
Quantum ComputingQuantum Computing 311
A generalization to three bits is the Controlled-Controlled-Not
(CCNOT) known as the Toffoli gate that can emulate any classical circuit.
In Fig. 15.4a the typical circuitry used in quantum circuits is illustrated and
in Fig. 15.4b the classical logic circuit.
15.3 Basic Mathematics Used in Quantum Computing
In this chapter, we used N, Z, Q, R, and C to denote the natural, integer,
rational, real and complex numbers respectively; therefore, we have that
. Most of the formulations in QC are achieved using
the sets R and C, since QM is founded in complex vectors. A vector space V
is a set on which two operations: ...