Page 84 - Principles and Applications of NanoMEMS Physics

2. NANOMEMS PHYSICS: Quantum Wave-Particle Phenomena 71

quantum gate transforming a qubit state such that 0 → 0 and

1 → exp ( )1tiω , would have the form [102],

ª1 0 º
U( θ) = « θ i » , (76)
¬ 0 e ¼

where θ = t ω . Since U is a unitary reversible transformation, the quantum
gate must be reversible. This means that, given the output, one must be able
to uniquely determine the value of the input. There are a number of
important quantum gates of which quantum information processing systems
are made of, namely, the identity gate [100-111],

0 → 0 , (77)

1 → 1 , (78)

the NOT gate,

0 → 1 , (79)

1 → 0 , (80)

the Z gate,

0 → 0 , (81)

1 → − 1 , (82)

and the Hadamard gate,

0 → 0 + 1 , (83)

1 → 0 − 1 . (84)

Quantum gates are represented graphically, as in Figure 2-12 [111]. In this
figure the operation of the gate is read from left to right using the following
convention. Each line represents the propagation or evolution of the input