```html Ababuneli: 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 zinengxolo, zikwazi ukugcina ulwazi ixesha elifutshane kwaye ziqulunqwe zii-qubits ezimbalwa, oko kukuthi, ii-qubits, ngokuyimfuneko zibekwe kwisinxibelelanisi esithile . Nangona kunjalo, izicelo ezininzi zekhompyutha ye-quantum zifuna ukuxhumana okungaphezu kwesidanga sesidanga esibonelelwa sisixhobo kwii-qubits ezininzi kunokuba zikhona kwi-quantum processing unit (QPU) enye. Uluntu lunethemba lokujongana nale mda ngokudibanisa ii-QPUs kusetyenziswa unxibelelwano lwekhompyutha, nto leyo engakhange ibonakaliswe ngokwezifundo. Apha sibonisa ngokwezifundo izijikelezi-hlala ezinempazamo kunye nesicatshulwa sesekethe ukwenza iindawo ze-quantum ezifuna ukuxhumana rhoqo kusetyenziswa ii-qubits ezifikelela kuma-142 ezihlahla ii-QPUs ezimbini ezinama-127 qubits nganye zidibene ngexesha lokwenyani kunye nesinxibelelanisi sekhompyutha. Kwisekethe ephuhlisayo, ii-gates ze-quantum zinokulawulwa yikhompyutha ngokusekelwe kwiziphumo zemilinganiso ye-mid-circuit ngaphakathi kwexesha lokubaleka, oko kukuthi, ngaphakathi kwesahlulo sexesha lokudibanisa lee-qubits. Isinxibelelanisi sethu sekhompyutha esisebenza ngexesha lokwenyani sixhasa ukusebenzisa i-quantum gate kwenye i-QPU ngokusekelwe kwisiphumo sokulinganisa kwenye i-QPU. Ngaphezu koko, ulawulo lwemigawo enempazamo oluphuculweyo luphucula ukuxhumana kwe-qubit kunye neseti ye-instruction zesixhobo ngaloo ndlela kuphucula ukuguquguquka kwezikhompyutha zethu ze-quantum. Umsebenzi wethu ubonisa ukuba sinokusebenzisa ii-processors ezininzi ze-quantum njengenye kunye nezijikelezi-hlala ezinempazamo eziphuhliswe yi-classical link yexesha lokwenyani. 1 Isiphelo Iikhompyutha zeQuantum zisebenzisa ulwazi olubhalwe kwii-qubits kunye neeyunithi zokusebenza. Nangona kunjalo, iikhompyutha ze-quantum zinengxolo kwaye uninzi lwemigaqo emikhulu yezixhobo yenza ii-qubits eziphantsi. Nangona kunjalo, ii-processors zangoku ezine-error mitigation zingakwazi ukulinganisa iimodeli ze-Ising ezibhalwe ngesixhobo kunye nee-127 qubits kwaye zilungelelanise izinto ezibonakalayo ngesikali apho iziqhamo ze-brute-force ngeekhompyutha ze-classical ziqala ukubona ubunzima . Ubungqina beekhompyutha ze-quantum buxhomekeke kulwandiso olongezelekileyo kunye nokoyiswa kokuxhumana kwazo okufanelekileyo kwe-qubit. Indlela ye-modular ibalulekile kulwandiso lweziprothesi ze-quantum ezinengxolo kwaye ekufumaneni inani elikhulu lee-qubits eziphantsi ezifunekayo ukugqitywa kweempazamo . Imiqolo ye-trapped kunye neye-neutral atom ingafikelela i-modularity ngokuthutha i-qubits ngokwenyama , . Kwixesha elingekude, i-modularity kwi-superconducting qubits ifumaneka ngeezinxibelelanisi ezimfutshane ezidibanisa ii-chips ezikufutshane , . 1 2 3 4 5 6 7 8 Kwixesha eliphakathi, ii-gates ezide ezisebenza kwimowudi ye-microwave zingasetyenziswa ngeentambo ezide zemveli , , . Oku kungavumela ukuxhumana kwe-qubit okungadumeliyo okufanelekileyo ukugqitywa kweempazamo . Indlela yexesha elide yile yokubophelela ii-QPU ezikude nge-optical link esebenzisa i-microwave ukuya kwi-optical transduction , nto leyo engakhange ibonakaliswe, ngokwazi kwethu. Ngaphezu koko, ii-circuits eziphuhlisayo zandisa iseti yeeyunithi zokusebenza zekhompyutha ye-quantum ngokwenza imilinganiso ye-mid-circuit (MCMs) kunye nolawulo lwekhompyutha lwe-gate ngaphakathi kwexesha lokudibana lee-qubits. Ziphucula umgangatho we-algorithm kunye nokuxhumana kwe-qubit . Njengoko siza kubonisa, ii-circuits eziphuhlisayo zikwavumela i-modularity ngokudibanisa ii-QPUs ngexesha lokwenyani nge-classical link. 9 10 11 3 12 13 14 Sithatha indlela echaseneyo esekelwe kwi-virtual gates ukwenza imisebenzi emide kwimigodini ye-modular. Siyadibanisa ii-qubits kwizikhundla ezingachazwanga kwaye senze izibalo zokudibana nge-quasi-probability decomposition (QPD) , , . Siyayithelekisa indlela ye-Local Operations (LO) kuphela neye-Classical Communication (LOCC) eyongeziweyo . Indlela ye-LO, eyabonakaliswa kwisetingi esinye se-qubit , ifuna ukwenziwa kweesekethe ezininzi ze-quantum ezinezibonelelo zasekuhlaleni kuphela. Ngokuchaseneyo, ukwenza i-LOCC, sisebenzisa i-virtual Bell pairs kwisetingi sokuhambisa ukwenza i-two-qubit gates , . Kwi-hardware ye-quantum enezidanga ezincinci kunye nezibonakalayo, ukwenza i-Bell pair phakathi kwama-qubits angachazwanga kufuna i-controlled-NOT (CNOT) gate emide. Ukuphepha ezi gates, sisebenzisa i-QPD phezu kwezibonelelo zasekuhlaleni ephumela kwii-Bell pairs ezisikiweyo ekusetyenziswa yiteleshiphu. I-LO ayifuni i-classical link kwaye ke ilula ukuyenza kune-LOCC. Nangona kunjalo, njengoko i-LOCC ifuna isetingi ethembekileyo ethembekileyo kuphela, ingcono ukuyihlanganisa kune-LO kwaye iindleko ze-QPD yayo ngaphantsi kweendleko zemodeli ye-LO. 15 16 17 16 17 18 19 20 Umsebenzi wethu wenza iminikelo emine ebalulekileyo. Okokuqala, sibonisa ii-circuits ze-quantum kunye ne-QPD ukwenza ii-multiple cut Bell pairs ukwenza ii-virtual gates kwi-ref. . Okwesibini, sibuyisela kwaye silungelelanise iimpazamo eziphuma kwi-latency yesixhobo solawulo lwekhompyutha kwii-circuits eziphuhlisayo ngokudibanisa i-dynamical decoupling kunye ne-zero-noise extrapolation . Okwesithathu, sisebenzisa ezi ndlela ukwenza imigaqo yomda wesetyhula kwi-103-node graph state. Okwesine, sibonisa uqhagamshelo lwekhompyutha lwangempela phakathi kwezimbini ii-QPUs ezahlukileyo ngaloo ndlela sibonisa ukuba inkqubo yee-QPUs ezisasazwe ingasebenza njengenye nge-classical link . Idityaniswe nezijikelezi-hlala eziphuhlisayo, oku kusivumela ukuba sisebenzise zombini ii-chips njengekhompyutha enye ye-quantum, esiyibonisa ngokwenza i-periodic graph state ehlanganisa izixhobo zombini kuma-142 qubits. Siyayixoxa ngendlela yokuya phambili yokwenza i-long-range gates kwaye sibonise isigqibo sethu. 17 21 22 23 Ukusikwa kweSeringana Siqhuba ii-circuits ezinkulu ze-quantum ezingafumaneki ngokuthe ngqo kwi-hardware yethu ngenxa yemida kwinani le-qubit okanye ukuxhunywa ngokusika ii-gates. Ukusikwa kwe-circuit kuyahlula isetingi enzima zibe zii-subcircuits ezingenza ukwenziwa ngokwe-individual , , , , , . Nangona kunjalo, kufuneka siqhube inani elonyukileyo leesekethe, esizibiza nge-sampling overhead. Iziphumo ezivela kulezi zi-subcircuits zize ziqokelelwe yi-classical ukuze zibonelele ngesiphumo sesekethe yoqobo ( ). 15 16 17 24 25 26 iindlela Njengoko enye yeminikelo ephambili yomsebenzi wethu kukwenziwa kwe-virtual gates nge-LOCC, sibonisa indlela yokwenza ii-cut Bell pairs ezifunekayo ngeezibonelelo zasekuhlaleni. Apha, ii-cut Bell pairs ezininzi zenziwe ngeesekethe ze-quantum ezithembekileyo, esizibiza nge-cut Bell pair factory (Fig. ). Ukusika ii-pairs ezininzi ngaxeshanye kufuna i-sampling overhead ephantsi . Njengoko i-cut Bell pair factory yenza ii-circuits ezimbini ze-quantum ezingadibanisi, sibeka i-subcircuit nganye kufutshane nee-qubits ezine-gates ezinde. Isixhobo esivelisiweyo emva koko siza kusetyenziswa kwisetingi sokuhambisa. Ngokomzekelo, kwiFig. , ii-cut Bell pairs zisetyenziswa ukwenza ii-CNOT gates kwi-qubit pairs (0, 1) kunye (2, 3) (bona icandelo 'Ukupheliswa kwe-cut Bell pair ). 1b,c 17 1b kwaye , Ukuchazwa kwemigodi ye-IBM Quantum System Two. Apha, ii-127 qubit Eagle QPUs ezimbini zidityaniswe kunye nesinxibelelanisi sekhompyutha sexesha lokwenyani. I-QPU nganye ilawulwa zizixhobo zayo kwi-rack yayo. Siyayihlanganisa ngokukhawuleza zombini iiracks ukuze sisebenzise zombini ii-QPUs njengenye. , Isigqityana sesetingi se-quantum sokwenza ii-virtual CNOT gates kwi-qubit pairs ( 0, 1) kunye ( 2, 3) nge-LOCC ngokusebenzisa ii-cut Bell pairs kwisetingi sokuhambisa. Imigca emibini ejikelezayo ibonisa isinxibelelanisi sekhompyutha sexesha lokwenyani. , Izimveliso ze-cut Bell pair 2( ) zezimbini ii-cut Bell pairs ngaxeshanye. I-QPD ineziphumo ezahlukeneyo zeeparameter ezingama-27 . Apha, . a b q q q q c C θ i θ i Imigaqo yomda wesetyhula Siyakwenza i-graph state | ⟩ kunye nemigaqo yomda wesetyhula kwi-ibm_kyiv, isiphehleleli se-Eagle , sidlula imida echazwe kukuxhumana kwayo ngokwenyama (bona icandelo 'Imigodi ye- ). Apha, ine ∣ ∣ = 103 ama-nodes kwaye ifuna imida emine emide lr = {(1, 95), (2, 98), (6, 102), (7, 97)} phakathi kwama-qubits aphezulu naphantsi esiphehleleli se-Eagle (Fig. ). Siyayilinganisa imigodi ye-node kwisetingi ngasinye ∈ kunye nemigodi ye-edge eyenziwe yimveliso kulo lonke i-edge ( , ) ∈ . Kwezi stabilizers, sakha i-entanglement witness , nto leyo engendawo ukuba kukho i-entanglement esithambileyo kwi-edge ( , ) ∈ (ref. ) (bona icandelo 'I-witness ye- ). Sigxila kwi-entanglement esithambileyo kuba yiyo imithombo esifuna ukuyiphinda nge-virtual gates. Ukulinganisa ii-witnesses zezinto ezingaphezu kwezimbini kubonisa kuphela umgangatho wee-gates ezingezizo ezobutyhakada kunye nemilinganiso yokwenza impembelelo yee-virtual gates ingacaci ngakumbi. G 1 kwaye G V E 2a Si i V SiSj i j E i j E 27 kwaye , Igrafu ye-heavy-hexagonal igotywe kuyo ngokwayo kwifomu ye-tubular nge-edges (1, 95), (2, 98), (6, 102) kunye (7, 97) eqala ngombala oluhlaza okwesibhakabhaka. Siyayisika le mi-edges. , Ii-stabilizers ze-node (phezulu) kunye neen-witnesses , (ezantsi), kunye ne-1 standard deviation yee-nodes kunye nee-edges ezikufutshane nee-edges ezinde. Imigca echaziweyo ethe nkqo iqela ii-stabilizers kunye nee-witnesses ngokomgama wabo kwii-edges ezisikiweyo. , Umsebenzi osasazwayo osasazwayo weempazamo ze-stabilizer. Iinkwenkwezi zibonisa ii-stabilizers ze-node ezine-edge enziwe yi-long-range gate. Kwi-dropped edge benchmark (red dash-dotted line), ii-long-range gates azenziwanga kwaye ii-stabilizers ezikhonjwe yinkwenkwezi ke ngoko zine-unit error. Indawo engwevu yiyona mass yobulunga ehambelana nee-stabilizers ze-node ezinempemelelo kwiisikiwo. – , Kwii-layout ezimbini zobungakanani, ii-nodes eziluhlaza ziphinda ii-nodes 95, 98, 102 kunye 97 ukubonisa ii-edges ezisikiweyo. Ii-nodes eziluhlaza okwesibhakabhaka kwi ziizixhobo ze-qubit zokwenza ii-cut Bell pairs. Umbala we-node yimpazamo epheleleyo ∣ − 1∣ ye-stabilizer elinganiweyo, njengoko iboniswe yibha yombala. I-edge imnyama ukuba izibalo zokudibana zifunyenwe kwinqanaba lokuthembeka lama-99% kwaye i-violet ukuba ayinjalo. Kwi , ii-long-range gates zenziwe nge-SWAP gates. Kwi , ii-gates ezifanayo zenziwe nge-LOCC. Kwi , azenziwanga kwaphela. a b Sj c Sj d f e i Si d e f Silungiselela i-| ⟩ sisebenzisa iindlela ezintathu ezahlukeneyo. Ii-edges ezibhalwe ngesixhobo zihlala zenziwa nge-CNOT gates kodwa imigaqo yomda wesetyhula yenziwa nge (1) SWAP gates, (2) LOCC kunye (3) LO ukudibanisa ii-qubits kwisidanga sonke. Umahluko omkhulu phakathi kwe-LOCC kunye ne-LO ngumsebenzi wokuhambisa phambili oqulunqwe ngemilinganiso ye-single-qubit kuxhomekeke kwiziphumo zemilinganiso emi-2 , apho liyilo leesikiwo. Kulo lonke iimeko ezingama-22 iyavusa indibaniselwano eyahlukileyo ye kwaye/okanye gates kwi-qubits ezifanelekileyo. Ukufumana iziphumo zemilinganiso, ukuchonga ityala elifanelekileyo kunye nokwenza ngokusekelwe kulo kwenziwa ngexesha lokwenyani yi-hardware yolawulo, ngeendleko zokuhlehlisa okungaguqukiyo. Siyayilungelelanisa kwaye siyibuyisela iimpazamo eziphuma kwezi latency nge-zero-noise extrapolation kunye ne-staggered dynamical decoupling , (bona icandelo 'Izikhokelo zokutshintsha kwesixhobo esilungelelaniswe ngempazamo ). G n n n X Z 22 21 28 kwaye Siyayivavanya i-SWAP, LOCC kunye ne-LO implementations ye-| ⟩ nge-hardware-native graph state kwi ′ = ( , ′) efunyenwe ngokususwa kwii-long-range gates, oko kukuthi, ′ = lr. Isitingi sokulungiselela i-| ′⟩ ke ngoko sifuna i-CNOT gates ezingama-112 ezibekwe kwii-layers ezintathu zilandelwa yindawo ye-heavy-hexagonal yesiphehleleli se-Eagle. Esi sitingi siya kuxela iimpazamo ezinkulu xa silinganiswa ii-node kunye nee-edge stabilizers ze-| ⟩ kwi-nodes ezikwisikiwo kuba yenzelwe ukwenza i-| ′⟩. Sibhekisa kule benchmark ye-hardware-native njenge-dropped edge benchmark. Isitayile esisekelwe kwi-SWAP sifuna i-CNOT gates eyongezelelweyo eyi-262 ukwenza ii-long-range edges lr, nto leyo enciphisa kakhulu ixabiso lee-stabilizers ezilinganiweyo (Fig. ). Ngokuchaseneyo, i-LOCC kunye ne-LO implementations zeesekiwo kwi lr azifuni SWAP gates. Iimpazamo zee-node kunye nee-edge stabilizers zazo kwi-nodes ezingabandakanyekanga kwisikiwo zilandela ngokufuphi i-dropped edge benchmark (Fig. ). Ngokuchaseneyo, ii-stabilizers ezibandakanyekayo kwigeyithi ebonakalayo zine-error ephantsi kune-dropped edge benchmark kunye ne-swap implementation (Fig. , iinkwenkwezi ezimakiweyo). Njengomlinganiso ongcono wobubona, siphinda siqale idibano yempazamo epheleleyo kwi-node stabilizers, oko kukuthi, ∑ ∈ ∣ − 1∣ (Extended Data Table ). I-SWAP overhead enkulu ibangela i-44.3 sum absolute error. I-13.1 error kwi-dropped edge benchmark ibalulwa yii-nodes ezisibhozo kwii-cuts ezine (Fig. , iinkwenkwezi ezimakiweyo). Ngokuchaseneyo, iimpazamo ze-LO kunye ne-LOCC zichaphazeleka yi-MCMs. Siyayibeka ityala i-1.9 eyongezelelweyo error ye-LOCC phezu kwe-LO kwiilayiso kunye nee-CNOT gates kwisetingi sokuhambisa kunye nee-cut Bell pairs. Kwi-SWAP-based results, ayifuni i-entanglement kwi-35 yee-edges ezili-116 kwinqanaba lokuthembeka lama-99% (Fig. ). Ngokomsebenzi we-LO kunye ne-LOCC, i-witnesses yezibalo zokudibana ezithambileyo kuwo onke ama-edges kwi kwinqanaba lokuthembeka lama-99% (Fig. ). Ezi milinganiselo zibonisa ukuba ii-virtual long-range gates zivelisa ii-stabilizers ezineempazamo ezincinci kune-decomposition yazo kwi-SWAPs. Ngaphezu koko, zigcina i-variance iphantsi ngokwaneleyo ukuqinisekisa izibalo zokudibana. 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-QPU ezimbini njengenye Ngoku sihlanganisa ii-Eagle QPUs ezimbini ezinama-127 qubits nganye kwii-QPU enye nge-classical connection yexesha lokwenyani. Ukusebenzisa izixhobo njengesixhobo esikhulu esinye, kwenziwa ii-circuits ze-quantum ezihlahla isidanga esikhulu sama-qubits. Ngaphandle kwe-unitary gates kunye nemilinganiso esebenza ngaxeshanye kwi-QPU edibeneyo, sisebenzisa ii-circuits eziphuhlisayo ukwenza ii-gates ezisebenza kwi-qubits kuzo zombini izixhobo. Oku kuxhaswa yi-synchronization engqongqo kunye nonxibelelwano olukhawulezayo lwekhompyutha phakathi kwezixhobo ezahlukeneyo ezifunekayo ukuqokelela iziphumo zemilinganiso kwaye
