Quantum

NOT gate is implemented by phase encoding technique of light waves in our

previous work 26. The realization of phase encoded quantum NOT gate is

briefly described in the following section.

Quantum

NOT gate matrix is expressed by Pauli-x matrix 27

The

quantum states and can be represented by the column vector

representation as,

= and = .

The

block diagram to implement quantum NOT gate by phase encoding technique is

shown in fig.1.

Fig.1 Schematic diagram of implementation of NOT gate by phase

encoding. Here ‘PS’, ‘BS’ and ‘M’ are ? phase shifter, beam splitter and mirror

respectively.

Here

the main light source is divided into three parts. The first one is considered

as the reference beam with the initial phase ?, and the other two parts serve

as the input signal beams. I1 and I2 respectively, which represent

two input light beams and O1 and O2 are the corresponding

output light beams. EOM1

and EOM2 are two Lithium niobate (LiNbO3) based electro-optic

modulators, operated simultaneously by the biasing voltage VNOT,

which causes an additional phase difference of ? to the input light beams.

Now,

at first, the quantum state is

taken, then the phases of input light at I1 and I2 are

(?+?) and ? with respect to the reference beam (with initial phase angle ?). The

phase shifter (PS) is to be used in any of the two inputs (I1 or I2)

to satisfy the desired input state. So the portion in fig. 1 with dotted area

serves as NOT logic gate.

Then

after passing through the modulators, the phase of the output light beams O1

and O2 becomes (?+2?) and (?+?). Therefore in other words it can be

said that the first output O1 is in same phase with the reference

beam and the second one is ? out of phase with the reference beam. So the

output logic state () is the inverted version of the input

logic state (). Therefore a quantum NOT operation is

done by the system. Table. 1 shows the phase encoded truth table for

representing the phases of the input and output signal beams with respect to

the reference beam.

Table 1: Input and Output phase

differences with respect to the reference beam.

Phase difference of

Input signal beams with respect to

reference beam

Phase difference of

Output signal beams with respect to

reference beam

I1

I2

O1

O2

?

0

2? (0)

?

0

?

?

2 ?

(0)