High-Performance Computing and Quantum Processing

Transcription

1 HPC-UA (Україна, Київ, - жовтня року High-Pefomace Computig ad Quatum Pocessig Segey Edwad Lyshevski Depatmet of Electical ad Micoelectoic Egieeig, Rocheste Istitute of Techology, Rocheste, NY 3, USA [email protected] URL: Abstact. We eseach ovel solutios ad apply ew tasfomative fidigs towads quatum pocessig egieeig high-pefomace ad eabled-capabilities data pocessig platfoms. I livig ogaisms, vaious ifomatio ad data pocessig tasks ae pefomed by micoscopic atomic ad biomolecula fabics usig quatum pheomea ad effects. We examie fudametals of quatum data pocessig o measuable, pocessable ad compatible eal-valued physical quatities (vaiables i micoscopic fabics. These fabics compise ad implemet devices, modules ad systems. The developed quatum data pocessig paadigm: ( Uifies ad eables cocepts of theoetical compute sciece, compute egieeig ad quatum mechaics; ( Cosistet with the fist piciples of quatum ifomatics, commuicatio ad pocessig; (3 Coheetly examies device physics, switchig algeba, pocessig aithmetics ad calculus; ( Fostes fudametally-cosistet ad pactical micoscopic hadwae solutios. We examie two coe poblems, e.g., algoithmic ad hadwae pemises. The micoscopic pocessig pimitives must exhibit utilizable quatum-effect state tasitios o the measuable physical vaiables (obsevables which esult i computable tasfoms fom viewpoits of devise physics, pocessig aithmetics, calculus ad desig. Ou ew coheet, cohesive ad cosistet paadigm pomises oe to: (i Ease eomous challeges; (ii Ovecome foemost icosistecies of aive algoithmically-cetic computig; (iii Eable ew pactical ioads, paadigms ad solutios; (iv Guaatee upecedeted pocessig capabilities esuig fa-eachig bechmaks; (v Advace theoy ad pactice of atual ad egieeed pocessig. Ou fidigs suppot a boad spectum of tasfomative eseach activities ad egieeig developmets. The esults may be used i assessig pefomace, capabilities ad bechmaks of atual ad egieeed pocessig ad computig. Keywods High-pefomace computig, ifomatio theoy, micoscopic systems, quatum computig, quatum pocessig. Itoductio High-pefomace computig is vey impotat to solve vaious computatioally-itesive poblems. The highpefomace computig is expected to achieve sustaiable pefomace esuig 5 (petaflops floatig poit opeatios pe secod (FLOPS i pactical applicatios. New eliable ad obust hadwae ad softwae to esue sustaied pefomace ad computig ae ude extesive developmets. Petascale supecomputes, i some applicatios, ca pocess oe quadillio ( tillio FLOPS. The computes ad pocessos pefomace ad capabilities ca be eabled by:. Advaced low-powe hadwae, self-awae softwae ad cohesive algoithms;. Eablig hadwae, softwae ad laguages which esue highly-pogammable systems; 3. Eabled-fuctioality low-powe aoscaled micoelectoics; etc. Vetebates ad ivetebates exhibit ifomatio ad data pocessig. The data pocessig i livig ogaisms exceeds exascale pefomace which by fa supassig the exaflops equivalece ad age applied i assessig of computig. A exaflop is oe quitillio ( FLOPS. This pefomace ad capabilities caot be esued ad sustaied by ay evisioed supe-compute platfoms due to fudametal ad techological limits. Advaced digital itegated cicuits (ICs ae used to implemet vaious distict computes desigs, ogaizatios ad achitectues. Eomous pogess was achieved i semicoducto devices ad ICs. The afoemetioed astoishig fudametal, applied ad techological developmets led to mass poductio of highpefomace ICs ad pocessos with billios of tasistos. Eablig mateials, pocesses ad tools led to a cuet lithogaphy-defied ~3-m DRAM Metal Half-Pitch which is also kow as a techology ode []. Vaious fudametal limits will emege withi a foesee scalig towads -m ad -m featues by 7 ad 3 []. The techology pefomace evaluatio citeia ae scalability, eegy efficiecy, o/off cuet, opeatioal eliability, opeatioal tempeatue, techology compatibility ad achitectue compatibility []. As the plaa solid-state devices ae scaled to oly hudeds of aomete i dimesios, the udesiable quatum pheomea sigificatly degaded the oveall device ad ICs pefomace ad fuctioality. The focused eseach activities have beig ceteed o quatumeffect devices. A sigificat pogess has accomplished i widely deployed esoat-tuelig devices, solid-state, -33-

2 HPC-UA (Україна, Київ, - жовтня року iogaic ad ogaic lases, etc. []. To fully utilize quatum pheomea ad eable ew featues, developmets pogessed beyod cuet macoscopic micoelectoic paadigms. We focus o quatum-mechaical micoscopic solutios. The micoscopic-cetic paadigm ultimately implies ew device physics of subatomic/atomic/molecula devices, ovel commuicatio ad pocessig piciples, ew itefacig ad etwokig schemes, iovative sythesis ad fabicatio, etc. Quatum pheomea ad effects, exhibited by micoscopic systems (subatomic, atomic, molecula ad othe, may be utilized to esue pocessig tasks. Thee ae eomous challeges ad complexities which age fom quatum-mechaical aalysis to sythesis, itefacig, testig ad chaacteizatio of micoscopic devices ad systems. Solutios of the afoemetioed poblem pomise oe to eable pocessig with upecedeted pefomace ad capabilities. The livig ogaisms povide udisputable evidece of biomolecula sesig, commuicatio ad ifomatio pocessig. The ifomatio pocessig i livig ogaisms has ot bee compeheded. By poposig, examiig ad establishig ew pemises i high-pefomace commuicatio ad pocessig, we itet to sigificatly cotibute to: (i Devisig of eablig egieeed pocessig platfoms; (ii Aalysis of evealig ad essetial aspects of quatum commuicatio ad pocessig. A exploatoy oadmap towads quatum pocessig is documeted i Figue [, 3]. Natual ad Egieeed Systems Molecula ad Biomolecula Pocessig Micoelectoics Solutios:. Micoscopic Devices. Netwoked Fabics 3. Quatum Pocessig. Pocessig Calculi 5. Quatum Commuicatio Pocessig i Livig Ogaisms IBM Blue Gee Supecompute 97 9 ENIAC AMD -bit Itel 9-pi dualcoe pocesso Fudametal ad Techological Limits 93, US Patet GB Patet 3957 Electo (Vacuum 9 US Patet Tubes 3 Naomete Micomete Picomete Millimete Mete Size (logaithmic scale Figue. Evisioed oadmap: Towads supe-high-pefomace sesig, commuicatio ad pocessig [, 3]. Ifomatio Theoy With Applicatios to Commuicatio ad Itefacig Ifomatio theoy is applied to examie commuicatio. Claude Shao itoduced ad applied the etopy i ode to measue the complexity of the set. The sets which have lage etopies equie moe bits to epeset them. Fo M objects (symbols i which have pobability distibutio fuctios p( i, the etopy is give as M H( = p( log p(,.., M, M. ( i i Example.. Coside a cubic dice with faces, ad, o-cubic dices. The commo polyhedo, Zocchihedo ad othe o-cubic dices may have a specific umbe of faces. Oe may esue uifom, omal ad othe distibutios. Fo the deltohedo, the umbe of faces is. Let =[a, b, c, d, e, f] with equal pobability /, ad =[a, b, c, d, e, f, g, h, k, l] with equal pobability /. The etopies H( ae foud to be M H ( = p( ilog p( i = M ad ( p( log p( = ( =.55 bit H = i i log =3.39 bit. -3-

3 HPC-UA (Україна, Київ, - жовтня року Example.. Let with pobability p =. The etopy H(, as a fuctio of p, is give as with pobability p M ( H = p( ilog p( i = p log p ( plog ( p. It is evidet that H is positive-defiite, H. That is, the umbe of bits equied by the Souce Codig Theoem is positive. I paticula, N idepedet ad idetically distibuted adom vaiables, each with etopy H(, ca be compessed ito moe tha NH( bits with egligible isk of ifomatio loss as N ; howeve, if these N adom vaiables ae compessed ito fewe tha NH( bits, it is vitually cetai that ifomatio will be lost. Examiig aalog computatio ad pocessig o cotiuous-time sigals, a diffeetial etopy ca be applied. Fo a cotiuous-time adom vaiable, the diffeetial etopy is give as H ( = p ( xlog p ( x dx, ( whee p (x is a oe-dimesioal pobability distibutio fuctio of x, p ( x dx =. I geeal, oe has H (,,...,, = p ( xlog p ( x dx. (3 The elative etopy betwee pobability desity fuctios p (x ad g (x is expessed by p ( x H R ( p g = p ( xlog dx ( g ( x The diffeetial etopies fo vaious commo distibutio fuctios ae deived. Fo Cauchy, expoetial, Laplace, Maxwell-Boltzma, omal ad uifom distibutios p (x, the esultig H( ae epoted i [, 3]. The diffeetial etopy ca be egative. The diffeetial etopy of a Gaussia adom vaiable with ( x a σ ( x e p =, <x<, <a<, σ> is H(=½l(πeσ, Thus, H( ca be positive, egative o zeo πσ depedig o the vaiace σ. Oe examies the mutual ifomatio I(,Y betwee the stimulus ad the espose Y i ode to measue how simila the iput ad output ae. We have I(,Y = H( + H(Y H(,Y, p x y p ( y x I Y p x y, Y (, Y (, = Y (, log dxdy = p y x p x dxdy Y p x py y ( ( log. (5, ( ( py ( y The chael capacity C is foud by imizig the mutual ifomatio subject to the iput pobabilities, ad C = I(, Y [bit/symbol]. ( p ( The aalysis of mutual ifomatio esults i C which depeds o p Y (y x. It is difficult to obtai o estimate the pobability distibutio fuctios. Coside a poit pocess chael [, 3]. The istataeous ate at which pulses occu caot be lowe tha mi ad geate tha which ae elated to the photo emissio, electomagetic adiatio, etc. Let the aveage sustaiable pulse is. Fo a Poisso pocess, the chael capacity of the poit pocesses + mi fo mi is mi mi mi C = + + mi e l + mi mi the expessio fo a chael capacity is, > el e. C = l <, l e mi mi. If the miimum ate is zeo ( mi =, Example. 3. Fo seial commuicatio, the goss bit ate depeds o the tasmissio time T t, ad, =/T t. N Fo the paallel commuicatio, the goss bit ate is log M i =, whee N is the umbe of paallel Ti chaels; M i is the umbe of symbols o modulatio levels i the ith chael; T i is the symbol duatio time fo the ith chael. The quatum tasductios occu withi ~ 5 sec. We assume that the imum ate vaies fom 3 to pulse/sec, the aveage ate chages fom to pulse/sec. Let mi assumes.5 to -35-

4 Міжнародна конференція "Високопродуктивні обчислення" HPC-UA (Україна, Київ, - жовтня року pulse/sec. Oe mi. < e mi mi has chael The capacity C(, is mi if mi. Figue documet thee-dimesioal plots fo C(, C= ( l l mi l mi mi if mi=.5 ad mi= pulse/sec. Fo mi=.5, oe fids C=. bits. A vey high chael capacity C is achieved. x x 5 3 C(, C(, 5 3 x x x 5 3 (a Figue. Thee-dimesioal plot fo the hael capacity C(,: (a C(, if mi=.5 pulse/sec; (b C(, if mi= pulses/sec. x (b 3. High-Pefomace Computig: Solutios ad Limits May eablig solutios wee implemeted esuig high-pefomace computig. The followig cocepts wee utilized i existig pocessos: paallelism, vecto pocessig, acceleatos, supepipeliig, aay pocessig, multi-coe achitectue, multitheadig, distibuted computig, multi-level shaed memoy, etc. These solutios dastically advaced pocessig pefomace ad capabilities. The advaces of compute egieeig ad micoelectoics eable ad suppot the afoemetioed cocepts. Thee ae fudametal, hadwae ad softwae limits associated with all solutios. Let us examie the paallelism. We itoduce the followig atio =tseial/tpaallel, whee tseial ad tpaallel ae the pocessig, commuicatio, itefacig, memoy access ad etieval, executio ad othe times of the seial (sequetial ad paallel (cocuet ad distibuted pocesses, tasks, algoithms, etc. Pocesses, tasks ad algoithms ae ot scalable, ad, may ae ot paallelizable. Not metioig memoy hieachy, eve, majoity of algoithms ae impossible to paallelizable. Iheetly seial algoithmic poblems ae majoity of sequetial ad combiatioal logics, coditioal statemets, umeic poblems, etc. Example 3. : Limits of Paallelism Thee ae may pocessig tasks which must be pefomed. Fo example, computig, logics, memoy access ad etieval, codig, commuicatio, itefacig, etwokig, etc. These tasks, may of which ca be pefomed oly i seies, ae hadwae-, softwae-, algoithms-, achitectue- ad ogaizatio-depedet, May opeatios ad tasks caot be paallelized. Oe of the majo quatity of paallelism is the speed-up measue Mspeed [, 3], defied as M speed = =, tseies tseies + ( seies seies + NP tseies + t paallel N P tseies + t paallel seies=tseies/(tseies+tpaallel, paallel= seies= tseies/(tseies+tpaallel, -3-

5 HPC-UA (Україна, Київ, - жовтня року whee t seies ad t paallel ae the aveaged times to pefom seies ad paallel pocessig will all elated tasks ad opeatios; N P is the umbe of pocessos; seies ad paallel ae the seies (ot paallelizable ad paallelizable atios. The speed-up measue M speed depeds o the degee of paallelism which ca be achieved. As oe may obtai the aveage estimate fo seies > we have paallel =( seies, paallel <. Thee ae vaious latecy delays, such as device/module/system tasiets, holds, potocols, algoithmic, sychoizatio, flow cotol, popagatio, tasmissio ad othe delays. These delays affect computig, memoy access ad etieval, logics, codig/decodig, commuicatio, etwokig, itefacig ad othe tasks which ae accomplished by meas of coespodig aithmetics, opeatios ad pocesses. The afoemetioed factos lead to the aveaged o effective seies. Assume a vey high level of paallelizable capabilities. We optimistically postulate that: (i % of tasks, opeatios ad pocesses could be pefomed i paallel; (ii Thee ae oly % of ot paallelizable udetakig tasks, opeatios ad pocesses. Hece, oe fids M speed =5 as N P. Theefoe, we may uppemost speed-up computatios by a facto of 5 with umbe of paallel pocessos N P. If N P = ad N P =, computatios ae speed-up by factos 3.57 ad.. The thee-dimesioal plot of M speed ( seies,n P if seies [.5 ] ad N P [ ] is illustated i Figue 3. M speed.5 seies N P Figue 3. Plot fo M speed ( seies,n P if seies [.5 ] ad N P [ ] Example 3. : Limits of Pipeliig Coside a deep data paths pipeliig by N pipelie stages. The total latecy of each istuctio is t l, while the ovehead time pe stage is t. This yields the expessio fo the fequecy as f=(t +t l /N Hz. Assume that baches costitute a factio I of all istuctios to be executed. Let, I also icludes pipelie stall o bubbles featues. The aveage umbe of cycles pe istuctio is CPI =+N I. N Fo a N-stage pipelie, the aveage thoughput T=f/ CPI is T = Nt + ti + N. I The optimal umbe of stages N optimal is foud by usig dt/dn=. Oe obtais the optimal umbe of stages ti Noptimal =. t I May factos affect N ad N optimal. These factos ae: data depedecies, peodeig, ucetaities, etc. I most advaced pocessos, N is usually less tha. If oe iceases the depth of pipeliig to N>N optimal, the pefomace degades. Usig the deived expessio fo ti Noptimal =, a thee-dimesioal plot fo N optomal ( l,t l /t, is illustated i t I Figue. 5 N optimal 5.5 I t I /t Figue. Plot fo N optomal ( l,t l /t, -37-

6 HPC-UA (Україна, Київ, - жовтня року. Quatum Pocessig Fudametals We iitiate tasfomative kowledge geeatio ad pefom fudametal eseach o [-5]:. Cosistet aalysis of electo- ad photo-iduced pheomea which lead to quatum state tasitios ad utilizable tasductios o detectable eal-valued measuable physical vaiables (obsevables. These measuable vaiables must be cotollable, algoithmically pocessable ad hadwae ealizable;. Quatum- ad device-physics cosistet fudametals of commuicatio ad pocessig by micoscopic egieeed ad atual systems; 3. Devisig, desig, substatiatio ad demostatio of pactical egieeig paadigms ad techologies o electoic, photoic ad photoelectoic sesig, commuicatio ad pocessig by molecula fabics. It is impotat to pogess fom theoy, to its substatiatio, egieeig solutios ad techologies by:. Studyig ad evaluatig quatum utilizable tasductios o detectable eal-valued measuable physical vaiables;. Veifyig piciples ad mechaisms of eegy covesio, sesig, commuicatio ad pocessig i micoscopic systems as applied to pactical egieeed solutios. Ude some hypotheses ad cojectues, micoscopic system ca be mathematically modeled (mapped by usig wave fuctios i diffeet spaces. Fo example, spatial, mometum ad othe spaces ae used. The spatiotempoal wave fuctio Ψ(,t=ψ(ϕ(t is foud by solvig the time-depedet Schödige equatio t Hˆ Ψ(, E i t Ψ(, t = ih, h iω t Ψ(, t = c t ψ ϕ t cψ e cψ e t Ψ (, = ( ( = ( = (, Ĥ, Ψ, c, (7 = = = whee Ĥ is the total Hamiltoia opeato, Ĥ=Ĥ +Ĥ E +Ĥ P ; Ĥ is the upetubed Hamiltoia i the absece of exteal excitatios, ad, fo a upetubed micoscopic system Ĥ ψ =E ψ, H ˆ = mh + Π ; Ĥ E ad Ĥ P ae the excitatio ad petubatio Hamiltoias; Π is the potetial fuctio; c (t ae the complex pobability amplitudes, ad, *c * is the pobability that a micoscopic system at ay give time t is i a state with E (the pobability that a measuemet of the eegy at t would yield E, c =. = Fom (7, usig Ψ(,t=ψ(ϕ(t, oe has E Ĥ ψ =E ψ, ϕ i t i h = E, h ϕ ( t = e. ( ϕ t Wave fuctios Ψ, deived usig vaious spaces, may yield mathematically-cosistet estimates o vaious quatities, such as pobabilities, allowed states, expectatio values, etc. The expectatio value of a quatum caoical vaiable C ú, with a associated opeato Ĉ, is * C t Cˆ = Ψ (, Ψ(, t dv, C ú. (9 The goveig equatio fo the opeato Ĉ is give as d ˆ ˆ C C = + [ Cˆ, Hˆ ], [Ĉ, Ĥ]=ĈĤ ĤĈ, Ĉ. ( dt t ih Ou quatum-mechaically-cosistet modelig ad aalysis esult i a set of equatios (7-( with the esultig model mappig of micoscopic systems as M(k(Ψ,Ĉ,C K Ĉ C, Ĉ, C ú. ( Vaious use of mathematical opeatios, maipulatios o opeatos, supepositio ad othe pemises of allalgoithmic quatum commuicatio ad pocessig wee outlied i [-]. Thee is a eed to depat fom abstact quatum computig which assumes the pacticality of [-]: Naive all-algoithmic computig o ot detectable, ot obsevable ad ot measuable mathematical opeatos; Algoithmic schemes of quatum logic gates aggegated withi postulated computig stuctues by meas of elusive quatum itecoects ad cicuits; Macoscopic micoelectoic devices icludig the so-called sigle-electo-tasisto, sigle-phototasisto, quatum dots ; etc. By applyig the afoemetioed solutios, it is uclea how oe may esue a pactical computig. It is ulikely that ay pocessig tasks ca be accomplished by diectly o idiectly abstactly usig quatum idetemiacy, icompleteess, mathematical opeatos (wave fuctios, pobability desity ad othes, hidde vaiables, supepositio of states, etc. We outlie the followig Thee Coe Piciples o which ou esults ae ceteed: Piciple : Egieeig Quatum Mechaics Coheet quatum physics ad ifomatio sciece as applied to ifomatio ad data pocessig; -3-

7 HPC-UA (Україна, Київ, - жовтня року Piciple : Desig ad Algoithmic Solutios Pocessig o detectable eal-valued measuable physical vaiables usig distiguishable, quatifiable ad computable tasfoms ad schemes with coespodig data pocessig aithmetics (logics ad calculi, ogaizatios ad achitectues; Piciple 3: Physical Implemetatio o Device ad System Levels Utilize quatum pheomea which lead to state tasitios ad utilizable tasductios o measuable physical vaiables (obsevables i molecula fabics. These vaiables should be quatum-mechaically achievable, algoithmically pocesssable ad hadwae ealizable to pefom pocessig. It is impotat that fo quatum pocessig, the time-depedet Shao etopy H(t,p is give as N H(t,p= p l p. ( i i 5. High-Pefomace Quatum Pocessig Usig thee piciples, we eseach quatum-mechaically cosistet, algoithmically cohesive ad hadwae coheet quatum data pocessig. We use the detectable eal-valued measuable physical vaiables (quatities duig cotollable quatum tasductios [-5]. Oly measuable ad algoithmically pocessable vaiables v V lead to quatum-mechaically, device- ad algoithmically (aithmetically cosistet pocessig. Fo example, v=[e, ω, λ, T, ] T. It is ulikely that computig ca be accomplished by usig wave fuctios, kets, eigekets o othe mathematical quatities, opeatos, etc. Coside cotolled physical micoscopic devices. We utilize the distiguishable ad computable tasfoms T which ae mappigs of the utilizable iitial, itemediate ad fial state tasductios (S I, S T ad S F o v=[v,,v k ] T. The micoscopic devices may accomplish the followig ievesible ad evesible utilizable tasductios S I:v I YS T:v T YS F :v F ad S I:v I ]S T :v T ]S F :v F. (3 Coside a physical micoscopic pocessig fabics with pocessig pimitives P,,P k. Each P j exhibits tasductios S j (v o detectable, measuable ad pocessable vaiables v j yieldig distiguishable ad computable tasfoms T j (S,v. Usig T j (S,v, cosistet with device physics ad admissible aithmetic opead A j, oe has T Σ=T B BT k. ( The pocessig ca be accomplished by usig the ifiite- ad fiite-valued logics. Aalog, digital ad hybid pocessig schemes may be suppoted by micoscopic devices. Cosideig multiple-valued logic, the switchig fuctio o -valued v j is f:{,, } F {,, } m with a tuth vecto F. Ay f ca be epeseted as f=a(f,t. (5 The evolutios of quatum tasductios ae mapped as v j,l ² Q v j,l+ =Q j (v j,l ( which defies the evolutio of physically-ealizable computable tasfoms T j (S,v. The tasductios S j (v o v i physical micoscopic systems (devices ca be cotolled by usig device-specific cotol schemes by vayig systems eegetics, potetial o othe quatities deoted as H [-]. The cotollable evolutios o measuable v j, ae mapped as v j,l ² Q v j,l+ =Q j (v j,l,h j,l, (7 whee Q j deotes tasductios S j o v j cosistet with A(F,T. The biay switchig fuctio is f:{,} F {,} m. A -vaiable -valued fuctio f, with {,, } ito a fiite set {,, } m, e.g., f:{,, } F {,, } m. ( Tuth vectos o biay ad -valued vaiables [x,,x ] ae F=[f(,f(,,f( ] T ad F=[f(,f(,,f( ] T. (9 Digital computig ad digital desig use algebaic maps, Boolea algeba, digital (biay ad multiple-valued logics, decisio diagams, data stuctues, fudametal expasios, polyomial expessios, sequetial etwoks, pobabilistic cocepts, stochastic schemes, ad othe appoaches [, 3]. If quatum-mechaical cosistecy, algoithmically cohesiveess ad hadwae coheecy ae satisfied, some afoemetioed cocepts may be applied fo quatum pocessig. Ay aithmetically- ad algoithmically-defied computable fuctio must be:. Defiable, ealizable ad implemetable as deived by usig the distiguishable ad computable tasfoms;. Implemetable usig the utilizable quatum tasductios o measuable ad algoithmically pocessable vaiables. The calculi ad aithmetics of quatum pocessig ae epoted i [-5,, 3]. diffeet combiatios, is defied as a mappig of a fiite set -39-

8 HPC-UA (Україна, Київ, - жовтня року. Coclusios We examied quatum pheomea which ae exhibited ad utilized to esue high-pefomace quatum pocessig. The followig thee-fold objectives wee achieved:. The micoscopic systems which may eable quatum commuicatio ad pocessig wee devices ad examied;. Pheomea ad mechaisms, possibly utilized by atual systems to accomplish high-pefomace commuicatio ad pocessig, wee studied; 3. A ovel paadigms of high-pefomace quatum pocessig was developed. We eabled a kowledge base ad discoveed ew solutios. Ou tasfomative fidigs ae substatiated by meas of basic, applied ad umeical studies which ae cosistet with expeimets, biophysics, quatum mechaics, ifomatio theoy, compute sciece ad compute egieeig. Refeeces. Iteatioal Techology Roadmap fo Semicoductos, 5, 9 ad Editios, Semicoducto Idusty Associatio, Austi, Texas, USA,.. S. E. Lyshevski, Molecula Electoics, Cicuits, ad Pocessig Platfom, CRC Pess, Boca Rato, FL, S. E. Lyshevski, Molecula ad BioMolecula Pocessig: Solutios, Diectios ad Pospects, Hadbook of Naosciece, Egieeig ad Techology, Ed. W. Goddad, D. Bee, S. E. Lyshevski ad G. Iafate, CRC Pess, Boca Rato, FL,.. S. E. Lyshevski, Hadwae, softwae ad algoithmic solutios fo quatum data pocessig, Poc. IEEE Cof. Naotechology, Bimigham, UK,. 5. S. E. Lyshevski, Quatum pocessig: Feasibility studies ad solutios, Poc. IEEE Cof. Naotechology, Potlad, OR, pp ,.. A. Baeco, C. H. Beett, R. Cleve, D. P. DiVicezo, N. Magolus, P. Sho, T. Sleato, J. A. Smoli ad H. Weifute, "Elemetay gates fo quatum computatio," Phys. Rev. A, vol. 5, o. 5. pp , C. H. Beett, I. Devetak, P. W. Sho ad J. A. Smoli, "Iequalities ad sepaatios amog assisted capacities of quatum chaels," Phys. Rev. Let., vol. 9, o. 55,.. A. Imamoglu, D. D. Awschalom, G. Bukad, D. P. DiVicezo, D. Loss, M. Shewi ad A. Small, Quatum ifomatio pocessig usig quatum dot spis ad cavity QED, Phys. Rev. Let., vol. 3, o., D. C. Maiescu ad G. M. Maiescu, The Boole Lectue Quatum ifomatio: A glimpse at the stage ad itiguig futue of ifomatio." The Compute Joual, vol. 5, pp. 55-5, 7.. M. Mosca, R. Jozsa, A. Steae ad A. Eket, Quatum-ehaced ifomatio pocessig, Tas. R. Soc., vol. A 35, pp. -79,.. A. Steae ad E. Reiffel, Beyod bits: The futue of quatum ifomatio pocessig, Compute, vol. 33, o., pp. 3-5,.. S. Yaushkevich, V. Shmeko ad S. E. Lyshevski, Compute Aithmetics fo Naoelectoics, CRC Pess, Boca Rato, FL, S. Yaushkevich, V. Shmeko ad S. E. Lyshevski, Logic Desig of Nao-ICs, CRC Pess, Boca Rato, FL, 5. --