

Obviously that B and C can be recovered by applying the gate to B and C. Tha-efore, the gate is reversible. Fredkin gate can be used to built an universal set of classical logic gates. 

A set G of logic gates is universal if an arbitrary ri-variable Boolean function T can be written as a composition of the logic gates in G a universal set of gates 9u- - dm is. sometimes also said to gorm a basis set for T. It is easy to show that the set consisting of the Boolean operators AND, OR and NOT, for example, is universal. ... 

The question which Landauer failed to ask in 1961 [land61] and which was answered first by Bennett in 1973 [benu73] and later, independently, by Predkin [fredkiu82], is whether irreversible logic gates are essential to computation. Might it be possible to construct a universal set out of reversible gates ... 

The ability of an experimental technique for preparing initial states and implementing an universal set of logic gates are two important features for its use in quantum information processing. Another equally important requirement is the characterization of the output state. In many cases we wish more than a simple readout, but a full characterization of the system state. This can achieved by determining all elements of the density matrix of the... 

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