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the use of quantum systems for information processing was first introduced by benioff @xcite . in 1985 deutsch described quantum computers which exploit the superposition of multi particle states , thereby achieving massive parallelism @xcite . researchers have also studied the possibility of solving certain types of problems more efficiently than can be done on conventional computers @xcite . these theoretical possibilities have generated significant interest for experimental realization of quantum computers @xcite . several techniques are being exploited for quantum computing and quantum information processing , including nuclear magnetic resonance ( nmr ) @xcite . nmr has played a leading role for the practical demonstration of quantum gates and algorithms . most of the nmr quantum information processing ( qip ) experiments have utilized systems having indirect spin - spin couplings ( scalar j couplings ) @xcite . recently nmr qip has been demonstrated in quadrupolar and dipolar coupled systems , obtained by orienting the molecules in liquid crystal media @xcite . in case of homo nuclear dipolar coupled systems , spins are often strongly coupled and hence can not be addressed individually @xcite . however the @xmath0 eigen states are collectively treated as an n - qubit system @xcite . similarly for quadrupolar systems ( spin @xmath1 1/2 ) , individual spins are treated as a multi - qubit system @xcite . resolved resonance lines provide access to the full hilbert space of @xmath0 dimension @xcite .    a quadrupolar nucleus of spin i has ( 2i+1 ) energy levels , which are equi - spaced in the high magnetic field and the 2i single quantum transitions are degenerate . in the presence of first order quadrupolar interaction this degeneracy is lifted and gives rise to 2i equi - spaced transitions @xcite . for molecules partially oriented in anisotropic media , such as liquid crystals , such a situation is often obtained @xcite . if @xmath2 , such a system can be treated as an n - qubit system @xcite . the advantage of such systems and the dipolar coupled systems , over the j - coupled systems is that the coupling values are one to two orders of magnitude larger , allowing shorter gate times or the use of shorter transition selective pulses . so far quadrupolar systems have been used for , quantum simulation , preparation of pseudo pure states , implementation of quantum gates and search algorithms @xcite . recently das et al have implemented cleve version of 2-qubit dj algorithm on a spin 7/2 nucleus @xcite . in all these cases the controlled gates are implemented by inverting populations between various levels , by using transition selective @xmath3 pulses . recently it has been demonstrated that non - adiabatic geometric phases can be used for implementing quantum gates @xcite . here we use non - adiabatic geometric phases to implement controlled phase shift gates and collins version of dj algorithm on a 3-qubit system obtained by eight eigen states of a spin-7/2 quadrupolar nucleus . the hamiltonian of a quadrupolar nucleus partially oriented in liquid crystal matrix , in the presence of large magnetic field @xmath4 , having a first order quadrupolar coupling , is given by ,    @xmath5}s(3i_z^2-i^2 ) = \omega_o i_z+2\pi \wedge ( 3i_z^2-i^2 ) ,   \label{6eqn1 } \end{aligned}\ ] ]    where @xmath6 is the resonance frequency , s is the order parameter at the site of the nucleus , and @xmath7 is the quadrupolar coupling . if the order parameter s is small , the effective quadrupolar coupling @xmath8 can be of the order of a few khz in spite of @xmath7 being of the order of several mhz . thus , it is possible to observe the satellite transitions due to first order quadrupolar coupling .    a 50 - 50 mixture of cesium - pentadecafluoro - octanate and @xmath9 forms a lyotropic liquid crystal at room temperature @xcite . the schematic energy level diagram of oriented spin-7/2 nucleus is shown in fig . ( [ equi]a ) . the 8 energy levels are labeled as the basis states of a three qubit system . in the high field approximation , effective quadrupolar coupling ( @xmath8 ) can be considered as a small perturbation to zeeman field . thus for population purposes the equilibrium density matrix can be considered to be proportional to @xmath10 ( fig . [ equi]a ) . partially oriented @xmath11 nucleus ( i=7/2 ) gives rise to a well resolved 7 transitions spectrum at room temperatures ranging from 290 k to 315 k fig ( [ equi]b ) . the effective quadrupolar coupling ( @xmath8 ) changes with temperature , since the order parameter is a function of temperature . all the experiments have been carried out here at temperature 307 k , which gives @xmath12 hz . the equilibrium spectrum is obtained by applying a @xmath13 pulse , is shown in fig.([equi]b ) . the integrated intensities are in the expected ratio 7:12:15:16:15:12:7 , as determined by the transition matrix elements of @xmath14 ( appendix ) @xcite . non - adiabatic geometric phase in nmr was first verified by suter et.al @xcite . non adiabatic geometric phases in nmr , were used to implement controlled phase shift gates , deutsch - jozsa ( dj ) and grover algorithms in weakly j - coupled and strongly dipolar coupled systems @xcite . a two level subspace ( r , s ) forms a fictitious spin-1/2 subspace , hence the states @xmath15 and @xmath16 can be represented on a bloch sphere ( fig . [ quad - bloch ] ) @xcite . the two @xmath3 pulses applied on a transition ( r , s ) , cyclically rotates each of the states @xmath15 and @xmath16 @xcite . the cyclic path followed by each of the two states , makes an equal solid angle ( @xmath17 ) at the center of the bloch sphere @xcite . the geometric phase acquired by the states @xmath15 and @xmath16 is given by @xmath18 and @xmath19 respectively @xcite , where the phase difference of @xmath20 between the states indicate that the two states are traversed in the opposite direction @xcite it is possible to obtain various solid angles , hence various phases , by shifting the phases of the two @xmath3 pulses with respect to each other ( fig . [ quad - bloch ] ) @xcite . it is shown that two @xmath3 pulses with phases @xmath21 and @xmath22 respectively , applied on a transition ( r , s ) , subtends a solid angle @xmath23 , thus the phase acquired by the states @xmath15 and @xmath16 is @xmath24 and @xmath25 respectively . however the internal hamiltonian evolves during the application of a transition selective @xmath3 pulse , and gives rise to an additional phase known as dynamical phase . in order to observe only the geometric phase , one has to refocus the evolution of internal hamiltonian . as shown in eq . ( [ 6eqn1 ] ) , the hamiltonian consists of larmor frequency term and quadrupolar coupling term . the larmor frequency is identical to the frequency of central transition d. thus the receiver frequency is set at frequency of transition d ( fig . [ equi]a ) , hence there is no evolution due to the larmor frequency term . the duration of the selective @xmath3 pulse is chosen in such a way that the phase acquired by the quadrupolar term makes a complete @xmath26 rotation , in other words @xmath27 , where @xmath28 is duration of the selective @xmath3 pulse which is equal to 1.425 ms . the phase information can be encoded in the coherences , hence in order to observe the phases the initial state should contain the coherences , which is obtained by applying a non - selective @xmath13 pulse on equilibrium state . figure ( [ gates]a ) shows the implementation of controlled phase shift gate , represented by the diagonal matrix @xmath29 $ ] , obtained by applying two selective @xmath3 pulses on transition ( 3,4 ) , with phases y and @xmath30 . the two states @xmath31 and @xmath32 acquire @xmath3 phase shift so the transitions b and d are inverted , confirming the phase gate . since the phases of two @xmath3 pulses are same , it is possible to combine the two @xmath3 pulses in to a single @xmath26 pulse . such pulses are used in section ( 3.1 ) .    in some quantum computing protocols ( for example grover search algorithm and quantum fourier transform ) one requires a phase gate such as @xmath33 ( table . 1 ) , which creates the relative phase @xmath24 at @xmath34 state , for example @xmath35=@xmath36 $ ] . such phase gates can be implemented by sandwiching various phase gates @xmath37 , as shown in table ( 1 ) . @xmath37 indicates the geometric phase shift gate obtained by applying a pair of selective @xmath3 pulses on a transition ( i , j ) with phases y and @xmath38 , thus the diagonal elements corresponding to i and j states , acquire a phase shift @xmath24 and @xmath25 respectively . for example , @xmath39=diag[@xmath40 , @xmath41 , 1 , 1 , 1 , 1 , 1 , 1 ] , which can be obtained by applying two selective @xmath3 pulse on transition ( 1,2 ) with phases y and @xmath42 . the method of constructing controlled phase shift gates ( table 1 ) , is explained here . for example , consider a system consisting of n energy levels and ( n-1 ) single quantum transitions between the levels ( 1,2 ) , ( 2,3), ..... (n-1,n ) , as shown in fig.([nlevels ] ) . in this system , the controlled phase shift gate @xmath43 $ ] , can be implemented by sandwiching ( n-1 ) phase shift gates , as ,    @xmath44    in eq . ( [ eqn5 ] ) , by putting n=8 one can obtain any of the @xmath33 shown in table ( 1 ) .    in table ( 1 ) , each of the operators , @xmath33 , requires seven pairs of selective @xmath3 pulses , where each pair of pulses will act on a single transition . however the @xmath3 pulses on unconnected transitions can be applied simultaneously . hence one can simultaneously implement @xmath45 , @xmath46 , @xmath47 , @xmath48 by using a pair of multi - frequency ( mf ) pulses , similarly @xmath49 , @xmath50 , @xmath51 can be implemented by using another pair of multi - frequency pulses . for example @xmath52 can be implemented by using seven geometric phase shift gates ( table 1 ) , obtained by using two pairs of multi - frequency @xmath3 pulse , as described below . @xmath53    the unitary operators of phase shift gates correspond to diagonal matrices which commute with each other , hence @xmath52 of eq . ( [ 6eqn13 ] ) can be rewritten as ,    @xmath54.[u_{(3,4)}^{5\phi/8}].[u_{(5,6)}^{3\phi/8}].[u_{(7,8)}^{\phi/8}]\}.\{[u_{(2,3)}^{3\phi/4 } ] . [ u_{(4,5)}^{\phi/2}].[u_{(6,7)}^{\phi/4}]\ } \nonumber \\ & = & \ { [ ( \pi)_y^a(\pi)_{y+\pi+7\phi/8}^a].[(\pi)_y^c(\pi)_{y+\pi+5\phi/8}^c].[(\pi)_y^e(\pi)_{y+\pi+3\phi/8}^e ] . [ ( \pi)_y^g(\pi)_{y+\pi+\phi/8}^g]\}.   \nonumber \\ & & \ { [ ( \pi)_y^b(\pi)_{y+\pi+3\phi/4}^b].[(\pi)_y^d(\pi)_{y+\pi+\phi/2}^d].[(\pi)_y^f(\pi)_{y+\pi+\phi/4}^f]\ } \nonumber \\ & = & \ { [ ( \pi)^{a , c , e , g}_y.(\pi)^{a , c , e , g}_{(y+\pi+7\phi/8),(y+\pi+5\phi/8),(y+\pi+3\phi/8),(y+\pi+\phi/8 ) } ]    \}.\nonumber \\   & & \ { [ ( \pi)^{b , d , f}_y.(\pi)^{b , d , f}_{(y+\pi+3\phi/4),(y+\pi+\phi/2),(y+\pi+\phi/4 ) } ]    \ }    \label{6eqn5}\end{aligned}\ ] ]    the @xmath3 pulses acting on unconnected transitions , a , c , e and g ( eq . [ 6eqn5 ] ) , can be combined ( added ) in to a single pulse , since the operators of the subspaces corresponding to these transitions , @xmath55 , @xmath56 , @xmath57 and @xmath58 @xcite , commute with each other . similarly one can combine the @xmath59 pulses acting unconnected transitions b , d and f ( eq . [ 6eqn5 ] ) . figure ( [ gates]b ) shows the spectrum obtained by a @xmath13 pulse followed by the implementation of @xmath60 using four mf-@xmath3 pulses ( eq . [ 6eqn5 ] ) , the state @xmath61 hence the transition a acquires a @xmath62 phase shift , confirms @xmath63 .    table ( 1 ) . unitary operators of controlled-@xmath64 phase shifted gates +     @xmath65=u_{(1,2)}^{7\phi/8}.u_{(2,3)}^{3\phi/4}.u_{(3,4)}^{5\phi/8}.u_{(4,5)}^{\phi/2}. u_{(5,6)}^{3\phi/8}.u_{(6,7)}^{\phi/4}.u_{(7,8)}^{\phi/8}$ ] + @xmath66=u_{(1,2)}^{-\phi/8}.u_{(2,3)}^{3\phi/4}.u_{(3,4)}^{5\phi/8}.u_{(4,5)}^{\phi/2}.u_{(5,6)}^ { 3\phi/8}.u_{(6,7)}^{\phi/4}.u_{(7,8)}^{\phi/8}$ ] + @xmath67=u_{(1,2)}^{-\phi/8}.u_{(2,3)}^{-\phi/4}.u_{(3,4)}^{5\phi/8}.u_{(4,5)}^{\phi/2}.u_{(5,6)}^ { 3\phi/8}.u_{(6,7)}^{\phi/4}.u_{(7,8)}^{\phi/8}$ ] + @xmath68=u_{(1,2)}^{-\phi/8}.u_{(2,3)}^{-\phi/4}.u_{(3,4)}^{-3\phi/8}.u_{(4,5)}^{\phi/2}.u_{(5,6)}^ { 3\phi/8}.u_{(6,7)}^{\phi/4}.u_{(7,8)}^{\phi/8}$ ] + @xmath69=u_{(1,2)}^{-\phi/8}.u_{(2,3)}^{-\phi/4}.u_{(3,4)}^{-3\phi/8}.u_{(4,5)}^{\phi/2}.u_{(5,6)}^ { 3\phi/8}.u_{(6,7)}^{\phi/4}.u_{(7,8)}^{\phi/8}$ ] + @xmath70=u_{(1,2)}^{-\phi/8}.u_{(2,3)}^{-\phi/4}.u_{(3,4)}^{-3\phi/8}.u_{(4,5)}^{-\phi/4}.u_{(5,6)}^ { -5\phi/8}.u_{(6,7)}^{\phi/4}.u_{(7,8)}^{\phi/8}$ ] + @xmath71=u_{(1,2)}^{-\phi/8}.u_{(2,3)}^{-\phi/4}.u_{(3,4)}^{-3\phi/8}.u_{(4,5)}^{-\phi/2}.u_{(5,6)}^ { -5\phi/8}. u_{(6,7)}^{-6\phi/8}.u_{(7,8)}^{\phi/8}$ ] + @xmath72=u_{(1,2)}^{-\phi/8}.u_{(2,3)}^{-\phi/4}.u_{(3,4)}^{-3\phi/8}.u_{(4,5)}^{-\phi/2}.u_{(5,6)}^ { -5\phi/8}.u_{(6,7)}^{-3\phi/4}.u_{(7,8)}^{-7\phi/8}$ ] + deutsch - jozsa ( dj ) algorithm determines in a single query , whether a given function is constant or balanced @xcite . a function is `` constant '' if it gives the same output for all inputs , and `` balanced '' if it gives one output for half the number of inputs and another for the remaining half @xcite . classically for an n bit binary function , at least ( @xmath73 ) queries are needed to determine whether the function is constant or balanced , whereas the dj algorithm requires only a single query @xcite . the cleve version of the dj algorithm requires an extra qubit ( ancilla qubit ) and uses controlled - not gates @xcite , whereas collins version does not require the ancilla qubit but needs controlled phase shift gates @xcite .    for a three qubit system there are 2 constant and 70 ( @xmath74=@xmath75 ) balanced functions @xcite . the quantum circuit of the collins version of the dj algorithm is shown in fig . ( [ djckt ] ) . the algorithm starts with a pure state ( pseudo pure state in nmr ) @xmath61 which is converted to a superposition state of eight basis states @xmath61 , @xmath76 , ..... , @xmath77 , by applying a pseudo hadamard gate on all the three qubits . thereafter a unitary operator @xmath78 ( oracle ) is applied , followed by detection . theoretically , after @xmath78 one has to apply the hadamard gate . in nmr , a hadamard gate is replaced by a pseudo hadamard gate , which is implemented by a @xmath79 pulse , and for detection another @xmath80 pulse is needed . these two pulses cancel each other and the result of the algorithm is available immediately after @xmath78 . the unitary operators ( u ) of the oracle , are eight dimensional diagonal matrices . for two constant functions , u s are given by ,    @xmath81=(-1).i . \end{aligned}\ ] ]    for balanced functions , we define the unitary operator as @xmath82 , which means that each of the four diagonal elements 1,k , l , and m are equal to -1 , whereas the remaining four diagonal elements are 1 . for example @xmath83 $ ] . the unitary operators of 35 balanced functions can be written as ,    @xmath84.i , \nonumber \\ where \hspace{0.2 cm } k < l < m , \hspace{0.2 cm } k=2,3 .. ,6 , \hspace{0.2 cm } l \ge k+1 , \hspace{0.2 cm } and \hspace{0.2 cm } m \ge l+1    \label{6eqn6}\end{aligned}\ ] ]    the unitary operators of the remaining 35 balanced functions are identical to one of the operators of eq . ( [ 6eqn6 ] ) , up to an overall phase factor @xmath20 @xcite . here we implement the unitary operators corresponding to 11 of the 35 balanced functions ( eq . [ 6eqn6 ] ) and one constant function ( @xmath85 ) .      * ( i)preparation of pseudo pure state ( pps ) @xmath86 : * a multi frequency pulse with six harmonics with appropriate amplitudes was applied . the six harmonics are the frequencies of the six leftmost transitions b , c , ... , ( [ equi]b ) . under the influence of this pulse , the populations of all the states except @xmath87 , start a collective population transfer among them as a linear chain of coupled oscillators @xcite . choosing the correct amplitudes of various harmonics and duration of the pulse , these six transitions can be simultaneously saturated with average population of these seven levels . the relative amplitudes of the six harmonics b , c , ... , and g are respectively given by 0.84 , 0.93 , 1 , 1.03 , 1.04 and 1.07 @xcite . the duration of the pulse is 2.05 ms . a gradient pulse was applied subsequently to kill ( dephase ) the coherences created during the process . the final populations were measured using a non - selective small - angle ( 5@xmath88 ) pulse . the small - angle pulse , converts the population differences between adjacent energy levels into single quantum transitions , within linear approximation . the spectrum of fig ( [ pps]b ) confirms the preparation of @xmath87 pseudopure state .    * ( iii ) coherent superposition : * after the creation of @xmath86 pps , a pseudo hadamard gate ( hard @xmath79 pulse ) creates a superposition of 8 basis states . it may be noted that unlike in weakly coupled spins , the state created here is not in equal superposition of eigenstates , since the coefficients of various eigenstates are different . however , as is shown here , the created coherent superposition can be utilized for quantum parallelism , to distinguish different classes of functions . the state of the system after a @xmath79 pulse on @xmath86 pps , is given by ,    @xmath89 \nonumber \nonumber \\   & = & \frac{1}{8\sqrt{2}}[\vert 1 \rangle + \sqrt{7 } \vert 2 \rangle + \sqrt{21 } \vert 3 \rangle + \sqrt{35 } \vert 4 \rangle + \sqrt{35 } \vert 5 \rangle + \sqrt{21 } \vert 6 \rangle + \sqrt{7 } \vert 7 \rangle + \vert 8 \rangle ] . \label{6eqn7}\end{aligned}\ ] ]    the corresponding density matrix can be written as ,    @xmath90    where the elements within the boxes represent single quantum transitions a , b , .. , g. figure ( [ pps]c ) shows the spectrum of @xmath91 , where the intensities of transitions are obtained by modulus of the product of single quantum elements of eq . [ 6eqn8 ] , with corresponding matrix elements of @xmath92 .    * ( iv ) implementation of u : * for constant function @xmath93 ( unit matrix ) , which requires no pulse , thus the final state @xmath94 is given by , @xmath95    as mentioned in section ( 2 ) , the controlled phase shift gate @xmath96 can be achieved by applying two @xmath59 pulses with same phase on transition ( i , j ) , which can be be combined in to a single @xmath97 pulse . for balance functions , u = @xmath82 ( eq . [ 6eqn6 ] ) , can be decomposed in to ,    @xmath98[u_{(l , l+1)}^{\pi}.u_{(l+1,l+2)}^{\pi} ... u_{(m-1,m)}^{\pi } ] \label{6eqn11}\end{aligned}\ ] ]    in eq . ( [ 6eqn11 ] ) , @xmath99 and @xmath100 are implemented by applying two @xmath101 pulses on transitions ( 1,k ) and ( l , m ) respectively , if ( 1,k ) and ( l , m ) does not correspond to single quantum transitions , then they can be decomposed in to a series of single quantum transitions , as shown in the second equality of eq . ( [ 6eqn11 ] ) , for example ,    @xmath102.[u_{(5,6)}^{\pi}. u_{(6,7)}^{\pi}.u_{(7,8)}^{\pi } ] \nonumber \\ & = & [ ( 2\pi)^a.(2\pi)^b.(2\pi)^c].[(2\pi)^e.(2\pi)^f.(2\pi)^g ] \nonumber \\ & = & ( 2\pi)^{a , c , e , g}.(2\pi)^{b , f } , \label{6eqn12}\end{aligned}\ ] ]    where in the last equality of eq . ( [ 6eqn12 ] ) , the pulses acting on unconnected transitions ( fig . [ equi ] ) are combined in to a single mf pulse . the required pulses for various @xmath82 of eq . ( [ 6eqn6 ] ) are given in table ( 2 ) , the @xmath26 pulses acting on unconnected transitions , are combined in to a single multi - frequency ( mf ) @xmath26 pulse . the duration of each transition selective pulse , is set such that the evolution due to quadrupolar coupling , makes a complete @xmath26 rotation . it is to be noted that , in eq . ( [ 6eqn12 ] ) and table ( 2 ) , one can use any phase for ( @xmath26 ) pulses , we have used y phase for all the pulses . the final state @xmath103 is given by    @xmath104    it can be seen that @xmath103 is same as @xmath91 , except that the basis states @xmath105 , @xmath106 , @xmath107 and @xmath108 acquire a phase factor @xmath20 ( = -1 ) . table ( 2 ) . unitary operators of balanced functions ( eq . [ 6eqn6 ] ) and corresponding pulse sequences , consisting of @xmath26 pulses , where all the pulses are applied with phase y.     sequence & u(1,k , l , m ) & pulse sequence + u(1,2,3,4 ) & @xmath109 & u(1,2,3,5 ) & @xmath109-@xmath110 & u(1,2,3,6 ) & @xmath111-@xmath110 + u(1,2,3,7 ) & @xmath111- @xmath112 & u(1,2,3,8 ) & @xmath113-@xmath112 & u(1,2,4,5 ) & @xmath114 + u(1,2,4,6 ) & @xmath114-@xmath115 & u(1,2,4,7 ) & @xmath116-@xmath115 & u(1,2,4,8 ) & @xmath116-@xmath117 + u(1,2,5,6 ) & @xmath118 & u(1,2,5,7 ) & @xmath118-@xmath119 & u(1,2,5,8 ) & @xmath120-@xmath119 + u(1,2,6,7 ) & @xmath121 & u(1,2,6,8 ) & @xmath121-@xmath122 & u(1,2,7,8 ) & @xmath123 + u(1,3,4,5 ) & @xmath114-@xmath124 & u(1,3,4,6 ) & @xmath114-@xmath125 & u(1,3,4,7 ) & @xmath116-@xmath125 + u(1,3,4,8 ) & @xmath116-@xmath126 & u(1,3,5,6 ) & @xmath118-@xmath124 & u(1,3,5,7 ) & @xmath118-@xmath127 + u(1,3,5,8 ) & @xmath120-@xmath127 & u(1,3,6,7 ) & @xmath121-@xmath124 & u(1,3,6,8 ) & @xmath121-@xmath128 + u(1,3,7,8 ) & @xmath123-@xmath124 & u(1,4,5,6 ) & @xmath111-@xmath124 & u(1,4,5,7 ) & @xmath111-@xmath127 + u(1,4,5,8 ) & @xmath113-@xmath127 & u(1,4,6,7 ) & @xmath129-@xmath124 & u(1,4,6,8 ) & @xmath129- @xmath128 + u(1,4,7,8 ) & @xmath130-@xmath124 & u(1,5,6,7 ) & @xmath129-@xmath131 & u(1,5,6,8 ) & @xmath129- @xmath132 + u(1,5,7,8 ) & @xmath130-@xmath131 & u(1,6,7,8 ) & @xmath113-@xmath131 & & +    * ( v ) detection : * the single quantum transitions ( a , b , .. g ) of the final states ( eq . [ 6eqn9],[6eqn10 ] ) are detected . figure ( [ dj1 ] ) shows the spectrum of @xmath133 and various @xmath103 . from the shape of the spectrum one can conclude , whether the final state represents a constant ( or ) a balanced function . for constant function ( @xmath133 ) none of the peaks are inverted , whereas for balanced functions ( @xmath134 ) atleast one of the peaks is inverted . furthermore the phases of transitions confirm the final state @xmath103 . for example in the spectrum of @xmath135 , transition d is negative since the phase difference between the states @xmath136 and @xmath137 is @xmath20 , while all others have zero phase difference , similarly one can confirm the other states . demonstration of quantum computing protocols on various nmr systems , is a promising research area for increasing number of qubits . in this work controlled phase shift gates are implemented on a oriented spin-7/2 nucleus , using non - adiabatic geometric phases obtained by using selective pulses on single quantum transitions . it is also demonstrated here that in an n level system , one can implement a controlled phase shift gate by sandwiching various geometric phase shift gates , this method can also be applied to weakly as well as strongly coupled spin-1/2 systems . the number of selective pulses are reduced by using multi frequency ( mf ) pulses . collins version of 3-qubit dj algorithm is implemented , where the eight basis states are collectively treated as a three qubit system . the required controlled phase shift gates of the algorithm , are implemented by using mf-@xmath97 pulses . the angular momentum operators of spin-7/2 nucleus , are given by @xcite ,                p. benioff , _ quantum mechanical models of turing machines that dissipate no energy _ lett . _ * 48 * , 1581 ( 1982 ) . d. deutsch , _ proc . london , ser . a _ * 400 * , 97 ( 1985 ) . d. deutsch and r. jozsa , _ rapid solution of problems by quantum computation _ , _ proc . a _ * 439 * , 553 ( 1992 ) . p. w. shor , _ polynominal - 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in this work controlled phase shift gates are implemented on a qaudrupolar system , by using non - adiabatic geometric phases . 
 a general procedure is given , for implementing controlled phase shift gates in an n level system . 
 the utility of such controlled phase shift gates , is demonstrated here by implementing 3-qubit deutsch - jozsa algorithm on a 7/2 quadrupolar nucleus oriented in a liquid crystal matrix .    .