Quantum robot: structure, algorithms and applications

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1 Qutum robot: tructure, lgorithm d pplictio Doyi Dog, Chuli Che, Chebi Zhg, Zoghi Che Deprtmet of Automtio, Uiverity of Sciece d Techology of Chi, Hefei, Ahui, 37, P. R. Chi emil: dydog@m.c.c (D.Dog) clche@ju.edu.c (C.Che) SUMMARY: A brd-ew prdigm of robot--qutum robot--i propoed through the fuio of qutum theory with robot techology. A qutum robot i eetilly complex qutum ytem which geerlly coit of three fudmetl compoet: multi-qutum computig uit (MQCU), qutum cotroller/ctutor, d iformtio cquiitio uit. Correpodig to the ytem tructure, everl lerig cotrol lgorithm, icludig qutum erchig lgorithm d qutum reiforcemet lerig lgorithm, re preeted for qutum robot. The theoreticl reult how tht qutum robot uig qutum erchig lgorithm c reduce the complexity of the erch problem from O( N ) i clicl robot to O( N N ). Simultio reult demotrte tht qutum robot re lo uperior to clicl robot i efficiet lerig uder ovel qutum reiforcemet lerig lgorithm. Coiderig the dvtge of qutum robot, ome importt potetil pplictio re lo lyzed d propected. KEYWORDS: Qutum robot; Qutum reiforcemet lerig; MQCU; Grover lgorithm Itroductio The dvcemet mde i the field of robotic re mog the mot importt chievemet i ciece d techology i the th cetury [-3]. With techologicl dvcemet [4-8], robot re icreigly ervig the commuity i wide rge of pplictio, uch idutril productio, militry ffir, tiol defee, medicl tretmet d ittio, vigtio d pceflight, public ecurity, d o o. Moreover, ome ew type of robot uch orobot, biorobot d medicl robot hve bee developed through the fuio of otechology, biologicl d medicl egieerig with robot techology. A viewed from the developmet tred of robot, icreig robotic itelligece d reducig the phyicl ize of robot re two importt reerch d developmet thrut. The key to icreig robotic itelligece lie i improvig the performce of

2 eor d icreig the peed of lerig d deciio mkig. At the me time, the reductio of phyicl ize will cue qutum effect to become more promiet. Hece my ew chllege mut be ddreed from ew gle. Qutum theory i oe of the crowig chievemet i the th cetury. I prticulr, my reult i qutum iformtio techology hve how tht qutum computer c effectively icree the efficiecy for olvig ome importt clicl problem d c eve olve ome hrd problem tht clicl computer cot olve efficietly. Furthermore, qutum ytem c relize higher degree of ecurity i telecommuictio ytem d c icree the cpcity of commuictio chel [9]. A reult, qutum ytem d their pplictio hve become importt reerch topic for my cietit. I thi pper, we coider the fuio of qutum theory d robotic, d ue qutum ytem to cotruct ew prdigm of robot qutum robot. The cocept of qutum robot h bee preeted from phyic perpective by Beioff i 998 [,]. Beioff emphized the pplictio of qutum computer i qutum robot; however, the qutum robot he decribed i ot wre of it eviromet, doe ot mke deciio, d doe ot crry out experimet or mke meuremet. We propoe brd-ew qutum robot from egieerig perpective d coider it iformtio exchge d lerig cotrol. Sice qutum robot pplie qutum effect, it olve difficultie reultig from the reductio of phyicl ize. Moreover, the performce of eor c be improved through equippig qutum robot with qutum eor [-6], d the peed of robot lerig d behvior deciio mkig c be icreed uig prllel computig, ft erchig d efficiet lerig from qutum lgorithm. The orgiztio of thi pper i follow. Sectio preet ytem tructure for qutum robot d decribe the fuctio of three fudmetl compoet, icludig multi qutum computig uit (MQCU), qutum cotroller/ctutor, d iformtio cquiitio uit. I Sectio 3 we pply the Grover lgorithm to qutum robot erch problem. I dditio, we propoe ovel mchie lerig lgorithm--qutum reiforcemet lerig (QRL) for qutum robot. The theoreticl reult how tht qutum robot c reduce the complexity of the erch problem from O( N ) i clicl robot to O( N N ) uig the Grover lgorithm. Simultio reult lo demotrte tht qutum robot re uperior to clicl robot i efficiet lerig uder the QRL

3 lgorithm. Sectio 4 compre qutum robot with clicl robot d ugget ome poible pplictio for qutum robot give their dvtge. Sectio 5 preet cocluio d remrk. Sytem Structure of Qutum Robot I 998, Beioff firt propoed the cocept of qutum robot, where qutum robot i decribed mobile qutum ytem tht iclude o-bord qutum computer d eeded cillry ytem []. He emphized the importce of qutum computer i qutum robot, but the robot decribed there h o wree of it eviromet d doe ot mke deciio or meuremet. I thi pper, we provide ltertive defiitio for qutum robot, which coider iterctio with the exterl eviromet vi eig d iformtio proceig. A qutum robot i mobile phyicl pprtu deiged uig qutum effect of qutum ytem, which c ee the eviromet d it ow tte, proce qutum iformtio d ccomplih meigful tk. I prticulr, qutum robot ytem iclude three iterctig compoet: multi qutum computig uit (MQCU), qutum cotroller d ctutor, d iformtio cquiitio uit. A detiled decriptio of the ytem d ech compoet i how i Fig..

4 Fig.. Sytem tructure of qutum robot. A qutum robot iclude three fudmetl compoet: MQCU, qutum cotroller d ctutor, d iformtio cquiitio uit.

5 MQCU. MQCU i the iformtio proceig ceter d ct the cerebrum of qutum robot. It receive tk decribed i qutum lguge d exchge iformtio with it eviromet vi qutum eor or exterl commuictio. By torig, lyzig, computig d proceig vriety of iformtio icludig tk iformtio, eviromet iformtio d eig iformtio, the cerebrum c coduct pproprite qutum cotrol lgorithm d geerte idictio igl for the qutum cotroller to direct the ctutor to perform certi opertio. Uully, MQCU i mde up of my qutum computig uit (QCU) d ech QCU ccomplihe ome pecific tk d exchge iformtio with ech other through qutum bu. The qutum bu my be refrehble etglemet reource [7] or ome other qutum circuit. Beide geerl fuctio of clicl bu uch CAN bu, PCI bu d PC4 bu, the qutum bu hould lo be ble to exchge or preproce qutum iformtio. Accordig to qutum iformtio theory, the QCU c exchge iformtio with ech other more rpidly d ecretly th MCU of clicl robot. Ech QCU i qutum iformtio proceor d it c perform ome cocrete tk uch qutum computig, qutum memory d tk decriptio. I the ctul pplictio, qutum computer c be ued the mi prt of QCU. A qutum computer i phyicl pprtu tht c proce qutum iformtio d perform prllel computtio by mipultig qutum tte i cotrolled fhio. I the qutum computer, iformtio uit (clled qutum bit, or qubit) c lie i the coheret uperpoitio tte of logicl tte d ; tht i to y, it c imulteouly tore d, o it c effectively peed up the computtio of ome clicl problem, d c eve olve ome hrd problem tht clicl computer cot olve efficietly. The eetil chrcteritic of qutum computtio re qutum uperpoitio d qutum coherece. With the rpid developmet of qutum computtio techology, ome qutum computer model c be cotructed uig ucler mgetic reoce (NMR), io trp, d photo. I the preet robot ytem, qutum computer c ct QCU d ccomplih ome pecific tk uch torig, lyzig, computig, d proceig vriety of iformtio to help the MQCU coduct pproprite qutum cotrol lgorithm. Qutum cotroller d ctutor. Thee re the executio d cotrol pprtu of qutum robot. A qutum cotroller receive d procee idictio igl from the MQCU d iform the ctutor to crry out correpodig ctio. It ct the coectio betwee the cerebrum (MQCU) d the rm (ctutor) of qutum robot. Uully, qutum cotroller i qutum

6 ytem, uch qutum CNOT gte. Moreover, oe my deig ueful qutum cotroller uder the directio of the rpidly developig qutum cotrol theory [8-3]. The ctutor execute ome ctio determied by the idictio igl from the qutum cotroller. A ctutor my be pure qutum ytem or emiclicl pprtu cpble of proceig qutum iformtio. Geerlly, the ctutor c exchge qutum iformtio well clicl iformtio with the qutum cotroller. I ome pecific circumtce, the ctutor d qutum cotroller c be coidered igle pprtu, which c directly receive iformtio from the MQCU d crry out ome ctio o it eviromet. I dditio to qutum eor, the ctutor i other iterctio chel betwee qutum robot d it eviromet. Iformtio cquiitio uit. A with clicl robot, qutum robot lo eed to perceive it eviromet d cquire iformtio through iformtio cquiitio uit. I qutum robot, qutum eor perceive the iformtio of it eviromet; the robot my lo receive ome other iformtio from ditt mifrme or other qutum robot through exterl commuictio uit. Uully, the iformtio to be cquired iclude qutum iformtio d clicl iformtio. However, ccordig to qutum theory, the cquiitio of qutum iformtio i difficult ice qutum meuremet detroy the qutum tte of ytem. Hece qutum odemolitio (QND) meuremet i importt tk i qutum robot. A qutum eor i kid of microtructure eor, which i deiged by pplyig qutum effect. To detect fit clicl igl, two kid of qutum eor, upercoductio qutum iterferece device (SQUID) eor [3,4] d qutum well Hll eor [5, 6], c be ued i qutum robot. SQUID eor re extremely eitive mgetic eor tht re cotructed bed o the priciple of upercoductivity, Meier effect, flux qutiztio, d Joepho effect. Uder Joepho effect, SQUID eor c covert miute chge i the curret or mgetic field to meurble voltge d c detect mgetic field mll - Tel. Qutum well Hll eor re kid of high-performce micro Hll eor d ue two-dimeiol electro ge to obti compromie betwee high mobility d high crrier cocetrtio while mitiig reobly high heet reitce. For exmple, we c cotruct qutum well Hll eor through dwichig thi IA lyer betwee AlGSb lyer. The eor h high mgetic eitivity d excellet temperture tbility the reult of good cofiemet of two dimeiol electro ge i qutum well tructure. Hece qutum well Hll eor c be ued to detect fit

7 electromgetic field uder differet circumtce. Due to the high eitivity d good temperture tbility of qutum eor, we c equip the preet qutum robot with thee eor to meure extremely wek electromgetic field. Simulteouly, cietit re tudyig other ew type of qutum eor which c cquire qutum iformtio. Oce they re relized, we my lo equip qutum robot with thee device to ee vriety of qutum igl d feed them bck ito the MQCU. Moreover, qutum robot hve commuictio iterfce to exchge iformtio with ditt mifrme or other qutum robot, which c cotitute multi qutum robot ytem how i Fig.. With exterl commuictio, qutum iformtio c be exchged d the dvtge of qutum commuictio uch high chel cpbility, perfect ecurity d qutum teleporttio c be fully utilized. mifrme qubot 4 qutum bu... qubot m qubot qubot qubot 3 Fig.. Multi qutum robot ytem (where qubot, i.e. qutum robot). Bed o the bove tructure, it i obviou tht qutum robot lo belog to importt cl of robotic ytem tht h the bility to ccomplih certi tk through perceivig eviromet vi eor d ctig upo thoe eviromet vi ctutor. The chrcteritic ret with the phyicl implemettio d their prticulr iformtio proceig cpbilitie. Suppoe the tk of the qutum robot i to it doctor with medicl ervice i biomedicie, the iformtio of tk decompoitio decribed by qutum lguge i et to the MQCU. Moreover, the MQCU lo receive eig iformtio from the exterl eviromet, d every QCU i i chrge of ome pecific work uch trckig, vigtio, etimtio, digoi, etc. Accordig to the proceig reult of the MQCU, the qutum cotroller obti idictio igl from the MQCU d iform the ctutor to crry out correpodig ctio o exterl eviromet. Repetedly, iformtio cquiitio uit perceive eviromet d ed eig iformtio to the MQCU. The MQCU procee the iformtio d geerte ew igl or lerig cotrol lgorithm to the qutum

8 cotroller d ctutor util the tk i ccomplihed. I thi proce, the deig of lerig cotrol lgorithm i key pect. Coiderig the chrcteritic of the qutum robot, we preet two lgorithm: Grover lgorithm [4] for robot erchig d qutum reiforcemet lerig (QRL) lgorithm for robot lerig. 3 Lerig Cotrol Algorithm for Qutum Robot A key pect of qutum robot deig i the developmet of high-efficiecy lerig cotrol lgorithm. A for clicl robot, it i difficult to perform lgorithm with high complexity while tifyig the requiremet for rel-time proceig becue the CPU cot compute ft eough d the itegrtio of chip i limited. However, qutum robot i eetilly mde up of my qutum ytem d the MQCU lie i the cetrl poitio of the etire qutum robot ytem. Hece oe c ue the bility of qutum prllel proceig to deig correpodig lerig cotrol lgorithm, which c effectively reduce the complexity of olvig problem d peed up iformtio proceig. After itroducig fudmetl cocept of qutum prllel computtio i ubectio 3., we cotiue to decribe the Grover lgorithm for qutum robot erch problem d propoe ovel QRL lgorithm for qutum robot lerig. 3. Prllel Proceig i Qutum Robot A qutum robot i eetilly complex qutum ytem d it tte i repreeted with qutum tte. To coveietly proce ll kid of iformtio, we coidered ecodig ll iformtio ccordig to qubit. I qutum iformtio theory, the tte of rbitrry qubit c be writte by uperpoitio tte follow: = α + β ψ () where α d β re complex coefficiet tht tify α + β =. d re two orthogol tte (lo clled eigette of qutum tte α ψ ), d they correpod to logic tte d repectively. repreet the occurrece probbility of whe the qubit i meured, β d i the probbility of obtiig the reult. The vlue of clicl bit i Boole vlue either or, but qubit c be prepred i the coheret uperpoitio tte of d, i.e.

9 qubit c imulteouly tore d, which i oe of the mi differece betwee clicl robot d qutum robot. Accordig to qutum iformtio theory, the qutum computig proce c be looked upo uitry lier trformtio U from iput qubit to output qubit. Sice qutum robot i eetilly qutum ytem d the MQCU lie i the cetrl poitio of the qutum robot, the proceig of the qutum robot c lo be looked upo correpodig trformtio. If oe pplie trformtio U to uperpoitio tte, the trformtio will ct o ll eigette of thi uperpoitio tte d the output will be ew uperpoitio tte by uperpoig the reult of eigette. Whe the qutum robot procee fuctio f (x) by thi method, the trformtio U c imulteouly work out my differet reult for certi iput x. Thi i logou to clicl prllel proceig, o we cll it prllel proceig of qutum robot. The bility of trog prllel proceig i importt dvtge of qutum robot over clicl robot. Coider -qubit cluter which lie i the followig uperpoitio tte: L ψ = C x x, = () x= L L C x x= L where the legth of x i, C i complex coefficiet d repreet the occurrece x probbility of x meurig tte ψ. x h vlue, o the uperpoitio tte c be looked upo the uperpoitio tte of ll iteger from to -. Sice U i lier, proceig fuctio Cx f (x) produce: L x x= L L U C x, = C U x, = C x, f ( x) (3) x x= L x, x, f ( x) L x x= L where repreet the iput joit tte d repreet the output joit tte. Bed o the bove lyi, it i ey to ee tht -qubit cluter c imulteouly proce tte. However, thi i differet from clicl prllel proceig qutum prllel proceig doe ot ecerily mke trdeoff betwee proceig time d required phyicl pce. I fct, it provide expoetil-cle proceig pce i the -qubit lier phyicl pce. So qutum robot c effectively peed up iformtio proceig for ome problem uch vigtio d deciio.

10 3. Serchig Algorithm for Qutum Robot Jut clicl robot, mot plig d cotrol problem of qutum robot c be poed erch problem. Thu we will put forth btrct robot plig problem, d pply qutum Grover lgorithm to it exmple. Firt coider robot plig ytem whoe tte evolve ccordig to certi tritio probbilitie tht deped o cotrol u. If the robot i i tte i d chooe cotrol u ccordig to policy π, it will move to tte j with probbility p ij (u) d cot g( i, u, j). Now uppoe tht the deirbility of tte i defied V, which me the vlue of tte. The tk of robot plig ytem i to fid out the optiml equece of m equtio V * V (tte), which tifie ome form of Bell- * ( i) = mi E[ g( i, u, j) + V ( j) i, u] (for ll i, j ) (4) u where E[ i, u] i the expected vlue. At certi tte i, the robot plig problem i imply utructured erch problem to fid the ctio (or the ext tte j ) which i optiml. i For utructured erch problem of erch pce N, the computtiol complexity i clicl computtio i O( N ). I robotic, it i importt tk to erch for uitble ctio from the ctio pce bed o the curret tte of the robot. If the complexity of the tte (or ctio) pce i N O( ), the problem complexity for clicl robot i O( ), where qutum robot c reduce N the complexity to O( N N ) by uig the Grover lgorithm. If there re N ltertive ctio ( N ), we c expre them with qubit: L = l= L where the legth of l i. For coveiece, (5) c lo be expreed Aumig the ctio to be foud correpod to erch tk. Firt, we prepre qutum tte ψ l l (5) = i= ψ i i (6) k, ow we ue Grover lgorithm to complete the

11 = (7) i= i which i equl weight uperpoitio tte. Thi c be ccomplihed by pplyig the Hdmrd trformtio to ech qubit of the -qubit tte L [9, 5]. The we cotruct reflectio trform U = I (8) U Geometriclly, whe ct o rbitrry vector, it preerve the compoet log d flip the compoet i the hyperple orthogol to. Thu if we pply U to ψ, we get U ψ ψ ψ = = ψ = i i i = ( i ) i (9) i= i= i= where Now we give other reflectio trform = i i= () U k = k k + I () where k i the k-th eigette d by pplyig it to tte ψ, we obti U k ψ = k k ψ + ψ = k k + ψ = i i k k () i=, i k It i ey to ee tht U k oly chge the mplitude ig of k i the uperpoitio tte. Thu we c form uitry trformtio (Grover itertio) [9, 4] U = U U (3) G k By repetedly pplyig the trformtio U G o ψ, we c ehce the probbility mplitude of k while uppreig the mplitude of y other tte i k [4]. After eough umber of itertio of the trformtio, we c perform meuremet o the ytem to mke the tte ψ collpe ito k with probbility of lmot.

12 i θ =/ Defie gle θ tifyig. After pplyig the j time to U G ψ, the mplitude of k become j k = i(( j + ) θ ) (4) If j = ( π θ )/ 4θ, the ( + ) θ = π / k = j j d. However, we mut perform iteger umber of itertio. Boyer h how i [6] tht the probbility of filure i o more th / N if we perform the Grover itertio it( π / 4θ ) time (here the fuctio it(x) retur the iteger prt of x ). Accordig to Grover lgorithm, whe N i lrge, qutum robot c fid the ctio correpodig to k with high probbility of [-O( / N )]. Sice Grover lgorithm c fid deired reult with probbility of lmot i N tep, the qutum robot reduce the complexity d c fid uitble ctio from the ctio pce bed o the curret tte of the robot. If the umber of tte i 4, coiderig differet umber of ctio, the problem complexitie i clicl robot d qutum robot c be compred how i Tble I. From the Tble, we c coclude tht the dvtge of qutum robot i more d more promiet with the icree i the umber of ctio. Tble I. Comprio of problem complexitie i clicl robot d qutum robot Number of ctio Complexity i clicl robot Complexity i qutum robot Lerig Algorithm for Qutum Robot The eece of robot lerig i to del with tte-ctio pir {Stte(t), Actio(t)} [3]. Lerig method re geerlly clified ito upervied, uupervied d reiforcemet lerig (RL). Supervied lerig require explicit feedbck provided by iput-output pir d give mp from iput to output. Uupervied lerig oly procee o the iput dt. However, RL ue clr vlue med rewrd to evlute the iput-output pir d ler by iterctio with eviromet through tril-d-error. Sice 98, RL h become importt pproch to mchie itelligece [7-3], d i widely ued i rtificil itelligece, epecilly i robot [3-34], due to it good

13 performce of o-lie dpttio d powerful lerig bilitie of complex olier ytem [7, 8, 35]. To dpt lerig lgorithm to qutum robot, we propoe ovel lerig method-- qutum reiforcemet lerig (QRL), ipired by qutum uperpoitio d qutum prllelim. Let N d N be the umber of tte d ctio, repectively. Chooe umber m d tifyig the followig iequtio: m N N, N N (5) Ue m d qubit to repreet tte et S={} d ctio et A={} repectively: : b b b m m, where i + b i =, i =,,... m : α α β β α, where αi + βi =, i =,,... β Thu thee my be i uperpoitio tte: L ( m) ( ) = C, = C (6) = L L = L where C x + iy d C = u + iv re complex umber. The mppig from tte to ctio = i f ( ) = π : S A d we will get: L ( ) f ( ) = = C (7) = L C deote the probbility of whe ( ) i meured. Bed o the bove expreio, the procedurl form of QRL c be decribed follow. Procedure QRL L ( m) ( ) Iitilize = C, f ( ) = = C d V () rbitrrily = L Repet (for ech epiode) L ( m) For ll tte = C : = L f () () Oberve d get ; L = L

14 ( m) () Tke ctio, oberve ext tte ', rewrd The updte: V ( ) V ( ) + α ( r + γv ( ') V ( )) r C r V ( ')) e λ( + C Util for ll tte Δ V ( ) ε. QRL i ipired by the tte uperpoitio priciple of qutum tte d qutum prllel computtio. The tte vlue c be repreeted with qutum tte d be obtied by rdomly obervig the imulted qutum tte, which will led to tte collpe ccordig to the qutum meuremet potulte. Ad the occurrece probbility of eigevlue i deoted by probbility mplitude, which i updted ccordig to rewrd. Thi pproch repreet the whole tte-ctio pce with the uperpoitio of qutum tte d mke good trdeoff betwee explortio d exploittio uig probbility. Moreover, the repreettio method i coitet with qutum prllel computtio d c peed up lerig drmticlly. I [7], Bertek d Titikli hve verified tht tochtic itertive lgorithm, uder certi explortio policie, coverge t the optiml tte vlue fuctio followig coditio hold ( where α k i the tepize): T * V () with probbility whe the lim α =, lim α < (8) T k= k T T k= QRL i imilr to RL, with the followig differece: () explortio policy i bed o the collpe theory of qutum meuremet while beig oberved; () prllel computtio. Hece the modifictio of RL doe ot ffect the chrcteritic of covergece d QRL lgorithm coverge whe (8) hold. To evlute the QRL lgorithm i prctice, coider exmple of grid eviromet with four room d urroudig corridor how i Fig. 3. Ech cell of the grid correpod to idividul tte of the eviromet. From y tte, the robot (or get) c perform oe of four primry ctio: up, dow, left d right; d ctio tht would led ito blocked cell re ot executed. The tk of the lgorithm i to fid optiml policy tht will let the robot move from S to G with miimized cot (or mximized rewrd). The imultio eviromet i bed o Widow d Viul C++. The reult re proceed with Mtlb 6.5. k

15 Experimetl et-up. I QRL, the ctio electig policy i obviouly differet from clicl RL lgorithm, which i ipired by the collpe theory of qutum meuremet. The probbility C mplitude i ued to deote the probbility of ctio defied f ( ) = ( ) = L 3( ~ ) C = L. For the four cell-to-cell ctio i iitilized uiformly. I thi 3 grid world, the iitil tte d the gol re cell(4,4) d cell(8,8) repectively. C Fig. 3. The exmple of room with corridor i gridworld eviromet with cell-to-cell ctio (up, dow, left d right). The lbel S d G idicte the iitil tte d the gol i the imultio experimet decribed i the text.

16 Fig. 4. Performce of QRL for the exmple how i Fig. 3. Reult d lyi. The lerig performce for QRL i plotted i Fig. 4. We oberve tht give proper tepize (lph <.) thi lgorithm ler extrordirily ft t the begiig phe, d the tedily coverge to the optiml policy tht cot 5 tep to the gol G. A the tepize icree from. to., thi lgorithm ler fter but more utedily. Whe the tepize i., it cot coverge to the optiml policy. Thee reult how tht thi QRL lgorithm re uperior to other RL lgorithm i two mi pect: () Actio electig policy mke good trdeoff betwee explortio d exploittio uig probbility, which peed up the lerig d gurtee the erch over the whole tte-ctio pce well. () Updtig i crried out i prllel, which will be much more promiet i the future whe prcticl qutum pprtu come ito ue ited of beig imulted o clicl computer. 4 Applictio of Qutum Robot Before preetig the potetil pplictio of qutum robot, we firt compre qutum robot with clicl robot i detil i Tble II.

17 Tble II. Comprio betwee qutum robot d clicl robot Compred item Qutum robot Clicl robot Sytem property Qutum ytem Mechicl ytem O-bord eor Qutum eor uch Ifrred eor, SQUID eor d ultroic eor, CCD qutum well Hll eor cmer d etc. Phyicl Lw Qutum mechicl lw Clicl mechicl lw Iformtio proceig MQCU (Multi qutum Clicl proceor uch cetre computig uit) clicl computer Iformtio Qutum iformtio d Clicl iformtio clicl iformtio Seitivity High Reltively lower Spce ize Microcomic Motly mcro Techicl difficulty More difficult Eier Commuictio mer Qutum commuictio Clicl commuictio d clicl commuictio Prllel proceig Powerful Wek bility Thu it c be ee tht the qutum robot, brd-ew robot, c olve difficultie reultig from the reductio of phyicl ize of robot. It mke ue of qutum eor to cquire qutum iformtio well clicl iformtio from it eviromet d h extremely high deliccy, which effectively overcome the limittio of exitig eor performce. At the me time, it c directly ue the dvtge of qutum iformtio techology to peed up the cotrol d deciio mkig. So it will hve wide pplictio propect i my field. Here, we outlie ome potetil pplictio of qutum robot. A qutum robot c be ued ptrol wrrior i militry ffir d tiol defee. If the mgetic field er importt port d militry be hve bee meured i dvce, the high eitivity of qutum eor llow qutum robot to perceive the fit chge i mgetic field reultig from the cloig of uke d cout to effectively forewr deciio-mker. I vitio d pceflight, qutum robot c be ued Mr d lur explortio vehicle with it dvtge of high eitivity i perceivig eviromet, it powerful bility to proce iformtio d it iherece ture tht llow for more ecure commuictio. I biomedicie, qutum robot c be ued for ptiet with cotgiou diee for exmiig or trckig tte of ille, d c ct SARS ure d cotgio doctor. Oce qutum robot i uccefully cotructed, it my be poible to etblih moleculr-cle medicl robot. Thu qutum robot c be ijected ito the body d move log with blood circultio to detect potetil pthologicl chge i body. At the me time, it my provide ovel wy to tudy life. I cietific reerch, it i poible to ue qutum robot to olve

18 mot complex problem with le phyicl reource d provide tet-bed for experimetl reerch i phyic, chemitry, d iformtio techologie o tht ome experimetl reliztio of qutum commuictio, qutum computtio, d qutum cotrol my be poible. I fety egieerig, oe my tke dvtge of the high eitivity d mll ize of qutum robot to pply them to my tk uch ti-terror forewrig, fire forectig, urveillce, d trffic cotrol. 5 Cocluio With techologicl dvcemet, robot hve bee widely pplied to my field. At the me time, ew type of robot uch orobot, biorobot d medicl robot hve lo bee uder developmet. Thi pper propoe other ew type of robot qutum robot, by the fuio of qutum theory with robotic techology. A qutum robot i mobile phyicl pprtu deiged uig qutum effect of qutum ytem, which c ee the eviromet d it ow tte, proce qutum iformtio d ccomplih meigful tk. It coit of three fudmetl compoet: MQCU, qutum cotroller d ctutor, d iformtio cquiitio uit. To dpt lgorithm to the ytem tructure of qutum robot, qutum erchig lgorithm d qutum reiforcemet lerig lgorithm re propoed for qutum robot. The theoreticl reult how tht qutum robot c reduce the complexity of the erch problem from of O( N ) i clicl robot to O( N N ) uig Grover lgorithm. Simultio experimet demotrte tht qutum robot re lo uperior to clicl robot i efficiet lerig ice qutum reiforcemet lerig mke good trdeoff betwee explortio d exploittio uig probbility. Hece qutum robot hve my potetilly importt pplictio i militry ffir, tiol defee, vitio d pceflight, biomedicie, cietific reerch, fety egieerig d other dily life tk. To implemet rel qutum robot i o doubt very chllegig miio, which coit of three kid of work: () ythei rchitecture for qutum robot ytem; () phyicl implemettio icludig computig uit, eor, ctutor d commuictio hrdwre; d (3) oftwre level reerche uch relted theorie d progrmmig iue. Though our work i oly the firt tep towrd prcticl qutum robot, it h promiig future give the rpid developmet d grdul mturtio of qutum iformtio techology d qutum cotrol theory.

19 Ackowledgemet We thk P. Beioff, L. Zhug, Z. Xi d S. Jig for helpful commet. Thi work h bee upported by the Iovtio Reerch Project of Sciece d Society Prctice of CAS for Grdute Studet (No. 4-8), d the Iovtio Fud of USTC for Grdute Studet (KD448). Referece. Z. X. Ci, Robotic (Tighu Uiverity Pre. Beijig, Chi, ). M. A. Slich, L. Moreo, Nvigtio of Mobile Robot: Ope Quetio, Robotic 8, 7-34 (). 3. G. N. DeSouz d A. C. Kk, Viio for Mobile Robot Nvigtio: A Survey, IEEE Tr. Ptter Al. Mch. Itell. 4, (). 4. O. Khtib, Rel Time Obtcle Avoidce for Mipultor d Mobile Robot, It. Jourl of Robotic Reerch 5, 9-98 (986). 5. L A. Meede, Tred i evolutiory robotic. L. C. Ji d T. Fukud (Ed.) Soft Computig for Itelliget Robotic Sytem. New York: Phyicl Verlg, 998: F. Hofm, G. Pfiter, Evolutiory Deig of Fuzzy Kowledge Be for Mobile Robot, It. Jourl of Approximte Reoig, 7, (997). 7. D. Floreo d F. Modd, Evolutiory Neuro-cotroller for Autoomou Mobile Robot, Neurl Network, (998). 8. S. Thru Lerig Metric-topologicl Mp for Idoor Mobile Robot Nvigtio, Artificil Itelligece 99, -7 (998). 9. M. A. Niele, I. L. Chug, Qutum Computtio d Qutum Iformtio (Cmbridge Uiverity Pre. Cmbridge, Egld, ). P. Beioff, Qutum Robot d Eviromet, Phy. Rev. A 58, (998).. P. Beioff, Some Foudtiol Apect of Qutum Computer d Qutum Robot, Superlttice. Microt. 3, (998).. J. Moriw, M. Otk, M, Kodm, T. Kto, S. Suzuki, Detectio of Itergrulr Crckig Suceptibility Due to Hydroge i Irrdited Auteitic Stile Steel with A Supercoductig Qutum Iterferece Device (SQUID) Seor, J. Nucl. Mter.3, 66 7 (). 3. A. E. Mhdi, D. J. Mpp, High-T c SQUID: the Ultr Seitive Seor for No-detructive Tetig d Biomgetim, Seor d Actutor 8, (). 4. G. Klli, E. Devli, C. Chritide, D. Nircho, High T c SQUID Seor Sytem for Nodetructive Evlutio, Seor d Actutor 85, (). 5. M. Behet, J. Bekert, J. De Boeck, G. Borgh, IA/Al. G.8 Sb Qutum Well Hll Effect Seor, Seor d Actutor 8, 3 7().

20 6. M. Behet, J. D, J. De Boeck, G. Borgh, IA/(Al, G)Sb Qutum Well Structure for Mgetic Seor, IEEE Tr. Mg. 34, 3 3 (998). 7. G. K. Bree, D. Sog, C. J. Willim, Qutum-Computer Architecture Uig Nolocl Iterctio, Phy. Rev. A 67, 53 (3). 8. D. D`Aledro, M. Dhleh, Optiml Cotrol of Two-level Qutum Sytem, IEEE Tr. Automt. Cotr. 46, (). 9. A. C. Doherty, S. Hbib, K. Jcob, H. Mbuchi, S. M. T, Qutum Feedbck Cotrol d Clicl Cotrol Theory, Phy. Rev. A 6, 5 ().. S. Lloyd, Coheret Qutum Feedbck, Phy. Rev. A 6, 8 ().. S.G. Schirmer, A. I. Solomo, J.V. Lehy, Degree of Cotrollbility for Qutum Sytem d Applictio to Atomic Sytem, J. Phy. A: Mth. Ge., 35, ().. F. Albertii, D. D Aledro, Notio of Cotrollbility for Bilier Multilevel Qutum Sytem, IEEE Tr. Automt. Cotr. 48, (3). 3. D. Y. Dog, C. B. Zhg, Z. H. Che, Qutum Feedbck Cotrol Uig Qutum Cloig d Stte Recogitio, Proc. of the 6th IFAC World Cogre, p.965, Prgue, July 4-8, L. K. Grover, Qutum Mechic Help i Serchig for Needle i Hytck, Phy. Rev. Lett. 79, (997). 5. J. Prekill, Qutum Iformtio d Computtio (Cltech, USA, 998) 6. M. Boyer, G. Brrd, P. Hoyer, Tight Boud o Qutum Serchig, Fortch. Phy. 46, (998). 7. R. Sutto, A. G. Brto, Reiforcemet Lerig: A Itroductio (MIT Pre. Cmbridge, MA, 998). 8. L. P. Kelblig, M. L. Littm, A. W. Moore, Reiforcemet Lerig: A Survey, J. Artif. Itell. Re. 4, (996). 9. C. Wtki, P. Dy, Q-lerig, Mch. Ler. 8, 79 9 (99). 3. D. P. Bertek, J. N. Titikli, Neuro-Dymic Progrmmig (Athe Scietific, Belmot, MA, 996). 3. H. M. Brberá, A Ditributed Architecture for Itelliget Cotrol i Autoomou Mobile Robot (Doctor thei, Uiverity of Murci, Spi, ). 3. H. R. Beom, H. S. Cho, "A Seor-Bed Nvigtio for A Mobile Robot Uig Fuzzy Logic d Reiforcemet Lerig", IEEE Trctio o SMC, 5, (995). 33. W. D. Smrt, L. P. Kelblig, Effective Reiforcemet Lerig for Mobile Robot, Proc. of the IEEE Itertiol Cof. o Robotic & Automtio () pp

21 34. N. H. C. Yug d C. Ye, A Itelliget Mobile Vehicle Nvigtor Bed o Fuzzy Logic d Reiforcemet Lerig, IEEE Tr. Syt., M, Cyber. B 9, 34-3 (999). 35. J. N. Titikli, Aychroou Stochtic Approximtio d Q-lerig, Mch. Ler. 6, 85- (994).

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