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2nd International Science, Social Science, Engineering and Energy Conference 2010: Engineering Science and Management

Quantum CNOT Gate Operation using Dark-Bright Soliton Pair

Suphanchai Punthawanunta , Preecha P. Yupapinb,*, Xaythavy Louangvilayc and Somsak Mitathad

aFaculty of Science, Kasem Bundit University Bangkok 10250, Thailand bNanoscale Science and Engineering Research Alliance, Advance Research Center for Photonics, Faculty of Science

King Mongkut’s Institute of Technology Ladkrabang Banglok 10520, Thailand cInsternational College, King Mongkut’s Institute of Technology Ladkrabang Bangkok 10520, Thailand

dHybrid Computing Research Laboratory ,King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand

Elsevier use only: Received 15 November 2010; revised 15 December 2010; accepted 20 December 2010

Abstract

A simple system of a quantum CNOT gate operation using dark and bright solitons in a Mach Zhender interferometer (MZI) is proposed. In this concept, two qubits are randomly generated by using the coincidence dark and bright soliton states within the

MZI, in which ( D ) and ( B ) represent the orthogonal dark and bright soliton states, which they are input into the MZI input ports simultaneously. The randomly input dark and bright soliton pulses can perform the random logical codes after propagating through a phase retarder of ( /2). By using low power soliton, the soliton power can reduce to a single photon power (10-6 W), where finally the quantum gate can be performed by using the single photon detection scheme. The quantum controlled-NOT (CNOT) gate is formed by controlling the input and coincidence solitons (photons), where in some cases the phase shifter is required to obtain the coincidence solitons. type your own text. This preparation guide is a slight modification of IEEE format. © 2010 Published by Elsevier Ltd.

Keywords: Quantum logic, Quantum gate, Photonic circuit, Dark-Bright soliton pair, Orthogonal soliton

1. Introduction

Quantum computer has been recognized as the interesting tool in various applications, in which the factoring power and efficient simulation dynamics are the important advantages, furthermore, the reversible operation of the quantum algorithm/computer is the another interesting aspect. In practice, the basic element of quantum computer is the logical device (gate), in which many research works have been reported the use of quantum gates for quantum computing operation [1-7]. To date, the quantum bit (qubit) generation based on an optical technique is one of the most successful techniques [8-14], which is regarded as a prominent candidate for the robustness against decoherence problem. Recently, the interesting behavior of dark-bright soliton conversion within the microring

* Corresponding author. Tel.: +6-689-445-2224; fax: +6-627-227-262 E-mail address: suphanchai@kbu.ac.th..

© 2011 Published by Elsevier Ltd.

1877–7058 © 2011 Published by Elsevier Ltd.doi:10.1016/j.proeng.2011.03.082

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device has been proposed [15, 16], in which the random output of both solitons can be separated and observed when the dark-bright soliton pair is propagated through a ( /2) phase retarder, for instance, an optical coupler or beam splitter. Hence, dark and bright soliton are the orthogonal pulses and can be recognized as an entangled photon pair. In this work, we present the use of a photonic circuit (Mach Zhender interferometer, MZI) for quantum CNOT gate operation, where the main concept is that the random logic codes can be formed by using dark and bright soliton pair, in which the difference in phase of these two solitons with ( /2) can be used to form the orthogonal photon components. In particular, the attenuated soliton power can be used to form the logic code in the same way of the single photon behavior. This means that the random logic code can be encoded by 0 D and 1 B , where D and B are the orthogonal components representing dark and bright solitons, respectively. We have also found that the synchronous quantum switching can be obtained by controlling the input codes, in which the coincidence in time between the input dark and bright soliton at the first and second couplers is the key concept of the random dark-bright soliton conversion. Therefore, if there is any change in phase of the coincidence soliton, the phase shifter is required as shown in Fig. 1, where finally, the quantum CNOT gate can operate. In practice, to avoid the external electrical source, the nonlinear device such as a nonlinear ring resonator is recommended to use as a phase shifter. From the simulation results, the obtained synchronous switching times are 0.5-2.0 ps and 0.5 ps, 1.6 ps, however, the switching time can be changed and provided by using the phase shifter.

2. Operating Principle

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Dark and bright solitons are the short optical pulses that can propagate into the optical medium for long period of time due to their nonlinear properties, for instance, self phase and cross phase modulations [17]. The lack of phase with (�/2) between dark and bright solitons can be used to form the orthogonal photon components (entangled photon). More details of dark and bright soliton generation and behaviors can be found in both theory and experiment in the references [18-20]. Here, the proposed model for quantum controlled-NOT (CNOT) gate generation system using dark-bright soliton conversion is as shown in Fig. 1. Qubits can be generated by dark-bright optical soliton conversion within the system, in which the zero logical state 0 (or dark soliton input pulse: D ) and the logical one 1 (bright soliton input pulse: B ) are encoded into MZI. The random states between dark and bright solitons can be established within the photonic circuit, in which the output of the orthogonal states can be randomly detected via the MZI output ports.

When the dark and bright soliton pulses are generated and input into the system, the optical fields propagate through the photonic circuit are expressed by Eqs. (1) – (3).

1 1

11 2 21 1

21 2 2

E In j AE A j In (1)

12

12 11

22 21

j

L

E E e

E E e (2)

1 1

12 222 21 1

22 22 2

Th E j EDrop E j E (3)

where In is an input field, A is an added field (control), E11 and E21 are fields spit into two arms of MZI passing through the first coupler as shown in Fig. 1. E12 and E22 are optical fields before merging into the second coupler. Th and Drop are the output field signals of quantum CNOT gate. L1 is a lower MZI arm, with length 8 m. is the nonlinear phase shift depending on In and A input signals, and j is a complex conjugate term.

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Fig. 1. A schematic of quantum CNOT gate based on MZI.

We are looking for the stationary dark and bright soliton pulses, which are introduced into the MZI ports as

shown in Fig. 1. The input optical fields, Ein and Eadd, of the dark and bright solitons, respectively, are given by [9]

tiLz

TTAtE

Din 0

0 2exptanh ,

tiLz

TThAtE

Dadd 0

0 2expsec (4)

where A and z are the optical field amplitude and propagation distance, respectively. T is a soliton pulse propagation time in a frame moving at the group velocity, T=t 1*z, where 1 and 2 are the coefficients of the linear and second-order terms of Taylor expansion of the propagation constant. LD=

20 2T is the dispersion length of the

soliton pulse. T0 in equation is a soliton pulse propagation time at initial input (or soliton pulse width), where t is the soliton phase shift time, and the frequency shift of the soliton is 0. This solution describes a pulse that keeps its temporal width invariance as it propagates, and thus is called a temporal soliton. When a soliton peak intensity

22 0T is given, then T0 is known. For the soliton pulse in the MZI device, a balance should be achieved

between the dispersion length (LD) and the nonlinear length (LNL=1/ NL), where =n2*k0, is the length scale over which dispersive or nonlinear effects makes the beam become wider or narrower. For a soliton pulse, there is a balance between dispersion and nonlinear lengths, hence LD = LNL.

3. Quantum CNOT Gate Operation

All paragraphs must be indented. All paragraphs must be justified, i.e. both left-justified and right-justified. In this simulation, dark and bright soliton with the center wavelength at 1.55 m is propagated into the MZI input ports. The attenuated soliton peak power at the input coupler is 1 mW, 20 ns pulse width, and the waveguide loss of 1dBmm-1 is included in the simulation data. In operation, the dark soliton D or bright soliton B fields are input into the In and A ports, in which the input fields are combined and split into two parts with the same amount via a 3dB coupler (50:50), which they are E11 and E21. The field E12 is the output field of E11 after propagating into the phase shifter. The first dark-bright soliton conversion pulses (E11 and E21) are formed by a first coupler. We found that the quantum Hadamard gate operation can be obtained via the coupler output, for instance, the obtained logical codes are DD DD , DB DB , BD BD and BB BB , as shown in Fig. 2(a)-(d), respectively. Finally, the fields are combined again at the second 3dB coupler after the phase controlled device (phase shifter), in which the random combination of the orthogonal pulses (dark and bright soliton pulses) can be obtained via the MZI ports. The Th port output is the required quantum CNOT gate result as shown in Fig. 3. Hence, the quantum CNOT gate operation using the single photon is also possible by using the soliton power attenuation. From Fig. 3(a)-(d), the quantum CNOT gate codes obtained in terms of wavelengths from the Th port are DD BD , DB BB , BD DD and BB DB , respectively. For the optimum case, the dark soliton D or bright soliton B states

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are required to control by using the In and A input fields and the phase shifter. If no phase shift device is introduced, the quantum CNOT operation is interrupted.

From the results in Fig. 2, the form of the quantum CNOT gate is expressed by DD DD DD , 2DB DB BD DB , 2BD DB BD BD , and BB BB BB , in which the first and second

arrows represent the action of the first and second quantum Hadamard gates, respectively. Fig. 4 shows the switching output power of quantum CNOT gate operation based on MZI, where we found that when In and A codes are input the same logical codes, for instance, DD or BB , the switching time of the logical signals at Th and Drop ports is faster than the one with different input codes, as shown in Fig. 4(a) and 4(d). When In and A input codes are DB , the switching time of the output at Drop port is faster than the Th port switching time, and when the In and A input codes are BD , the switching time of output code at Th port is faster than Drop port. Here, one interesting aspect of the results is that the synchronous switching (same switching time) between the Th and Drop port codes can be operated throughout the operation time (from 0.5 to 2 ps), which is confirmed by the results in Fig. 4(a) and 4(d). The synchronous quantum switching times of the results in Fig. 4(b) and 4(c) are 0.5 and 1.5 ps. This means that the switching control of quantum clock of 1 ps is noted, which is available for quantum memory application. In application the quantum memory time can be adjusted by the phase shifter, i.e. phase controller. Hence, the synchronous switching operation is provided by using the synchronous time between drop and through port signals, in which the reference time is recognized by the drop port. The next switching code can be operated after the previous switching operation, in which the time interval of both switching periods is the clock/memory time, i.e. quantum clock.

Fig. 2. Simulation results of dark and bright solitons when the logical inputs are (a) DD , (b) DB , (c) BD , and (d) BB

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Fig. 3. Simulation results of the quantum CNOT gate operation in terms of wavelengths when the logical inputs are (a) DD , (b) DB , (c) BD , and (d) BB .

Fig. 4. Simulation results of the switching time of quantum CNOT gate operation, when the logical inputs are (a)

DD , (b) DB , (c) BD , and (d) BB .

4. Conclusion

We have proposed the new technique of quantum CNOT gate operation, in which the simple quantum logic gate system based on MZI and dark-bright soliton conversion can be realized. By using two states of soliton pulses (Dark and Bright solitons), the random states between dark and bright soliton can be established within the system, in which the soliton states can be randomly detected. Moreover, the Hadamard gate operation and result is also seen. The novelty of the work is that the use of dark-bright soliton conversion to form the random qubits has never presented elsewhere. The obtained synchronous quantum switching times are 0. 5- 2.0 ps, 0.5 and 1.6 ps, which

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they are available for quantum synchronous switching applications, where in this case the quantum memory time of 1ps is noted. In this work, the simulation result is based on the use of practical device parameters, whereas the device fabrication to form the realistic device and application is plausible. The obtained output power of nW to W is seen, which is available for single photon gate application. Furthermore, the switching time delay may be solved by using the phase shifter, where the number of codes (quits) can be increased by using the same circuit incorporating a nonlinear device, for instance, a nonlinear ring resonator, which will be our continuing works.

5. Acknowledgment

We would like to give our acknowledge to the AUN/SEED-Net for the fully financial support to Mr. Xaythavy LOUANGVILAY in higher education at International College, King Mongkut’s Institute of Technology Ladkrabang(KMITL), Bangkok 10520, Thailand. References [1] M. R. Geller, E. J. Pritchett, A. Galiautdinov, and J. M. Martinis, “Quantum logic with weakly coupled qubits,” Phys. Rev. A 81, 012320

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