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Paper text:
the growing interest in quantum computation stimulates the search for new schemes to prepare and manipulate qubits .
numerous proposals have been introduced for experimental realization of a quantum computer ( qc ) zel , n . from the theoretical point of view qc could in principle be realized by a one - dimensional array of simple two state systems , such as single electron spins , coupled via the heisenberg interaction ( see , for example , refs .
the ising - spin chain has also been proposed as a model system which allows to implement a quantum computer lloyd , berman . moreover
, the switchable heisenberg interaction alone can provide the universal quantum computation @xcite .
however , in many proposals for quantum computation , two bit operations , whose implementation depends on the interaction between qubits , require to switch on and off the couplings between qubits , which is not experimentally easy to realize . for these schemes it is required precise control of the magnitude of the heisenberg interaction and effectively turn on and off it .
there are also proposals with the permanent interaction between qubits ( see , for example refs .
however , perpetual untunable coupling of qubits causes certain problems for realization of quantum gates , depending on the particular form of the interaction . particularly for the one dimensional ising spin chain qc complicated protocols with many
_ pulses ( for correcting phase and probability errors ) are needed for single and two qubit gates @xcite , which requires high precision and complicates the operation .
for example , @xmath0 _ rf _ pulses with the particular set of phases are necessary for not gate and @xmath1 pulses for control - not gate between neighboring qubits .
the possibilities avoiding switching of interaction between qubits have been investigated in refs .
@xcite . in ref .
@xcite it has been considered architecture of the qc showing that the heisenberg interaction can be effectively negated by inserting epr spin pairs ( in singlet state ) between the information carrying qubits . in ref .
@xcite it has also been considered architecture of the qc with ising interaction . with the encoded qubits ( two physical qubits ) ising interaction can also be negated . in ref .
@xcite it has been shown that one can perform quantum computation in a one dimensional heisenberg chain in which the interactions are always on , provided that one can abruptly tune the zeeman energies of the individual qubits .
other schemes avoiding problems of perpetual coupling exist too .
for instance , in ref .
@xcite authors describe an architecture of qc based on a processing core where multiple qubits interact perpetually , and a separate ` store ' where qubits exist in isolation .
the obstacles connected with implementation of single and two bit gates with permanent interaction between qubits are also overcome in the proposal of qc , which is known as one way quantum computer  @xcite . here
one can implement a quantum computer on a lattice of qubits with only single bit measurements on a cluster states @xcite , which are created with the controllable ising interaction .    in this work we consider the model of quantum computer , which is represented as a ising spin lattice where qubits ( spin - half systems ) are separated by the isolators ( two spin - half systems ) .
this architecture is analogous to one considered in ref .
@xcite for off diagonal interactions between qubits where it was proposed to implement a virtual switch by carrying out the steps of the quantum computation in and out of designed interaction free subspaces .
in contrast to ref .
@xcite the architecture considered in the present paper is based on the ising type interaction and it is not required turning on and off couplings between isolators . hence , this scheme allows to compute without switching the couplings and simplifies the operation of qc compared to one dimensional ising spin chain qc @xcite .
the paper is organized as follows .
the ising spin quantum computer model is described in sec .
ii . the realization of the universal gates are considered in sec .
iii . in sec .
iv we summarize our results .
architecture of the quantum computer with the ising spin lattice is shown in fig .
1 . it is assumed that information carrying qubits are situated in the middle chain and do not directly interact .
qubits in the upper and lower chains play the rule of isolators .
we assume that in the idle mode or at the single bit operations the spins of isolators are oppositely directed . in this case for two neighboring qubits of middle chain , the total ising interaction is vanished for arbitrary states of qubits .
this can be achieved at the initialization of the system by two ways .
firstly , if one applies a strong global field in the @xmath2 direction to all qubits , at low temperatures all spins will line up with the field
. then one should flip the states of the qubits situated at either above or below chains .
secondly , one can assume that the global fields are inverted for the upper and lower spin chains .
hence , if larmor frequencies of qubits are much greater than ising interaction constant , then ground state of our model will coincide with the desired initial state of qc .
then for the initialization of the qc one should just cool the system .
note , that this architecture is also relevant to a system with the heisenberg interaction .
as is known , if the frequency difference between the neighboring spins is much greater than the spin - spin interaction , then the heisenberg interaction tends to an effective ising form @xcite . in this case
the main technical challenge is the creation of a large gradient of the magnetic field and the decoherence caused by the sources of the magnetic field .
the latest development of the micropattern wires technique provides the magnetic field gradients @xmath3 @xcite and opens new possibilities for realization of ising spin qc .
the hamiltonian for the ising spin lattice ( fig .
1 ) placed in an external nonuniform magnetic field can be represented as@xmath4@xmath5    here @xmath6 , @xmath7 is the operator of the @xmath2 component of @xmath8th spin ( @xmath9 ) with larmor frequency @xmath10 , @xmath11 is the interaction constant between qubits and isolators , and @xmath12 is the interaction constant between isolators . to distinguish the isolators from the information carrying qubits we additionally label these qubits via subscripts @xmath13  ( upper qubits ) and @xmath14  ( lower qubits ) .
the initial wave function of the qc can be represented as@xmath15with the energy@xmath16 .
\label{energy}\ ] ]    we assume that single bit gates are easy and fast to implement either by individual addressing of single qubits or by selective electromagnetic pulses whose frequencies are close ( resonant transition ) to the larmor frequencies of the desired qubits . for the latter case
it has been assumed nonuniform magnetic field in the hamiltonian ( [ ham ] ) .
since qubits are not coupled to each other , fully parallel operations are possible .
in contrast to one dimensional ising chain @xcite in the considering model there is no need of complicated protocols for correcting the phase and probability errors due to permanent interaction between the qubits . as we will see below two qubit universal gate between neighboring qubits
can be realized simply operating on the isolators .
in this section we describe the protocols for the two qubit universal gates . for this purpose
it is sufficient to consider one elementary cell , with two qubits and isolators .
the hamiltonian of elementary cell in the external _ rf _ field can be represented as@xmath17@xmath18 + s_{a}^{+}\exp \left [ i\omega _ { a}t\right ] \right\ } , \label{hceel}\]]where @xmath19 , @xmath20 is the frequency of the pulse , and @xmath21 is the rabi frequency .
we assume that the initial state is@xmath22@xmath23 is the possible overall phase .    under the condition @xmath24 ( @xmath25 ) the pulse effectively affects only above located spin ( resonant transition ) .
in this case , evolution of the wave function ( [ iwf ] ) is confined within subspace ( 8 dimensional ) of the entire hilbert space of four qubits and can be written in the form ( in the interaction picture)@xmath26@xmath27\]]@xmath28@xmath29 ,   \label{wf}\]]where @xmath30 and @xmath31 ( @xmath32 ) are probability amplitudes of the states with energies:@xmath33@xmath34@xmath35@xmath36@xmath37from the schrdinger equation@xmath38one can obtain the equations for the probability amplitudes @xmath30 and @xmath39 .
system of coupled differential equations for the coefficients @xmath30 , @xmath31 splits into four independent groups .
each group consists of two equations of the form@xmath40@xmath41the detunings in eq .
( [ eqc ] ) are @xmath42@xmath43assuming rectangular _ rf _ pulse , for the initial conditions@xmath44the solution of eq .
( [ eqc ] ) is@xmath45@xmath46where @xmath47 is the pulse duration and @xmath48 .    for the realization of controlled phase gate ( [ cphase ] ) we will consider two cases , depending on the magnitude of spin - spin interaction . if the spin - spin interaction is strong enough , i.e. @xmath49 @xmath21 , then under the resonance condition @xmath50 we have@xmath51and for the couplings@xmath52@xmath53the states @xmath54 , @xmath55 and may be neglected:@xmath56for the resonant states we have@xmath57and the @xmath58 pulse with the pulse duration @xmath59 will be sufficient for the cphase gate ( [ cphase ] ) ( at that isolator returns to its initial state ) . in this case
the clock speed of qc will be @xmath60 .    if @xmath61 , then all states will be excited and as it follows from eq .
( [ sol ] ) for the control - phase gate one should require@xmath62@xmath63solving these equations for the couplings and detuning we obtain@xmath64@xmath65particularly for @xmath66 from eqs .
( [ nonr ] ) we have@xmath67and for the pulse duration from eq .
( [ mcond ] ) we obtain @xmath68 .
the resulting unitary transformation is@xmath69which is an entangling gate . in this case
the clock speed of qc will be @xmath70 .
it is easy to show that this gate , along with two suitable single - qubit gates ( rotations around the z axis ) , generates the known universal phase gate : @xmath71where the overall phase is @xmath72 .
it is simple to use established formalisms @xcite to generate a cnot gate by sandwiching a cphase gate between @xmath73 and @xmath74 qubits with hadamard gate @xmath75 .
in conclusion , we have described the model of quantum computer , which is represented as a ising spin lattice where qubits are separated by the isolators . for this architecture single and
two qubit gates are easy and fast to implement either by individual addressing of single spins or by selective electromagnetic pulse in contrast to one dimensional ising chain where due to permanent interaction between qubits complicated protocols for correcting the phase and probability errors are needed @xcite .
we discussed two possible physical realizations of the universal phase gate ; one when rabi frequency is much smaller than ising interaction constant and the other when rabi frequency is larger or comparable with ising interaction constant . in both cases the universal phase gate can be realized with the single pulse applied to isolator .
compared with the similar proposal of qc with encoded qubits @xcite , considered architecture is less complex in terms of the steps involved in generating one and two qubit gates .
we consider the model of quantum computer , which is represented as a ising spin lattice , where qubits ( spin - half systems ) are separated by the isolators ( two spin - half systems ) . in the idle mode or at the single bit operations the total spin of isolators is 0 . 
 there are no need of complicated protocols for correcting the phase and probability errors due to permanent interaction between the qubits . 
 we present protocols for implementation of universal quantum gates with the rectangular radio - frequency pulses .    
 ising spin quantum computer , universal gates . 
 03.67.lx , 03.67.-a