Abatshisi: Almudena Carrera Vazquez Caroline Tornow Diego Ristè Stefan Woerner Maika Takita Daniel J. Egger Isishwankathelo Iikhompyutha zeQuantum zisebenzisa imithetho ye-quantum mechanics ukucubungula ulwazi. Izixhobo ze-quantum zangoku zinomsizi, zinokugcina ulwazi ixesha elifutshane kwaye zilinganiselwe kwiibits ezimbalwa ze-quantum, oko kukuthi, i-qubits, eziqhele ukubekwa kuqwalaselo lwenqwelomoya . Nangona kunjalo, izicelo ezininzi zokubala nge-quantum zifuna unxibelelwano oluninzi kunonxibelelwano lwenqwelomoya olunikezelwa zezixhobo kwi-qubits ezininzi kunoko zifumaneka kwiyunithi enye yokucubungula i-quantum (QPU). Indibano yethemba lokujongana nala maxesha ngokudibanisa iiQPUs kusetyenziswa unxibelelwano lwekhompyutha, nto leyo engakhange iboniswe ngovavanyo. Apha senze izixhobo ze-dynamic circuits eziphathwe yimpazamo kunye nokusika izangqa ukwenza imeko ze-quantum ezifuna unxibelelwano oluphindaphindayo kusetyenziswa ii-qubits ezifikelela kuma-142 ezisasazeke kuzo zombini iiQPUs ezinama-qubits ali-127 ngalinye, eziqhagamshelwe ngexesha lokwenyani kunye nonxibelelwano lwekhompyutha. Kwisangqa esine-dynamic, ii-gates ze-quantum zinokulawulwa yi-classical ngokwemiphumo yomlinganiselo we-mid-circuit ngaphakathi kwexesha lokubaleka, oko kukuthi, ngaphakathi kwesahlulo sexesha lokuhambelana kwe-qubits. Unxibelelwano lwethu lwekhompyutha lwangempela lvusila ukuba singasebenzisa i-quantum gate kwenye i-QPU exhomekeke kumiphumo yomlinganiselo kwenye i-QPU. Ngaphezu koko, ulawulo oluphathwe yimpazamo lonyusa unxibelelwano lwe-qubit kunye neseti yemiyalelo yezixhobo ngaloo ndlela lonyusa ukuguquguquka kwezikhompyutha zethu ze-quantum. Umsebenzi wethu ubonisa ukuba sinokusebenzisa ii-processors ezininzi ze-quantum njenge-nye kunye ne-dynamic circuits ezilawulwa yimpazamo ezisetyenziswa yinxibelelwano yexesha lokwenyani. 1 Into enkulu Iikhompyutha zeQuantum zisebenzisa imithetho ye-quantum mechanics ukucubungula ulwazi olufakwe kwi-quantum bits nge-unitary operations. Nangona kunjalo, ii-quantum computers zinomsizi kwaye uninzi lwezixhobo ezinkulu zicwangcisa ii-qubits ezingokoqobo kuluhlu lwenqwelomoya. Ngaphandle koko, ii-processors zangoku ezine-error mitigation zinokulinganisa ii-Ising models zemveli ezine-qubits ezili-127 kwaye zilungelelanise i-observables ngesikali apho iindlela zokwenza ngokuphindaphinda ngeekhompyutha ze-classical ziqala ukulwa . Ukusetyenziswa kwezi-quantum computers kuxhomekeke ekwandisweni okunye nasekunqobeni unxibelelwano lwazo olulinganiselweyo lwe-qubit. Indlela ye-modular ibalulekile ekwandiseni ii-quantum processors zamanje ezinomsizi kunye nasekufezekiseni amanani amakhulu e-physical qubits afunekayo kwi-fault tolerance . Izakhiwo ze-trapped ion kunye ne-neutral atom zingafumana i-modularity ngokuhambisa ii-qubits ngokwas physical , . Kwixesha elingekude, i-modularity kwi-superconducting qubits ifunyanwa ngeenxibelelanisi ezimfutshane eziqhagamshela iichips ezikufutshane , . 1 2 3 4 5 6 7 8 Kwixesha eliphakathi, ii-gates ezikude ezisebenza kwiregim ye-microwave zingasetyenziswa ngocingo olude lwe-conventional , , . Oku kungavumela unxibelelwano lwe-qubit olungeyiyo i-planar olulungele ukulungisa impazamo okusebenzayo . Enye indlela yexesha elide kukuqhagamshela iiQPUs ezikude ngonxibelelwano lwe-optical kusetyenziswa i-microwave ukuya kwi-optical transduction , nto leyo engakhange iboniswe, ngokwazi kwethu. Ngaphezu koko, ii-dynamic circuits zandisa iseti ye-operations ye-quantum computer ngokwenza imilinganiselo ye-mid-circuit (MCMs) kunye nolawulo lwe-classical yeqela ngaphakathi kwexesha lokuhambelana kwe-qubits. Zonyusa umgangatho we-algorithmic kunye nonxibelelwano lwe-qubit . Njengoko sizakubonisa, ii-dynamic circuits zikwenza kube lula i-modularity ngokudibanisa iiQPUs ngexesha lokwenyani ngenxibelelwano lwe-classical. 9 10 11 3 12 13 14 Sithatha indlela eyahlukileyo esekelwe kwii-gates ezibonakalayo ukwenza imisebenzi ekude kwisixhobo esiyimodular. Siyadibanisa ii-qubits kwindawo ezithile kwaye senze izibalo zokunxibelelana nge-quasi-probability decomposition (QPD) , , . Siyayithelekisa inkqubo ye-Local Operations (LO) kuphela neye-Classical Communication (LOCC) eyongeziweyo . Inkqubo ye-LO, eboniswe kwisetingi se-qubit ezimbini , ifuna ukwenziwa kwezangqa ezininzi ze-quantum ezine-operations ezisemgangathweni kuphela. Ngokungafaniyo, ukwenza i-LOCC, sisebenzisa iibhayi ze-Bell ezibonakalayo kwisangqa sokuhambisa ukwenza ii-gates ezimbini ze-qubit , . Kwii-hardware ze-quantum ezinoxanduva olungabonakaliyo kunye nolwenqwelomoya, ukwenza i-Bell pair phakathi kwe-qubits ezingafaniyo kufuna i-CNOT gate ekude. Ukuphepha ezi gates, sisebenzisa i-QPD phezu kwe-operations ezisemgangathweni ephumela kwii-Bell pairs ezisikiweyo ezisetyenziswa yi-teleportation. Ii-LO azifuni nxibelelwano lwe-classical kwaye ngoko ke kulula ukuyenza kunokwenza i-LOCC. Nangona kunjalo, njengoko i-LOCC ifuna isangqa setemplate esinye kuphela, kulula ukusiguqulela kunokwenza i-LO kwaye iindleko ze-QPD yayo ziphantsi kunokwenza i-LO scheme. 15 16 17 16 17 18 19 20 Igalelo lethu libalulekileyo linegalelo ezine. Okokuqala, sibonisa ii-quantum circuits kunye ne-QPD ukwenza ii-Bell pairs ezisikiweyo ezininzi ukwenza ii-virtual gates kwi-ref. . Okwesibini, sinciphisa kwaye silawule iimpazamo ezivela kwi-latency ye-hardware yelawulo lwe-classical kwii-dynamic circuits ngokudibanisa i-dynamical decoupling kunye no-zero-noise extrapolation . Okwesithathu, sisebenzisa ezi ndlela ukuyila imeko yomda ophindaphindayo kwi-graph state enee-nodes ezili-103. Okwesine, sibonisa unxibelelwano lwe-classical ngexesha lokwenyani phakathi kwezi-QPU ezimbini ezahlukeneyo ngaloo ndlela sibonisa ukuba inkqubo ye-QPUs ezisasazekileyo ingasetyenziswa njenge-nye ngonxibelelwano lwe-classical . Idibene ne-dynamic circuits, oku kusivumela ukuba sisebenzise zombini iichips njenge-quantum computer enye, esiyibonisa ngokuyila i-periodic graph state eyandisa zombini izixhobo kwi-qubits ezili-142. Siyaxoxa ngendlela yokuya phambili yokwenza ii-gates ezikude kunye nokubonelela ngesigqibo sethu. 17 21 22 23 Ukusikwa kwee-Circuits Sisebenzisa ii-quantum circuits ezinkulu ezingenakwenziwa ngokuthe ngqo kwizixhobo zethu ngenxa yemida kwinani le-qubit okanye unxibelelwano ngokusikwa ii-gates. Ukusikwa kwee-Circuits kwahlula i-circuit eyiyo kwiincazelo ezincinci ezinokwenziwa ngokwahlukileyo , , , , , . Nangona kunjalo, kufuneka sisebenzise inani elongeziweyo lezangqa, esizibiza ngokuba yi-sampling overhead. Iziphumo ezivela kwezi nkcazo ziye zihlaziywe kunye kunye ukuze kuveliswe isiphumo sesangqa sokuqala ( ). 15 16 17 24 25 26 Methods Njengenye yegalelo elikhulu lomsebenzi wethu kukwenza ii-virtual gates kunye ne-LOCC, sibonisa indlela yokwenza ii-Bell pairs ezisikiweyo ezifunekayo kunye ne-operations ezisemgangathweni. Apha, ii-Bell pairs ezisikiweyo ezininzi ziyilwe ngeezangqa ze-quantum ezinemparamenta, esizibiza ngokuba yi-cut Bell pair factory (Fig. ). Ukusika ii-pairs ezininzi ngaxeshanye kufuna i-sampling overhead ephantsi . Njengoko umzi we-Bell pair osikiweyo wenza ii-quantum circuits ezimbini ezahlukene, sibeka incazelo nganye yazo kufutshane ne-qubits enee-gates ezikude. Umthombo osisiphumo uya kusetyenziswa kwisangqa sokuhambisa. Ngokomzekelo, kwiFig. , ii-Bell pairs ezisikiweyo zisetyenziswa ukwenza ii-CNOT gates kwi-qubit pairs (0, 1) kunye (2, 3) (bona icandelo ‘ ’). 1b,c 17 1b Cut Bell pair factories , Umzekelo wesakhiwo se-IBM Quantum System Two. Apha, ii-Eagle QPUs ezimbini ezinama-127 qubits ziqhagamshelwe ngonxibelelwano lwe-classical ngexesha lokwenyani. I-QPU nganye ilawulwa zii-electronics zayo kwi-rack yayo. Siyakulungelelanisa kakuhle zombini ii-racks ukuze sisebenzise zombini iiQPUs njenge-nye. , Isangqa se-template ye-quantum sokwenza ii-CNOT gates ezibonakalayo kwi-qubit pairs ( 0, 1) kunye ( 2, 3) kunye ne-LOCC ngokusebenzisa ii-Bell pairs ezisikiweyo kwisangqa sokuhambisa. Imigca emibini emdaka ijongana nonxibelelwano lwe-classical ngexesha lokwenyani. , Iimfama ze-Bell pair ezisikiweyo 2( ) ngee-Bell pairs ezisikiweyo ezimbini ngaxeshanye. I-QPD ineenqanaba ezahlukeneyo ezingama-27 zeeparameter . Apha, . a b q q q q c C θ i θ i Imida yeBoundary yePeriodic Sakha i-graph state | ⟩ kunye nemida ye-boundary ye-periodic kwi-ibm_kyiv, i-Eagle processor , sidlula imida ebekwe lulwakhiwo lwayo (bona icandelo ‘ ’). Apha, ine-nodes ezili-103 ∣ ∣ kwaye ifuna ii-edges ezimbini ezikude lr = {(1, 95), (2, 98), (6, 102), (7, 97)} phakathi kwe-qubits ephezulu nasezantsi ze-Eagle processor (Fig. ). Silinganisa ii-stabilizers ze-node kwi-node nganye ∈ kunye nee-stabilizers zejelo ezakhiwe yimveliso kulo lonke ijelo ( , ) ∈ . Kwezi stabilizers, sakha isiqinisekiso sokunxibelelana , esingezizo ezakhelayo ukuba kukho unxibelelwano lwe-bipartite kulo lonke ijelo ( , ) ∈ (ref. ) (bona icandelo ‘ ’). Sigxila kunxibelelwano lwe-bipartite kuba yiyo imbeko esifuna ukuyiphinda ngee-virtual gates. Ukulinganisa ii-witnesses zokunxibelelana phakathi kwemvaba kunye nezimbini kwi-zimbini kuyalinganisa umgangatho we-non-virtual gates kunye nemilinganiselo eyenza umphumo we-virtual gates ube ngaphantsi. G 1 Graph states G V E 2a Si i V SiSj i j E i j E 27 Entanglement witness , Igrafu ye-heavy-hexagonal igotywe ngaphakathi kuyo ifoma yetyuba ngeejelo (1, 95), (2, 98), (6, 102) kunye (7, 97) ezikhanyiswe ngombala oluhlaza. Siyazisika ezi jelo. , Ii-stabilizers ze-node (phezulu) kunye nee-witnesses , (ezantsi), kunye 1 standard deviation yee-nodes kunye nee-edges ezikufuphi nee-edges ezikude. Imigca eqhawukileyo yentsimbi iqokelela ii-stabilizers kunye nee-witnesses ngobude bazo kwii-edges ezisikiweyo. , Umsebenzi wokuhanjiswa okuphindaphindayo weempazamo ze-stabilizer. Iinkwenkwezi zibonisa ii-stabilizers ze-node ezinejelo eyenziwe nge-gate ekude. Kwibenchmark ye-dropped edge (red dashed-dotted line), ii-gates ezikude azenziwanga kwaye ii-stabilizers ezibonisiweyo ngeenkwenkwezi zine-unit error. Indawo engwevu yimass yobulungisa ehambelana nee-stabilizers ze-node ezichaphazelekayo kusiko. a b Sj c Sj Silungiselela i-| ⟩ kusetyenziswa iindlela ezintathu ezahlukeneyo. Iijelo zemveli zezixhobo zisetyenziswa ngeen-CNOT gates kodwa imida ye-boundary ye-periodic iveliswa nge (1) i-SWAP gates, (2) i-LOCC kunye (3) i-LO ukudibanisa ii-qubits kulo lonke ulwakhiwo. Umahluko omkhulu phakathi kwe-LOCC kunye ne-LO ngumsebenzi we-feed-forward oquka ii-gates ze-single-qubit ezixhomekeke kwimiphumo yomlinganiselo we-2 , apho ngumngako weesiko. Iseshini nganye kwezi-22 imeko ibangela umdibaniso owahlukileyo we-X kunye/okanye ii-Z gates kwi-qubits ezifanelekileyo. Ukufumana iziphumo zemilinganiselo, ukuchonga imeko ehambelanayo kunye nokusebenza ngokusekelwe kuyo kwenziwa ngexesha lokwenyani yihardware yolawulo, ngendleko ye-latency eyongeziweyo. Silawula kwaye sinciphise iimpazamo ezivela kule latency nge-zero-noise extrapolation kunye ne-staggered dynamical decoupling , (bona icandelo ‘ ’). G n n n 22 21 28 Error-mitigated quantum circuit switch instructions Siyayibuyekeza i-SWAP, LOCC kunye ne-LO implementations ye-| ⟩ nge-graph state yemveli kwis Xing' ′ = ( , ′) efunyenwe ngokukhupha ii-gates ezikude, oko kukuthi, ′ = lr. Isangqa sokulungiselela i-| ′⟩ ke ngoko sifuna ii-CNOT gates ezili-112 ezicwangcisiweyo kwii-layers ezintathu zilandelwa yi-heavy-hexagonal topology ye-Eagle processor. Esi sangqa singabika iimpazamo ezinkulu xa silinganisa ii-node kunye nee-edge stabilizers ze-| ⟩ yee-nodes ezikwisiqo esisikiweyo kuba siyilelwe ukwenza i-| ′⟩. Siyibiza le benchmark yemveli ngokuba yi-dropped edge benchmark. Isangqa esisebenzisa i-SWAP sifuna ii-CNOT gates ezingaphezulu ezili-262 ukwenza ii-edges ezikude lr, nto leyo ephantsisa kakhulu ixabiso lee-stabilizers ezilinganisiweyo (Fig. ). Ngokungafaniyo, i-LOCC kunye ne-LO implementation yee-edges kwi- lr ayifuni ii-SWAP gates. Iimpazamo zazo ze-node kunye nee-edge stabilizers kwi-nodes ezingachaphazelekiyo sisiqo esisikiweyo zilandela kakhulu i-dropped edge benchmark (Fig. ). Ngokungafaniyo, ii-stabilizers ezibandakanya i-virtual gate zinempazamo ephantsi kune-dropped edge benchmark kunye ne-SWAP implementation (Fig. , iinkwenkwezi ezimakiweyo). Njengomlinganiselo wobulunga ngokubanzi, sokuqala sibonisa isum yokungabi ngqo kwi-node stabilizers, oko kukuthi, ∑ ∈ ∣ − 1∣ (Extended Data Table ). I-overhead enkulu ye-SWAP iphethe isum yempazamo engu-44.3. Impazamo eli-13.1 kwi-dropped edge benchmark iphethwe yii-nodes ezisibhozo kwiisiko ezine (Fig. , iinkwenkwezi ezimakiweyo). Ngokungafaniyo, ii-LO kunye ne-LOCC errors zichaphazeleka yi-MCMs. Siyichaza impazamo eyongeziweyo eyi-1.9 ye-LOCC phezu kwe-LO kwii-delays kunye nee-CNOT gates kwisangqa sokuhambisa kunye nee-Bell pairs ezisikiweyo. Kwiziphumo ezisebenzisa i-SWAP, ayiyifumani i-entanglement kwi-116 ye-edges kwinqanaba le-99% ye-confidence (Fig. ). Kwi-LO kunye ne-LOCC implementation, iyayibona izibalo ze-entanglement kulo lonke ijelo kwi- kwinqanaba le-99% ye-confidence (Fig. ). Le milinganiselo ibonisa ukuba ii-virtual gates ezikude zivelisa ii-stabilizers ezinempazamo ezincinci kunokwazo ziguqulwe zibe ngama-SWAPs. Ngaphezu koko, zigcina i-variance iphantsi ngokwaneleyo ukuze ziqinisekise izibalo ze-entanglement. G G V E E EE G G G E 2b–d E 2b,c 2c i V Si 1 2c 2b,d G 2e Ukusebenzisa ii-QPUs ezimbini njenge-nye Ngoku sidibanisa ii-Eagle QPUs ezimbini ezine-qubits ezili-127 ngalinye kwii-QPU enye ngonxibelelwano lwe-classical ngexesha lokwenyani. Ukusebenzisa izixhobo njenge-processor enye, enkulu kubandakanya ukwenziwa kwezangqa ze-quantum ezandisa irejista enkulu ye-qubit. Ngaphandle kwe-unitary gates kunye nemilinganiselo esebenza ngaxeshanye kwi-QPU edibeneyo, sisebenzisa ii-dynamic circuits ukwenza ii-gates ezisebenza kwi-qubits kwiizixhobo zombini. Oku kunikwa amandla kuku-synchronization egqithisileyo kunye nonxibelelwano lwe-classical olukhawulezileyo phakathi kwezixhobo ezihlukeneyo ngokwas physical ezifunwa ukuqoqa iziphumo zemilinganiselo kunye nokuchonga indlela yolawulo kuyo yonke inkqubo . 29 Siyayivavanya le nxibelelwano lwe-classical ngexesha lokwenyani ngokuyila i-graph state kwi-qubits ezili-134 eyakhiwe kusetyenziswa imibhoxo ye-heavy-hexagonal ehamba kuzo zombini iiQPUs (Fig. ). Le mibhoxo yanyulwa ngokukhupha ii-qubits ezichaphazelekayo ziinkqubo ezimbini ze-level kunye nemiba yokuphuma ukuqinisekisa i-graph state esemgangathweni. Le graph yenza umbhoxo kwi-dimensions 3
