In conventional computers, the computation carrying out

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1 nternational Conference on Communication and Signal Processing, pril 3-5, 24, ndia Design Of ll Optical Reversible Logic Gates Kuki ordoloi, T. Theresal, Shanthi Prince bstract-considering the benefits of Quantum and Optics, if the logic gates in the quantum field and electronic structure are implemented using optical elements, then it will be benefited from advantages of Quantum and design, and these processing circuits can be used in optical computing and quantum computing, genetic processes, and other useful nanotechnology applications. dvantages of reversible logic systems and circuits have drawn a significant interest in recent years as a promising computing paradigm having application in low power COS, quantum computing, nanotechnology, and optical computing. n this study, we have introduced reversible optical Double Feynman gate using optical ach-ehnder interferometer () switches with new design. The proposed optical Double Feynman gate will be optical logic gate and reversible. s the proposed gate is a complete one, it can implement all the -based quantum circuits. ndex Terms- Feynman Gate, ach-ehnder interferometer (), Optical Double Feynman Gate, Reversible Logic.. NTRODUCTON n conventional computers, the computation carrying out is irreversible i.e. once logic block generates the output bits, the input bits are lost []. ut it is not in the case of reversible logic circuits. The classical set of gates such as ND, OR and EOR are not reversible as they are all multiple input single output logic gates. gate is reversible if the gate's inputs and outputs have a one-to-one correspondence, i.e. there is a distinct output assignment for each distinct input [2]. Therefore, a reversible gate's inputs can be uniquely determined from its outputs. Reversible logic gates must have an equal number of inputs and outputs [3]. Then the output rows of the truth table of a reversible gate can be obtained by permutation of input rows. Reversible logic circuits have emerged as a promising technology in the field of information processing. rreversible hardware computation results in energy dissipation due to information loss. On the other hand, the reversible logic circuits offer an alternative that allows computation with arbitrary small energy dissipation. There is number of existing reversible gates in literature like Fredkin, Feynman and Toffoli gates etc [4]. Each of these gates is universal, i.e. any logical reversible circuit can be implemented using these gates. ll-optical logic for optical network is an exciting field of research where we can expect much innovation. High capacity, low cost communication systems are needed to keep up with the increasing demand for the broad band communications. Photon being the ultimate unit of information with unmatched speed and with data package in a signal of zero mass, the techniques of computing with light may provide a way out of the limitations of computational speed and complexity inherent in electronics computing. Different optical logic gates have already been proposed to perform irreversible logic function. ut, reversible computation in a system can be performed if the system is composed of reversible gates. The all optical implementation of reversible gates can be designed based on semiconductor optical amplifier (SO) based ach-ehnder interferometer () due to its significant advantages such as high speed, low power, fast switching time and ease in fabrication. Semiconductor optical amplifier (SO) based ach-ehnder interferometer () can play a significant role in this field of ultra-fast all-optical signal processing. The interferometer employs bidirectional couplers and semiconductor amplifier in one of its arms. nterferometer acts as a very high speed switch since it does not need any conversation from optical to electronic and vice versa. This paper is organized as follows. n section, principle and operation of based optical switch is discussed. n section, all-optical circuit of Feynman gate is discussed. ll-optical circuit of Fredkin gate is discussed in section V. Simulation results using OptiSystem software confirming describe methods are also given in this paper. n section V, a new design of reversible optical Double Feynman gate is proposed. Finally, the conclusions are formulated.. SO SED CH-EHNDER NTERFEROETER () Kuki ordoloi is with Department of Electronics and Communication Engineering, SR University, Kattankulathur , Tamil Nadu, ndia ( kukibordoloi622@gmail.com). T.Theresal is a assistant professor in Department of Electronics and Communication Engineering, SR University, Kattankulathur , Tamil Nadu, ndia ( theresa24@gmail.com). Shanthi Prince is a professor in Department of Electronics and Communication Engineering, SR University, Kattankulathur , Tamil Nadu, ndia ( shanthi.p@ktr.srmuniv.ac.in) /4/$3\. 24 EEE SWTCH ach-ehnder nterferometer () Switch, as shown in the Fig.l and Fig.2 is a very powerful optical device to realize ultra-fast all optical switching [5]. n this switch a semiconductor optical amplifier is inserted in each arm of. The incoming signal to be switched is split between the +,EEE dvancing Technology for Humanity 583

2 arms of the interferometer. The interferometer is balanced so that, in the absence of a control signal, the incoming signal emerges from one output port. The presence of a strong control pulse changes the refractive index of the medium. change in the index adds a phase shift between the two arms of the interferometer, so that the incoming signal is switched over to another output port. This method of switching is based on cross-phase modulation (P). simulate optical links in the transmission layer of modern optical networks [7].... Opta T Dcft:.ulVltOlbr OpacoTlll Domai V-_3r_2 ::t::s:,gnr'«j 6i'OOl.8(arPort).(CrossPort) Fig. 3. Simulation Setup of switch in OptiSystem. Fig.. Semiconductor optical amplifier based ach-ehnder interferometer. The simulated results of based switch using OptiSystem as obtained in the optical time domain visualizer is given in Fig. 4. ncoming Signal - Control Signal z ar Port ---- ( u pper channel) ---_ Cross Port (lower channel).,- ' _--'=_.=L-,---'--,--, :::oo,-t w i ' _. ='-_ :,:. c -x v. rc_,_ Fig. 2. ach-ehnder interferometer based all optical switch. There two input ports and called as incoming signal port and control signal port respectively and two output ports called as bar port and cross port respectively in a switch [6]. We consider no light or absence of light as the logic value O. When there is an incoming signal at port and control signal at port then there is a light present at the output bar port and there is no light at the output cross port. n the absence of control signal at the input control port and when there is an incoming signal at input port then the outputs of are switched and result in the presence of light at the output cross port and no light at the bar port. n the absence of incoming signal at the input port there is no light at both the output ports. The above behavior of can be written as oolean functions having inputs to outputs mapping as (,) to ( =, = ), given in Table. Table T Truth Table of l based switch nput ncoming Signal Control Signal ar Port Cross Port The simulation setup of based switch using OptiSystem software is shown in Fig. 3. OptiSystem is a comprehensive design suite that enables users to plan, test, and nput () R- _ c2-:::>:r::...,':..rn=:'.u.llze 3 i,;'-' -..L..=----'------''''t x yt,'.' o :. v'j, nput () <GOp () () Fig. 4. Simulated inputs and outputs of switch. U :.: ;=o. ''''' ' _.,.,..,, u...- :..:r;::,'.::o.,.u,. -'- 584

3 . SED FENN GTE.i Feynman gate is a 2x2 reversible gate having and as input vector and and as output vector, where =, =G;> [8], given in Table...i L <. =. <,_ o...,,,_, ;,;. Optical Tme DOOleln Visualizer ' li r'n.coioo. rcooog,_ () L <O.,''''..._,.. Optical Time Domain Vlsualizer_,, (, :=: nput () f-----+x U P ut',... c_-i',,, 5(...-, * -'.,---=-k o- / t The circuit of all- optical based Feynman gate is shown in Fig. 5. and the simulation setup Feynman gate using OptiSystem software is shown in Fig. 6. 'it-' ='---'-''---'' -' '''-; -'\'owoo< Optical Time Domain Vlsuallzer_3 Table Truth Table of Feynman Gate nput <. =. < '''' o,.,_, r v Fig. 5. ll-optical circuit of Feynman gate. C: beam combiner, : EDF, S: 5:5 beam splitter Cal i rlnve..colo.. rcooog,_ () Fig. 7. Simulated inputs and outputs of Optical Feynman gate. --- V. SED FREDKLN GTE Fredkin gate is a 3x3 reversible logic gate having,,c as input vector and,, as output vector, where =, ---, = E9 C, = C E9 [9], given in Table. Table Truth Table of Fredkin Gate nput C. ---, Fig. 6. Simulation Setup of Feynman gate. The simulated results of optical Feynman gate using OptiSystem is given in Fig. 7. The all-optical circuit of Fredkin gate is shown in Fig. 8. and the simulation setup of the same using OptiSystem software is shown in Fig. 9. nput () 585

4 S - l c '.' Optical Time Domain VisuaUzer_3 _ <_._. _ '.oo, i----+y i---+ () 2 Fig. 8. ll-optical circuit of Fredkin gate.... Vlauallz... r_4... Optical Time Domain _<,.''.oo, ii Hi :l=:=,.\ J\P y T7., () =i?--' Fig. 9. Simulation Setup of Fredkin gate. () The simulated results of optical Fredkin gate using OptiSystem is given in Fig.. Fig.. Simulated inputs and outputs of Optical Fredkin gate. V. PROPOSED SED LL-OPTCL DOULE FENN GTE er T y; Double Feynman gate is 3x3 reversible logic gate having,, C as input vector and,, as output vector, where =, =(j;) and =(j;)c []. The schematic block diagram is shown in Fig. and truth table is given in Table V., nput ()...uanz.h _c..?t<}=..?:':nr:;-' o,;,;... J. J\ y T _ '. :::2j :::wwi...-,, r c,o,_ r. ' Fig.. Table V Truth Table of Double Feynman Gate i Ho...t...=..?';::nln';, ;'.uallz.- o.,; o / x O. -=-=-==--= :_:'.9'= _ o oooo O' ':_u<,==..r_. W w V nput () Schematic diagram of Double Feynman gate. nput ().J. DFG C :;;,::;:: : : :::_ =: j.. /\ {J: 2 nput C The all optical circuit of Double Feynman gate using OptiSystem is shown in Fig

5 () When ==C=O, i.e. when no inputs are given(absence of light), then there is no output ===O. (2) When ==O and C=, incoming signal is absent at -l, -2 and -4,then no light comes out through cross or bar port of -l, -2 and -4. ncoming signal is present at -3 but control signal is absent. Hence, the light beam emerging out through C3 gives the output =.Therefore, when ==O and C= then =O, =O, =. t satisfies the second row of the truth table given in Table V given in Table V. (7) When == and C=O, then the -3 receives no light in the incoming port, so 3=C3=. -l, -2 and -4 receives the incoming signal. Since c=o there is no control signal in -4 thus 4= and C4=, which gives =. oth the -l and -2 receives both the incoming and the control signal thus,=2= and C,=C2=, which gives = and =O.Therefore, when = and = and c=o then == and =o. t satisfies the seventh row of the truth table given in Table V. (8) When ==C=, then -l, -2, -3 and - 4 receives both the control and the incoming signal. Thus,=2=3=4= and C,=C2=C3=C4=, which gives =, =O and z=o. Therefore, when = and = and C= then = and =z=o. t satisfies the eight row of the truth table given in Table V. The truth table for the proposed optical Double Feynman gate is verified theoretically. The proposed model of optical Double Feynman gate is being simulated using OptiSystem. The simulation setup of the proposed optical Double Feynman using OptiSystem software is shown in Fig. 3. c ---''+--> OJ:o:or.. o..._ Fig. 2. ll-optical circuit of Double Feynman gate. C: beam combiner, [> EDF, S: 5:5 beam splitter. (3) When =C=O and = then incoming signal is absent at -2, -3 and -4. So no light comes out through cross or bar port of -2, -3 and -4.For -l since incoming signal = and control signal =O thus bar port receives no light i.e.,=o and cross port receives light so C,= which gives the output =. Therefore, when =C=O and = then =O, =, z=o. t satisfies the third row of the truth table given in Table V. (4) When =O and =C=, then the -2 and -4 receives no light in the incoming port, so 2=C2=4=C4=. -l and -3 receives the incoming signal and no control signal thus,=3= and C,=C3= which gives x=o and ==. Therefore, when =O and =C= then =O, =, =. t satisfies the fourth row of the truth table given in Table V. (5) When = and =C=O, then the -l and -3 receives no light in the incoming port, so,=c,=3=c3=. -2 and -4 receives the incoming signal and no control signal thus 2=4= and C2=C4=, which gives ===. Therefore, when = and =C=O then ===. t satisfies the fifth row of the truth table given in Table V. (6) When =C= and =O, then the -l receives no light in the incoming port, so,=c,=o. -2, -3 and -4 receives the incoming signal. ut since =O there is no control signal in -2 thus 2= and C2=, which gives = and =. oth the -3 and -4 receives both the incoming and the control signal thus 2=4= and C2=C4=, which gives =O.Therefore, when = and =O and C= then == and z=o. t satisfies the sixth row of the truth table.:;':-) m: oi_ OllltOl :. C\a:.Or.. }...) Qr:ooo T... Fig. 3. Simulation Setup of optical Double Feynman gate. The simulated results of proposed optical Double Feynman gate using OptiSystem is given in Fig. 4. Optical Tlrne Domain Viaualizer_2 K =.., O.y,.,,_,.,_ o o-- --.=. er. Poweo- \ Power y Tj nput () Sjgnllnde, r necqo< r Coc<G,,,,d... ::t:l, 587

6 Optical Time Domain Vi.ualier_3.. a,,,n an«o.. g.' Se.. ct oom Rag'n. Pr.. Cont<O K.. y a n.a Sign'llnde: :E) V. CONCLUSON n this paper, the all-optical design of reversible Double Feynman gate is proposed and described. The simulation of existing all-optical Feynman and Fredkin gates using OptiSystem software are also done. ll these gates can be considered as basic gates and the arithmetic and logic operations in reversible systems can be performed. L-. =. -= _:; _v nput ( lo ) Optical Time Domain Vi.ualier_8 ;;. j, Co. ' o o, < So.d OOm Ro, oo' =.,,,.o Co. nput () ;;, ;; L... auo':':ct<:;=;o:=:;':' K ncl L :l r nve,tcoo<$ r CoO<G.cie REFERENCES [] R.Landauer, rreversibility and heat generation in the computational process, Journal of research and developrnent, 83-9 (\96). [2] C.H.ennett, Logical reversibility of computation, Journal of research and development. 7, (973). [3] Tanay Chattopadhyay, ll-optical modified fred kin gate, Selected Topics in Quantam Electronics, EEE Journal, vol. PP, no.99, pp.-8, 22. [4] Shweta grawal, etaphorical study of reversible logic gate, nternational Journal of nnovative Research in Computer and Communication Engineering, Vol., issue 4,June 23. [5] Saurabh Kotiyal, Himanshu Thapliyal and Nagarajan Ranganathan, ach-ehnder interferometer based design of all-optical reversible binary adder, EEE 22. [6] Saurabh Kotiyal, Himanshu Thapliyal and Nagarajan Ranganathan, ach-ehnder nterferometer ased all-optical Reversible NOR Gates, EEE 22. [7] [8] Prashant R. elekar and Sujata S.Chiwande, Design of sequential circuit using reversible logic, EEE CES- arch 3, 3, 22. [9] Sujata S.Chiwande, Shilpa S.Katre, Sushmita S.Dalvi, Jyoti C Kolte, Performance analysis of sequential circuits using reversible logic, nternational Journal of Engineering Science and nnovative Technology, Vol. 2, issue l,january 23. [O] ahram Dehghan, Design of asynchronous sequential circuits using reversible logic gates, nternational Journal of Engineering and Technology, Vol 4, No 4 ug-sep 22.. =. <=r /. P v 7 f.l () J- 9 Optical Tme Domain Visuall:z.er_ Co., -., '... d oom R.,... =.,_, «.. _ c. : i - (). Optical Tlme Domain Vlsualler_5 Co. Ro., < So.d oom R.,.... =.... oo. Co.... r/l...-..x_v/' t (OlOllOlO) Fig. 4. Simulated inputs and outputs of optical double Feynman gate. 588