processing information 
 with quantum states is expected to outperform 
 current computation technologies in some specific tasks . the main challenge continues to be finding suitable , 
 robust , and scalable physical systems for its implementation . individual 
 spins are natural candidates to realize the basic information units 
 of a quantum computer , that is , the qubits . molecules carrying several , individually addressable , spin qubits 
 can perform as quantum sensors , with sensitivities 
 exceeding those of most powerful classical devices , or even as quantum 
 processors , able to implement simple quantum algorithms . the first 
  quantum calculation  was , in fact , carried out using 
 the c and h nuclear spins of chloroform ( chcl3 ) . because nuclear spins are , 
 however , very difficult to initialize , such computations are performed 
 on distributions of thermally populated nuclear spin states ( nmr quantum 
 computation is , for this reason , often termed ensemble quantum 
 computation  ) rather than on individual quantum states , which 
 obscures their interpretation and limits their usefulness . electron 
 spins can , by contrast , be efficiently initialized by the application 
 of sufficiently strong magnetic fields at low temperatures . for this reason , a lanthanide ion with a doubly 
 degenerate magnetic ground state appears as a convenient realization 
 of a spin qubit . within this framework , 
 a promising approach toward realizing multiqubit 
 logic gates , such as the paradigmatic universal cnot gate ( see scheme 1 ) , coordination chemistry 
 offers the possibility of designing multimetallic molecular architectures 
 with predetermined structures . however , 
 given the very close chemical reactivities of all lanthanide metals , 
 it is extremely challenging to selectively position different 4f metals 
 on intended locations within the same molecule . most of the scarce existing examples of heterometallic 
 complexes have been prepared through stepwise procedures . otherwise , such species have been prepared and studied as part of 
 statistical mixtures , containing the corresponding fractions of the 
 homometallic analogues . given the well - known lanthanide contraction along the series attempts 
 of preparing 4f4f molecules under thermodynamic control 
 exploiting this property have been made using ligand systems that 
 generate disparate coordination sites . however , only deviations from 
 the expected statistical distributions have been achieved at most . here , we report a reaction system involving an asymmetric bridging 
 ligand , which leads to the direct formation of pure homo- or heterometallic 
 dinuclear complexes of lanthanide(iii ) ions sitting at intended positions 
 solely determined by their size differences . the synthetic method 
 reported here enables then the preparation of molecules containing 
 a large number of combination of two 4f metals . sufficient differences 
 in ionic radii have thus allowed the production of many [ lnln ] 
 molecules with a high degree of purity , quasi - on - demand , thus opening 
 the possibility of exploring such architectures as prototypes of two - qubit 
  molecular quantum processors  . the [ ceer ] species was 
 chosen as a close to ideal candidate to test this idea . ce(iii ) and 
 er(iii ) exhibit very different magnetic configurations : according 
 to hund s rules , ce(iii ) is characterized by a net angular 
 momentum j = /2 and a gyromagnetic 
 ratio gj = /7 , whereas er(iii ) has j = /2 and gj = /5 . in addition , both are kramer s 
 ions , thus meaning that the crystal field interaction leads to a doubly 
 degenerate ground state , i.e. , to a proper definition of qubit states . 
 and , finally , all stable ce isotopes have nonmagnetic nuclei , while 
 only 22.9% of the stable isotopes of er carry a nuclear spin . we experimentally show that this molecule fulfills 
 the necessary requirements to carry out universal quantum logic operations , 
 such as the cnot quantum gate . the cnot switches a target 
 bit if and only if a control bit is in a particular state ( here defined 
 as state |0 ) . each qubit state is typically represented by 
 a point on the surface of a bloch sphere , describing a quantum superposition 
 of states . the quantum gate operation is depicted , for simplicity , 
 on a target qubit in state |0. the ligand 6-(3-oxo-3-(2-hydroxyphenyl)propionyl)pyridine-2-carboxylic 
 acid ( h3l ) was prepared according to a previously published 
 procedure . a yellow solution of h3l ( 30.0 mg , 0.105 mmol ) in pyridine 
 ( 10 ml ) was added into a colorless 
 solution of ce(no3)36h2o ( 15.2 
 mg , 0.035 mmol ) and er(no3)35h2o ( 15.5 mg , 0.035 mmol ) in pyridine ( 10 ml ) . the mixture was stirred 
 for 2 h , and the resulting orange solution was layered with et2o . after 2 weeks , the complex was obtained as orange crystals 
 in 61% yield . calcd ( found ) for 11.3h2o1.7py : c 47.63 ( 47.58 ) , h 3.15 ( 3.04 ) , n 6.36 ( 6.46 ) . metal composition calcd ( found ) for 11.3h2o1.7py : ce 9.50 ( 9.37 ) , er 11.4 ( 10.9 ) . ir ( kbr pellet , cm ) : 3403 mb , 
 1618 s , 1584 s , 1558 m , 1528 s , 1463 m , 1401 s , 1384 s , 1324 m , 1299 
 m , 1240 w , 1201 w , 1147 w , 1120 w , 1060 w , 951 w , 890 w , 763 w , 706 
 w , 664 w , 635 w , 569 w. a yellow 
 solution of h3l ( 30.0 mg , 0.105 mmol ) in pyridine ( 10 ml ) 
 was added into a colorless 
 solution of la(no3)36h2o ( 15.2 
 mg , 0.035 mmol ) and er(no3)35h2o ( 15.5 mg , 0.035 mmol ) in pyridine ( 10 ml ) . the mixture was stirred 
 for 2 h , and the resulting orange solution was layered with et2o . after 2 weeks , the complex was obtained as yellow crystals 
 in 69% yield . calcd ( found ) for 41.7h2o1.2py : c 46.66 ( 46.59 ) , h 3.10 ( 2.98 ) , n 6.02 ( 6.12 ) . metal composition calcd ( found ) for 41.7h2o1.2py : la 9.64 ( 9.23 ) , er 11.6 ( 11.2 ) . ir ( kbr pellet , cm ) : 3447 mb , 
 1617 s , 1584 s , 1559 m , 1533 s , 1464 m , 1399 s , 1384 s , 1323 m , 1298 
 m , 1239 w , 1198 w , 1148 w , 1120 w , 1060 w , 951 w , 890 w , 764 w , 706 
 w , 668 w , 635 w , 568 w. a yellow 
 solution of h3l ( 30.0 mg , 0.105 mmol ) in pyridine ( 10 ml ) 
 was added into a colorless 
 solution of ce(no3)36h2o ( 15.2 
 mg , 0.035 mmol ) and y(no3)36h2o ( 13.4 mg , 0.035 mmol ) in pyridine ( 10 ml ) . the mixture was stirred 
 for 2 h , and the resulting orange solution was layered with et2o . calcd ( found ) for 51.8py : c 
 51.30 ( 51.13 ) , h 3.21 ( 3.22 ) , n 6.90 ( 7.09 ) . metal composition calcd 
 ( found ) for 51.8py : ce 10.1 ( 10.3 ) , y 6.44 ( 6.24 ) . 
 esi ms : m / z = 1078.97 [ cey(hl)2(h2l ) ] . ir ( kbr pellet , cm ) : 3446 mb , 1617 s , 1584 s , 1559 m , 1533 s , 1464 m , 1399 s , 1384 
 s , 1323 m , 1298 m , 1239 w , 1200 w , 1147 w , 1120 w , 1060 w , 951 w , 
 891 w , 763 w , 706 w , 664 w , 635 w , 569 w. a yellow solution 
 of h3l ( 30.0 mg , 0.105 mmol ) 
 in pyridine ( 10 ml ) was added into a colorless solution of ce(no3)36h2o ( 7.6 mg , 0.018 mmol ) and 
 y(no3)36h2o ( 20.1 mg , 0.053 
 mmol ) in pyridine ( 10 ml ) . the mixture was stirred for 2 h , and the 
 resulting orange solution was layered with et2o . after 
 2 weeks , orange crystals of 6 were obtained in 41% yield . calcd ( found ) for 60.5h2o1.3py : 
 c 50.81 ( 50.68 ) , h 3.21 ( 3.33 ) , n 6.61 ( 6.99 ) . esi ms : m / z = 1078.95 [ cey(hl)2(h2l ) ] and 1027.95 [ y2(hl)2(h2l ) ] . ir ( kbr pellet , cm ) : 3400 mb , 1618 s , 
 1584 s , 1558 m , 1529 s , 1464 m , 1404 s , 1384 s , 1325 m , 1299 m , 1240 
 w , 1206 w , 1148 w , 1121 w , 1059 w , 951 w , 891 w , 755 w , 707 w , 665 
 w , 636 w , 569 w. a yellow 
 solution of h3l ( 30.0 mg , 0.105 mmol ) in pyridine ( 10 ml ) 
 was added into a colorless 
 solution of la(no3)36h2o ( 15.2 
 mg , 0.035 mmol ) and y(no3)36h2o ( 13.4 mg , 0.035 mmol ) in pyridine ( 10 ml ) . the mixture was stirred 
 for 2 h , and the resulting yellow solution was layered with et2o . after 2 weeks , the complex was obtained as yellow crystals 
 in 40% yield . calcd ( found ) for 73.9h2o : c 45.92 ( 45.51 ) , h 3.30 ( 2.87 ) , n 5.35 ( 5.52 ) . ir ( kbr pellet , cm ) : 
 3445 mb , 1618 s , 1583 s , 1557 m , 1530 s , 1463 m , 1402 s , 1382 s , 1325 
 m , 1299 m , 1239 w , 1202 w , 1148 w , 1120 w , 1060 w , 951 w , 891 w , 762 
 w , 707 w , 664 w , 635 w , 569 w. crystals systematically suffer 
 from deterioration of crystallinity once out of their mother liquor , 
 likely due to lattice solvent loss . single crystals were therefore 
 selected and mounted directly from their mother liquor using the oil - drop 
 method and mounted as fast as possible into the cold n2 stream on the goniometer . data for compounds 15py , 65py , and 73py were collected using mo k 
 radiation (  = 0.710  73  ) at 150 k with an oxford 
 diffraction excalibur diffractometer with enhanced mo k radiation 
 (  = 0.710  73  ) at the x - ray diffraction and fluorescence 
 analysis service of the servicio general de apoyo a la investigacin - sai , 
 universidad de zaragoza . cell refinement , data reduction , and absorption 
 corrections were performed with the crysalispro suite . data for compounds 45.5py 
 and 55py were collected at 100 k with a bruker 
 apex ii ccd diffractometer on the advanced light source beamline 11.3.1 
 at lawrence berkeley national laboratory , from a silicon 111 monochromator 
 (  = 0.7749  ) . structures were solved with either sir97 or shelxs and refined on f with the shelxtl suite . hydrogens were placed geometrically 
 on their carrier atom and refined with a riding model . in all cases 
 displacement parameters restraints were used to refine some of the 
 lattice solvent molecules as well as a few atoms of the main residue . 
 for 15py , 65py , and 73py , void space with only diffuse electron density remaining 
 at the end of the refinement was analyzed and taken into account with 
 squeeze as implemented in the platon package . the heterometallic composition and the relative position of the 
 two metal ions were confirmed by much poorer final agreement factors 
 as well as worse or even unreasonable relative displacement parameters 
 in any of the other possibilities ( inverted positions or homometallic 
 composition ) . crystallographic and refinement parameters are summarized 
 in table s1 ( supporting information , si ) . all details can be found in the supplementary 
 crystallographic data for this paper in cif format with ccdc numbers 
 973881 , 973882 , 973883 , 973884 , and 973885 for compounds 1 , 4 , 5 , 6 , and 7 , respectively . these data can be obtained free of charge from the 
 cambridge crystallographic data centre via www.ccdc.cam.ac.uk/data_request/cif . magnetic susceptibility  
 data were measured , between 2 and 300 k , with a commercial magnetometer 
 equipped with a squid sensor and a commercial physical properties 
 measurement system ( ppms ) , both hosted by the physical measurements 
 unit of the servicio general de apoyo a la investigacin - sai , 
 universidad de zaragoza . direct current 
 ( dc ) data were collected between 2 and 300 k with an applied field 
 of 1000 oe . alternating current ( ac ) data were collected in the range 
 2100 k with an applied field of 4 oe oscillating at different 
 frequencies in the range 0.1    10  000 
 hz . ac susceptibility measurements were extended to the region of 
 very low temperatures using an integrated micro - squid susceptometer , 
 recently developed by some of us , which 
 works in the temperature region from 13 mk up to 3 k and for frequencies 
 from 0.03 hz up to 200 khz . the excitation field amplitude of the 
 microsquid susceptometer is 0.01 oe . for sufficiently low frequencies 
 ( typically ,  < 5 hz ) , the susceptibility becomes independent 
 of  at any temperature . continuous wave epr measurements were taken 
 in a bruker elexys 580 spectrometer operating in x- and q - band . the 
 same spectrometer working in x - band the length of the /2 and  pulses was 16 and 32 ns , respectively , 
 and the sampling time was 4 ns . finally , heat capacity data were also 
 measured between 350 mk and 300 k on compact pellet samples using 
 a commercial ppms . positive - ion esi mass spectrometry experiments 
 were performed using a lc / msd - tof ( agilent technologies ) with a dual 
 source equipped with a lock spray for internal reference introduction 
 at the unitat d'espectrometria de masses ( ssr ) of the university 
 of 
 barcelona . the 
 ligand h3l ( figure 1 ) features three 
 different coordination pockets 
 arranged in a completely asymmetric manner . we previously showed that 
 three ( partially ) deprotonated h3l ligands bridge two ln(iii ) 
 ions to form a quasi - isostructural series of asymmetric dimers , with 
 formula [ ln2(hl)2(h2l)(no3)(py)(h2o ) ] ( ln = la , ce , pr , nd , sm , eu , gd , tb , dy , 
 ho , er , tm , yb , lu , and also y ) . the 
 two metal centers within each complex then necessarily have markedly 
 different environments . inspection of the molecular structures revealed 
 that one of the metal sites ( site 1 ) of the assembly offers a cavity 
 that is systematically smaller than the other one ( site 2 , figure 
 s1 , si ) . there is an average distance 
 difference , o , between both sites of 0.030.05 
  ( for homogeneous comparison , only donor atoms of hl and h2l are included ) . it was thought 
 that this property could be advantageously exploited in order to face 
 one of the current challenges in synthetic coordination chemistry : 
 the controlled preparation of heterometallic 4f4f 
 complexes , here embodied as a series of dinuclear molecules with formulas 
 [ lnln(hl)2(h2l)(no3)(py)(h2o ) ] ( abbreviated [ lnln ] ) . in considering the best 
 candidates to fabricate a molecular quantum processor , the ideal properties 
 of the ce(iii)/er(iii ) combination rendered it a highly desired one . a solution with equimolar amounts of ce(no3)3 and er(no3)3 in pyridine produces , in the 
 presence of h3l and after layering with et2o , 
 a homogeneous phase of yellow crystals that was found to consist of 
 pure [ ceer(hl)2(h2l)(no3)(py)(h2o ) ] ( 1 , figure 1 ) . ( a ) representation of 
 ligand 6-(3-oxo-3-(2-hydroxyphenyl)propionyl)pyridine-2-carboxylic 
 acid ( h3l ) . ( b ) superposition of a selected area of the 
 mass spectrograms of complexes [ ceer(hl)2(h2l)(no3)(py)(h2o ) ] ( 1 ) , [ ce2(hl)2(h2l)(no3)(py)(h2o ) ] ( 2 ) , and [ er2(hl)2(h2l)(no3)(py)(h2o ) ] ( 3 ) , 
 emphasizing the absence of any trace of homometallic species on the 
 diagram from heterometallic [ ceer ] . ( c ) molecular structure of [ ceer(hl)2(h2l)(no3)(py)(h2o ) ] ( 1 ) showing each ligand in a different color ( black , green , 
 or yellow ) , pyridine in purple , ce(iii ) in pink , er(iii ) in blue , 
 water in red , and nitrate in pink . ( d ) molecular 
 representation of [ ( ce0.7y0.3)y(hl)2(h2l)(no3)(py)(h2o ) ] ( 6 ) , showing the occupancy of ce(iii ) ( pink ) and y(iii ) ( yellow ) , consistent 
 with the composition as well as the ratio of mono- and didentate no3 . c is in gray , o in red , and n in violet ; 
 h atoms not shown . the heterometallic nature 
 of 1 was established by 
 single - crystal x - ray crystallography ( see below ) , which shows that 
 the cation of smaller size , er(iii ) , occupies 
 site 1 , as expected , whereas the larger cation , ce(iii ) , goes to the position favoring larger ln  o / n 
 bonds ( site 2 ) . the 1:1 metal composition of 1 was confirmed 
 by icp - aes spectroscopy ( see above ) , whereas conclusive evidence for 
 its formulation came from mass spectrometry ( ms , figures 1 and s2 and s3 , si ) , 
 which produced only signals of heterodimetallic fragments . the availability 
 of the homometallic derivatives [ ce2(hl)2(h2l)(no3)(py)(h2o ) ] ( 2 ) and 
 [ er2(hl)2(h2l)(no3)(py)(h2o ) ] ( 3 ) was important 
 to corroborate the purity of 1 in the bulk , as this conclusion 
 follows from the absence of any detectable amount of homodimetallic 
 fragments in the mass spectrogram of the latter ( figure 1 ) . the successful preparation of 1 suggests 
 that this coordination system constitutes a host  guest assembly , 
 capable of discriminating between two different lanthanides by their 
 size , by selectively distributing them over two different locations . site selectivity between different lanthanides is extremely difficult 
 to achieve , given the chemical similarity that exists among them . in the present case , the system is in addition 
 adaptive ; when only one type of metal is present , it is hosted in 
 both sites . in order to evaluate 
 the metals in 1 as suitable qubits , 
 their study in their respective environments , without the magnetic 
 influence of the other , was necessary . the plasticity of this coordination 
 architecture enables the design and preparation of the analogues [ laer ] 
 and [ cey ] , where er and ce occupy the same position they hold in 1 but are now accompanied by a diamagnetic cation [ la(iii ) 
 and y(iii ) , respectively ] . for these pairs , the differences in ionic 
 radii are r = 0.21  ( laer ) and 0.15 
 ( cey ) , respectively . the same synthetic procedure 
 described above was carried out using er(no3)3 or ce(no3)3 , in combination with la(no3)3 and y(no3)3 , respectively , 
 producing successfully pure [ laer(hl)2(h2l)(no3)(py)(h2o ) ] ( 4 ) and [ cey(hl)2(h2l)(no3)(py)(h2o ) ] ( 5 ) . the results from single crystal x - ray crystallography are consistent 
 with the identity of both complexes ( see below ) as well as metal analysis 
 ( confirming equimolar contents of both metals in each case ) . mass 
 spectrometry measurements ( si ) convincingly 
 evidence that crystals of 4 and 5 are only 
 made of heterometallic molecules ( figures s4s7 , si ) , while the magnetic properties of both compounds 
 also support the formulated composition ( see below ) . the need to investigate 
 the possible effects of dipolar interactions between the spin magnetic 
 moments of er(iii ) or ce(iii ) in the bulk of [ laer ] ( 4 ) or [ cey ] ( 5 ) ( see below ) prompted attempts to dilute 
 these molecules within an isostructural diamagnetic lattice . the synthetic 
 work described above suggests that a mixture of ce(no3)3 and y(no3)3 ( 1:3 molar ratio ) in a 
 pyridine solution of h3l should lead to an equimolar mixture 
 of [ cey(hl)2(h2l)(no3)(py)(h2o ) ] and [ y2(hl)2(h2l)(no3)(py)(h2o ) ] . x - ray diffraction studies performed 
 on a single crystal from this reaction system indicate that both complexes 
 are present within a homogeneous solid solution ( see below ) , randomly 
 distributed in a 70:30 molar ratio : [ cey(hl)2(h2l)(no3)(py)(h2o)]0.7[y2(hl)2(h2l)(no3)(py)(h2o)]0.3 or [ ( ce0.7y0.3)y(hl)2(h2l)(no3)(py)(h2o ) ] ( 6 ) . very low temperature heat capacity experiments ( figure 
 s8 , si ) were conclusive with regard to 
 the successful dilution of [ cey ] molecules within this single phase . mass spectrometry of these crystals shows the existence of heterometallic 
 [ cey ] and homometallic [ y2 ] fragments , but no trace of 
 [ ce2 ] moieties ( figure s9 , si ) . the complex [ lay(hl)2(h2l)(no3)(py)(h2o ) ] ( 7 ) was also obtained 
 using the 
 same synthetic procedure , with the aim of measuring the nonmagnetic 
 energy contributions to the specific heat in these compounds . the 
 identity and purity of 7 was established by single - crystal 
 x - ray diffraction , ir spectroscopy , mass spectrometry ( figure s10 , si ) , and microanalysis . the above experiments 
 confirm a new method for locking a large 
 number of combinations of two lanthanide ions within a well - defined 
 molecular entity ( figure 1 ) . this represents 
 a huge step toward the goal of obtaining pure heterometallic 4f4f 
 complexes from one - pot reactions . the single - crystal structures 
 of compounds 1 and 47 were determined by x - ray diffraction ( si ) . the neutral complex [ ceer(hl)2(h2l)(no3)(py)(h2o ) ] ( 1 , figures 1 and s11 , si ) is chiral , with both 
 enantiomers present in the crystal lattice . the unit cell belongs 
 to the monoclinic space group p21/c and contains four asymmetric units ( table s1 , si ) . each of the latter comprises one dinuclear 
 [ ceer ] complex and five molecules of pyridine . the complex exhibits 
 a ce(iii ) ion and an er(iii ) center surrounded by three partially 
 deprotonated h3l ligands ( two as hl and one as h2l ) in the same way as 
 its homometallic congeners . each ligand 
 chelates both metals through two distinct coordination pockets , a 
 -diketonate and a dipicolinate - like cavity , both sharing a 
 common central o donor which participates in a ce  o  er 
 bridge . two of the ligands lie in a mutual head - to - head configuration , 
 while the third one points in the opposite direction . an important 
 consequence is that the metals , which lie 3.851  apart , are 
 in different coordination environments ; ce(iii ) is located within 
 two tridentate ( o , n , o ) pockets and one -diketonate ( o , o ) 
 one , whereas er(iii ) is bound to one ( o , n , o ) and two ( o , o ) donor 
 groups , respectively ( table s2 , si ) . a 
 9-fold coordination around the latter metal is completed by one molecule 
 of pyridine and one of water , whereas ce(iii ) exhibits 10-fold coordination , 
 with the concurrence of a -no3 ligand . this anion provides the one negative charge necessary for 
 the complex to be electrically neutral . the nature of the metal on 
 each position could be unambiguously established from the refinement 
 of the diffraction data , yielding unreasonable displacement parameters 
 or agreement factors whenever any other metal distribution was considered . it might then be concluded that the metal ion with the smallest radius 
 ( er ) goes to the site with the shortest coordination distances ( site 
 1 ) , while ce accommodates into the other site ( site 2 ) . a further 
 consequence is that , in the present ( heterometallic ) complex , the 
 difference o = 0.17  between the average 
 ln  o distances in both sites is larger than those observed 
 for any of the analogous homometallic complexes studied previously . the four ionizable protons remaining on the ligands have all been 
 identified crystallographically and are located on the phenol groups 
 and on one carboxylic moiety . a pyridine solvate molecule is forming 
 a strong hydrogen bond to the latter ( figure s12 , si ) . complexes [ laer(hl)2(h2l)(no3)(py)(h2o ) ] ( 4 , figure s13 , si ) and [ cey(hl)2(h2l)(no3)(py)(h2o ) ] ( 5 , figure s14 , si ) are analogous to the heterometallic complex 1 . the empirical differences in ionic radii ( r ) of both metals in each complex are 0.21 
  ( la > er ) and 0.15  ( ce > y ) . accordingly , er(iii ) 
 and 
 y(iii ) occupy site 1 of 4 and 5 , respectively , 
 whereas la(iii ) and ce(iii ) are in site 2 . larger disparities in ionic 
 radii within one complex also enhance differences between sites 1 
 and 2 . therefore , this difference is slightly larger in 4 than in 5 , namely o = 0.18 
 and 0.15  for [ laer ] and [ cey ] , respectively ( table s2 , si ) . the metal metal separations are 3.857 
  ( laer ) and 3.851  ( cey ) . compound [ cey(hl)2(h2l)(no3)(py)(h2o)]0.7[y2(hl)2(h2l)(no3)(py)(h2o)]0.3 ( 6 , figures 1 and s15 , si ) constitutes a solid solution containing 70% of the heterometallic 
 complex [ cey ] and 30% of the diamagnetic [ y2 ] species , 
 both molecules occupying the same space of the unit cell . in fact , 
 the positions of all atoms from both species coincide , except for 
 the metal on site 2 ( ce or y ) and three atoms of the no3 ligand . each of these four atoms is disordered 
 over two locations with 0.7:0.3 occupancy ratios . therefore , two metalmetal 
 separations have been resolved ( 3.695 and 3.880  for yy 
 and cey , respectively ) as well as two coordination 
 modes of no3 ( mono- and didentate for 
 coordination to y and ce , respectively ) . the only nondisordered atom 
 of no3 is the oxygen atom with the shortest 
 distance to the metal . in addition to the disordered [ lny ] molecule , 
 the asymmetric unit of the structure contains five molecules of pyridine . the heterometallic complex [ lay(hl)2(h2l)(no3)(py)(h2o ) ] ( 7 , figure s16 , si ) is isostructural to 1 with three 
 pyridine molecules in the asymmetric unit ( instead of five ) . the value 
 of r for la(iii ) and y(iii ) is 0.18  , which leads to o = 0.18  and a lay 
 distance of 3.869(1 )  . as expected , the la(iii ) center exhibits 
 10-fold coordination , with the nitrate ligand in the terminal -no3 coordination mode . the synthetic tool reported 
 here allows choosing almost any desired pair of lanthanide ions for 
 the fabrication of a molecular qugate . in order to build a molecular 
 cnot gate , the combination of ce(iii ) with er(iii ) this heteronuclear combination minimizes the amount 
 of nuclear spins located at the lanthanide sites [ none for ce(iii ) 
 and only 22.9% of the er isotope with i = /2 for er(iii ) ] , thus contributing to reduce 
 decoherence . it should be noted , however , that nuclear spins strongly 
 coupled to the electronic ones might enhance the computational space 
 of each qubit or act in situ as quantum memories . such additional possibilities are , of course , 
 compatible with the same chemical structures reported here , which 
 can be realized with lanthanide ions having nonzero i [ such as e.g. pr(iii ) , tb(iii ) , or ho(iii ) ] . the present physical 
 characterization , which is described in the following , aims to show 
 that 1 fulfills the following conditions : ( i ) each lanthanide 
 behaves , at sufficiently low temperatures , as an effective spin-/2 , thus providing a good realization of spin qubits , 
 and ( ii ) these spin qubits are magnetically nonequivalent and ( iii ) 
 weakly coupled , thereby enabling the realization of  single 
 shot  quantum gate operations . complexes [ laer ] ( 4 ) 
 and [ cey ] ( 5 ) were prepared and studied to characterize 
 each of the two lanthanide ions of [ ceer ] ( 1 ) in their 
 respective local coordination environments , isolated from the influence 
 of the other magnetic center . in 4 and 5 , er(iii ) and ce(iii ) metals occupy the same positions they take 
 in 1 , being accompanied by the diamagnetic ions la(iii ) 
 and y(iii ) , respectively . according to hund s rules , free er(iii ) 
 and ce(iii ) ions are characterized by j = /2 with gj = /5 and j = /2 with gj = /7 , respectively . in a material , these 
 multiplets are split into kramers doublets by the interaction of 4f 
 electrons with the crystal field ( magnetic anisotropy ) . information 
 on the magnetic energy level structure and the nature of the ground 
 state doublet , which forms the computational qubit basis , can be obtained 
 from linear magnetic susceptibility  and electron paramagnetic 
 resonance ( epr ) experiments . results of experiments performed on powder 
 samples of 4 and 5 are shown in figure 2 . the plateau in the t product 
 observed at sufficiently low t ( t  3 k for [ laer ] and t  7 k for 
 [ cey ] ) reflects the magnetic behavior of the ground - state doublet . 
 in this temperature region , each lanthanide effectively behaves as 
 a two - level system and can therefore be described by a simple effective 
 spin-/2 hamiltonian1where i is the effective gyromagnetic tensor of spin i [ i = 1 , 2 refer to er(iii ) and ce(iii ) 
 ions , respectively ] , with principal values gxi , gyi , and gzi . these 
 values have been determined by fitting epr spectra measured at a frequency 
  = 9.8 ghz ( x - band ) on complexes 4 and 5 , as shown in figure 2 . the low - t limit of t is then ( t)t0 = ( nab/4kb)gi , where 
 gi = ( gxi + gyi + gzi)/3 which , using the epr values , 
 amounts to 0.35 and 3.70 emu k / mol oe for cey and laer , respectively , 
 in good agreement with the results of magnetic measurements . it is 
 worth mentioning that the principal axes of sites 1 and 2 need not 
 be collinear to each other . at finite temperatures , t increases , showing the gradual population of excited kramers 
 doublets . this behavior can be described using van vleck s 
 general formalism for the susceptibility of anisotropic spins . for temperatures where only the populations of the ground and first 
 excited doublets , separated by an energy gap  , are significant , 
 van vleck s expression reduces to the following2where c0 , c1 , and c2 are numerical coefficients 
 that depend on the electronic 
 structure of each doublet . it can be seen in figure 2a , b that eq 2 accurately describes the 
 temperature dependence of the susceptibility and , therefore , that 
 it enables an accurate determination of . the lowest lying 
 magnetic energy level structures of complexes 4 and 5 are shown in figure 2 . both lanthanide 
 ions have a ground - state doublet that is energetically isolated from 
 all excited levels , therefore providing a proper definition of qubit 
 states . below t = 0.1 k , the susceptibility of [ laer ] 
 deviates from the pure paramagnetic behavior and shows a peak that 
 can be associated with the onset of magnetic order likely induced 
 by dipolar interactions between spins in different molecules . in [ cey ] , 
 such interactions are even weaker , in agreement with the smaller magnetic 
 moment of this ion , and no significant deviation from paramagnetism 
 is observed . in fact , the extent of the 
 dipolar intermolecular interactions was corroborated by comparing 
 the specific heat of the [ cey ] complex with that of the magnetically 
 dilute analog [ ( ce0.7y0.3)(y ) ] system ( figure 
 s8 , si ) . ( a 
 and b ) temperature dependence 
 of the equilibrium magnetic susceptibility of , respectively , [ laer ] 
 ( 4 ) and [ cey ] ( 5 ) molecular complexes . open 
 symbols represent zero - field ac susceptibility data recorded , at 1.5 
 hz , with a microsquid susceptometer ( circles , ac field amplitude 0.01 
 oe ) and a commercial squid magnetometer ( squares , ac field amplitude 
 4 oe ) . solid symbols are dc susceptibility data measured under a 1000 
 oe applied magnetic field . the agreement between data measured by 
 different techniques shows that they correspond to the linear response , 
 i.e. , to the zero - field susceptibility . the solid lines are least - squares fits based 
 on eq 2 . ( c and d ) x - band continuous wave epr 
 spectra of 4 and 5 , respectively . the fits 
 are based on a spin-/2 hamiltonian ( eq 1 ) describing the magnetic properties of the ground - state 
 doublet , which defines each qubit basis . panels e and f show both 
 complexes and their low - energy magnetic level structures . these results also imply that , for almost any given 
 magnetic field 
 intensity and orientation , the zeeman splitting of the two qubit levels 
 of 4 is different from that of 5 , i.e. , 
 that these qubits are magnetically inequivalent and therefore separately 
 addressable by either changing frequency or magnetic field . a further 
 salient feature is that gxi and gyi are on the 
 same order as gzi . this 
 result is in striking contrast with values reported for other lanthanide 
 spin qubits , for which the ratios gx / gz and gy / gz are typically on the order of 10 or even less . it probably results from the low symmetry of the local 
 coordination of er(iii ) and ce(iii ) and has important implications 
 for the coherent control of these spins . the gyromagnetic ratios determine 
 the rabi frequencies r of transitions between qubit 
 states induced by radiofrequency ( rf ) electromagnetic fields . therefore , we expect that 4 and 5 show very high r values for almost any 
 orientation of the external dc and rf magnetic fields . with the information obtained already 
 on both lanthanide ions separately , it is straightforward to test 
 the magnetic coupling between them . for this , we compare in figure 3 the magnetic susceptibility of the double qubit 
 system [ ceer ] ( 1 ) to those measured on the single qubit 
 molecules [ laer ] ( 4 ) and [ cey ] ( 5 ) . above 
 approximately 0.2 k , the  of this compound almost coincides 
 with the sum of the susceptibilities of [ cey ] ( 4 ) and 
 [ laer ] ( 5 ) . interqubit coupling effects become visible 
 only below this temperature , where  of [ ceer ] clearly drops 
 below the value expected for the two uncoupled spins . the 
 existence of a finite intramolecular coupling is confirmed by the 
 results of epr experiments . the x - band spectrum of 1 at 
 5 k is clearly not a simple superposition of the spectra of 4 and 5 . furthermore , spectra measured on 1 at different frequencies do not scale when they are plotted 
 against the ratio h/ , as they should if the 
 spins of ce(iii ) and er(iii ) were uncoupled and simply described by 
 eq 1 . ( a ) temperature 
 dependence of the 
 equilibrium magnetic susceptibility ( open circles , zero - field ac susceptibility 
 data at 1.5 hz ; open squares , dc susceptibility under a 1000 oe applied 
 field ) of [ ceer ] ( 1 ) , compared to the sum of susceptibilities 
 of [ laer ] and [ cey ] ( solid symbols ) . the blue dotted and purple solid 
 lines show , respectively , the susceptibilities of two uncoupled and 
 two coupled effective spin-/2 moments with 
 noncollinear i tensors ( eq 3 ; see the text ) . ( b ) epr spectra of 1 measured at 5 k and two different frequencies . panel c shows the 
 [ ceer ] complex and panel d a scheme of its low - energy magnetic level 
 structure . the same conclusions can be drawn 
 from specific heat data ( figure 
 s17 , si ) . the specific heat of 1 deviates from that expected for molecules consisting of two noninteracting 
 spins only at very low temperatures . this effect becomes clear from 
 measurements performed on 1 at zero field , which below 
 1 k exceed the sum of the specific heats of 4 and 5 . this extra heat capacity reflects the splitting in energy 
 of different ferro- and antiferromagnetic configurations of the two 
 spin qubits , confirming the latter as the ground state . it gradually 
 vanishes with increasing magnetic field , thus suggesting that the 
 differences observed at zero field are due to the presence , in complex 1 , of a finite exchange interaction between ce(iii ) and er(iii ) . from the above discussion , it follows that [ ceer ] behaves , 
 at sufficiently low temperatures , as a system of two anisotropic and 
 weakly coupled effective s-/2 spins . the underlying physics and its operation as a quantum gate 
 can be described with the following effective hamiltonian , which is 
 derived in the si:3where j12 is an 
 exchange constant describing the coupling between the angular momenta 
 of ce(iii ) and er(iii ) ions in 1 . it follows from eq 3 that  drops below the paramagnetic response 
 for j12 < 0 . however , no accurate fit 
 can be achieved if the local principal axes of the two spins are collinear 
 to each other . this situation obviously arises from the strong asymmetry 
 of the molecule and was already observed in homonuclear compounds 
 of the same family . the results are compatible 
 with a tilt of one of the local easy magnetization axes , say z2 , with respect to the other , z1 , of about 70 with respect to each other . results for 
  calculated in a particular situation , where y2 and z2 have been rotated along x2 = x1 , account reasonably 
 well for the data measured on [ ceer ] , as shown in figure 3 . although the fit does not univocally fix the relative 
 orientations of the 1 and 2 tensors , thus other solutions giving 
 similar results , the structure of magnetic energy levels , shown in 
 figure 4 as a function of hz1 , remains qualitatively the same . ( a ) magnetic field dependence of the four 
 lowest - lying energy levels of 1 calculated with the effective 
 spin hamiltonian eq 3 for j12/kb = 0.015 k and 
 a magnetic field parallel to the z1 axis [ easy 
 magnetization axis of er(iii ) ] . at 0hz1 = 470 mt , x - band photons ( 9.5 ghz ) 
 are only resonant with the |00  |01 transition , 
 thus providing realization of a single - shot cnot gate . ( b ) echo - detected 
 epr spectrum of a meoh / etoh frozen solution of 1 measured 
 at a fixed separation  between the /2 and  pulses of 140 ns . the inset shows the decay with 
  of the spin - echo measured at a magnetic field 0h = 470 mt . an exponential fit gives a decoherence 
 time t2 = 410 ns . at any magnetic field , the four lowest - lying levels of 1 are unequally separated , meaning that there are no degenerate 
 transitions . this is a consequence of the very different magnetic properties of 
 er(iii ) and ce(iii ) and their weak coupling . the four - dimensional 
 hilbert space defined by the energy eigenstates ( hereafter labeled 
 simply as { |00 , |10 , |01 , |11 } ) provides 
 then a suitable computational basis for a molecular spin quantum gate . for instance , if we set 0hz1 = 470 mt ( figure 4 ) , only the |00  |01 transition is resonant 
 with x - band photons ; i.e. , under these conditions the interaction 
 with the radiation field flips qubit 2 if , and only if , qubit 1 is 
 in state  0  ; thus , it provides a simple realization 
 of a single - shot cnot gate ( scheme 1 ) . notice 
 that , because of the low symmetry of the two lanthanide sites , the 
 wave functions are not simple products of states of each lanthanide 
 ion . an important consequence is that all possible transitions , and 
 sequences of them , can be induced by electromagnetic radiation of 
 the appropriate frequency . this ensures the feasibility of any operation 
 linking any two states of the hilbert space defined by the computational 
 basis . therefore , this molecule can operate as a universal two - qubit 
 spin quantum processor , controlled by either electromagnetic frequency 
 or magnetic field . a further crucial step for ascertaining the 
 suitability of 1 for quantum information processing is 
 to evaluate the coherence 
 times associated with these transitions . a convenient method to examine experiments were performed on 
 this complex dissolved in meoh / etoh , which unveiled that indeed coherent 
 spin dynamics can be generated from the molecule through radiofrequency 
 pulses ( figure 4 ) . an echo signal was detected 
 for 0h = 0.47 t , which approximately 
 corresponds to the |01  |00 transition , associated 
 with a cnot gate operation where the first qubit acts as control ( figure 4 ) . while these experiments do not represent a full 
 realization of the quantum gate operation , or quantum tomography , 
 they evidence that such coherent manipulations are feasible and provide 
 the first evaluation of the decoherence time scales on a two - qubit 
 molecular spin quantum gate . the estimated decoherence time t2 of this resonance , approximately 410 ns , is 
 still short as compared to values obtained for other physical realizations . further experiments will serve to identify the main sources of decoherence 
 and to engineer adequate methods to reduce its effects . small differences in the ionic radius of ln(iii ) atoms can be exploited 
 with the ligand h3l for the preparation of pure heterodimetallic 
 [ lnln ] complexes for a large number of combinations , opening 
 a very important synthetic pathway for many applications . here , this 
 potential has been used to prepare an optimal molecular assembly to 
 act as a two - qubit spin quantum processor , the complex [ ceer(hl)2(h2l)(no3)(py)(h2o ) ] ( 1 ) . to assist in the qubit and qugate characterization , the 
 analogues [ cey ] , [ laer ] , [ lay ] and the diluted [ ( ce0.7y0.30)y ] where also prepared and studied . epr , ultralow temperature 
 micro - squid , and heat capacity measurements and analysis have served 
 to demonstrate that the individual qubits in 1 feature 
 the appropriate computational qubit basis and the properties to exhibit 
 large rabi oscillation frequencies between qubit state transitions , 
 as required . in addition , the energy eigenstates of the two qubits 
 coupled within the [ ceer ] molecule form a four - dimensional hilbert 
 space suited for the realization of universal two - qubit logic operations . time - resolved epr experiments show that this molecule exhibits coherent 
 spin dynamics , from where a decoherence time t2 of about 400 ns has been extracted . these molecules could 
 now be coupled to quantum devices in a significant step forward toward 
 the goal of realizing quantum information processing .
a major 
 challenge for realizing quantum computation is finding 
 suitable systems to embody quantum bits ( qubits ) and quantum gates 
 ( qugates ) in a robust and scalable architecture . 
 an emerging bottom - up 
 approach uses the electronic spins of lanthanides . 
 universal qugates 
 may then be engineered by arranging in a molecule two interacting 
 and different lanthanide ions . 
 preparing heterometallic 
 lanthanide species is , however , extremely challenging . 
 we have discovered 
 a method to obtain [ lnln ] complexes with the appropriate requirements . 
 compound [ ceer ] is deemed to represent an ideal situation . 
 both ions 
 have a doubly degenerate magnetic ground state and can be addressed 
 individually . 
 their isotopes have mainly zero nuclear spin , which 
 enhances the electronic spin coherence . 
 the analogues [ ce2 ] , [ er2 ] , [ cey ] , and [ laer ] have also been prepared to 
 assist in showing that [ ceer ] meets the qugate requirements , as revealed 
 through magnetic susceptibility , specific heat , and epr . 
 molecules 
 could now be used for quantum information processing .