Ababhali: Almudena Carrera Vazquez Caroline Tornow Diego Ristè Stefan Woerner Maika Takita Daniel J. Egger Isishwankathelo Iikhompyutha zeQuantum ziprosesa ulwazi ngokusebenzisa imithetho ye-quantum mechanics. Izixhobo ze-quantum zangoku zinengxolo, zinokugcina ulwazi ixesha elifutshane kwaye zinqongophala kwii-qubits ezimbalwa, oko kukuthi, ii-qubits, ngokubanzi zicwangciswe kuqhagamshelwano olunye . Nangona kunjalo, ezininzi izicelo zokubala nge-quantum zifuna uqhagamshelwano olunye kune-lattice olunikezelwa zizixhobo kwii-qubits ezininzi kunokuba zikhona kwi-quantum processing unit (QPU) enye. Uluntu nethemba lokujongana nolu thintelo ngokudibanisa ii-QPUs kusetyenziswa unxibelelwano lwe-classical, olungenela kwabonwa ngokwezifundo. Apha sibonisa ngokwezifundo ii-dynamic circuits ezilawulwe yi-error kunye nesekethe yokusika ukudala imibutho ye-quantum efuna uqhagamshelwano rhoqo kusetyenziswa ii-qubits ezifikelela kuma-142 ezijikeleze ii-QPUs ezimbini kunye nee-qubits ezili-127 nganye ziqhagamshelwe ngexesha lokwenyani kunye nolungelelwano lwe-classical. Kwi-dynamic circuit, iigeyimu ze-quantum zingalawulwa yi-classical ngokusekelwe kwimiphumo yeenqanawa zokulinganisa phakathi kwesekethe ngexesha lokusebenza, oko kukuthi, ngaphakathi kwesahlulo sexesha lokuphazamiseka kwe-qubits. Ulungelelwano lwethu lwe-classical ngexesha lokwenyani lusivumela ukuba sisebenzise igeyimu ye-quantum kwenye i-QPU ixhomekeke kwimiphumo yomlinganiselo kwenye i-QPU. Ngaphezu koko, ulawulo olulungisiweyo lwe-error lwandisa uqhagamshelwano lwe-qubit kunye nesethi yemiyalelo yesixhobo ngaloo ndlela sandisa ukuguquguquka kwezikhompyutha zethu ze-quantum. Umsebenzi wethu ubonisa ukuba sinokusebenzisa ii-processor ezininzi ze-quantum njengeyona enye kunye nee-dynamic circuits ezilawulwe yi-error ezisekelwa kulungelelwano lwe-classical ngexesha lokwenyani. 1 Isitshixo Iikhompyutha zeQuantum ziprosesa ulwazi olufakwe kwi-qubits ye-quantum nge-unitary operations. Nangona kunjalo, ii-quantum computer zinengxolo kwaye uninzi lwezicwangciso ezinkulu zicwangcisa ii-qubits zomzimba kwi-planar lattice. Ngaphandle koko, ii-processor zangoku ezine-error mitigation sele zingakwazi ukufanisa ii-Ising models ezifaniswa ne-hardware kunye nee-qubits ezili-127 kwaye zilayile izinto ezilinganisiweyo kwisikali apho iindlela zokucofa ngeekhompyutha ze-classical ziqala ukubandezeleka . Ukusebenza kwezi khompyutha ze-quantum kuxhomekeke ekwandeni okungaphezulu kunye nokoyiswa kobunye uqhagamshelwano lwazo olunqongophala kwi-qubit. Indlela yemodyuli ibalulekile ekwandeni kwezixhobo ze-quantum ze-quantum ezinexhalanga kwaye ekufezekeni kwenani elikhulu lee-qubits zomzimba ezifunekayo kubulungisa obupheleleyo . Iingqokelelo ze-trapped ion kunye nee-atom ezingathathi cala zingafikelela kumodularity ngokuthwala ii-qubits ngokwasemzimbeni , . Kwixesha elingekude, imodularity kwi-superconducting qubits ifikelelwa ngokusebenzisa unxibelelwano olufutshane olunxibelelanisa ii-chip ezikufutshane , . 1 2 3 4 5 6 7 8 Kwixesha eliphakathi, iigeyimu ezide ezisebenza kwirejimeni ye-microwave zingasetyenziswa ngentambo eziqhelekileyo ezinde , , . Oku kungavumela uqhagamshelwano lwe-qubit olungekho mkhwa olulungele ukulungiswa kwe-error okusebenzayo . Enye indlela yexesha elide kukuphazamisa ii-QPU ezikude kunye nolungelelwano lwe-optical olusebenzisa i-microwave ukuya kwi-optical transduction , olungenela kwabonwa, ngokwazi kwethu. Ngaphezu koko, ii-dynamic circuits zandisa isethi yokusebenza kwekhompyutha ye-quantum ngokwenza imilinganiselo phakathi kwesekethe (MCMs) kunye nolawulo lwe-classical lwegeyimu ngaphakathi kwexesha lokuphazamiseka kwe-qubits. Ziyayonyusa umgangatho we-algorithmic quality kunye noqhagamshelwano lwe-qubit . Njengoko siza kubonisa, ii-dynamic circuits zikwavumela imodularity ngokudibanisa ii-QPUs ngexesha lokwenyani nge-link ye-classical. 9 10 11 3 12 13 14 Sithatha indlela eyongezelelweyo esekelwe kwii-gates zokwenyani ukwenza imisebenzi emide kwisicwangciso semodyuli. Siyadibanisa ii-qubits kwiindawo ezingaqhelekanga kwaye sidale iinkcukacha zokubambana nge-quasi-probability decomposition (QPD) , , . Sithelekisa indlela ye-Local Operations (LO) kuphela kulungisiweyo yi-Classical Communication (LOCC) . Indlela ye-LO, eyabonakaliswa kwisetingi ye-qubit ezimbini , ifuna ukwenza ii-circuits ezininzi ze-quantum kunye ne-local operations kuphela. Ngokuchaseneyo, ukwenza i-LOCC, sisebenzisa i-virtual Bell pairs kwiseti ye-teleportation ukwenza iigeyimu ezimbini ze-qubit , . Kwi-hardware ye-quantum enoqhagamshelwano olungacacanga nolunye, ukudala i-Bell pair phakathi kwama-qubits angaqhelekanga kufuna i-CNOT gate ende. Ukuphepha ezi gates, sisebenzisa i-QPD phezu kwee-local operations ezivelisa i-Bell pairs ezisikiweyo ezisetyenziswa yi-teleportation. I-LO ayifuni i-link ye-classical ngoko ke kulula ukuyenza kunokuba yi-LOCC. Nangona kunjalo, njengoko i-LOCC ifuna iseti enye kuphela ye-template circuit, kulula ukuyilungisa kunokuba yi-LO kwaye iindleko ze-QPD yayo ngaphantsi kweendleko zesetingi ye-LO. 15 16 17 16 17 18 19 20 Imisebenzi yethu yenza igalelo elibalulekileyo eline. Okokuqala, sibonisa ii-circuits ze-quantum kunye ne-QPD ukudala ii-multiple cut Bell pairs ukwenza iigeyimu zokwenyani kwi-ref. . Okwesibini, sithintela kwaye silungise ii-error ezivelayo kubulali bokulibaziseka kwe-hardware yolawulo lwe-classical kwii-dynamic circuits kunye nokudityaniswa kwe-dynamical decoupling kunye ne-zero-noise extrapolation . Okwesithathu, sisebenzisa ezi ndlela ukuyila imibandela yomda we-periodic kwi-graph state enee-nodes ezili-103. Okwesine, sibonisa unxibelelwano lwe-classical ngexesha lokwenyani phakathi kwama-QPU amabini ahlukeneyo ngaloo ndlela sibonisa ukuba inkqubo ye-QPUs ezisasazekileyo ingasetyenziswa njengeyona enye nge-link ye-classical . Ndawonye nee-dynamic circuits, oku kusivumela ukuba sisebenzise zombini ii-chip njengekhompyutha enye ye-quantum, esiyibonisa ngokuyila i-periodic graph state eyakhelwe kwizixhobo zombini kuma-qubits ali-142. Siyixoxa indlela yokuya phambili yokudala iigeyimu ezinde kunye nokunika isigqibo sethu. 17 21 22 23 Ukusikwa kwe-Circuit Sisebenzisa ii-circuits ezinkulu ze-quantum ezingekho ngqo kwizixhobo zethu ngenxa yemida kwisayizi ye-qubit okanye uqhagamshelwano ngokuyisika iigeyimu. Ukusikwa kwe-Circuit kucalucalula i-circuit eyinkimbinkimbi ibe ngama-subcircuits anokwenziwa ngokwahlukileyo , , , , , . Nangona kunjalo, kufuneka senze inani elongezelelweyo lee-circuits, esizibiza nge-sampling overhead. Iziphumo ezivela kwii-subcircuits ziya kuhlanganiswa ngokwe-classical ukubuyisela isiphumo se-circuit yoqobo ( ). 15 16 17 24 25 26 Methods Njengokuba enye yezona zinto ziphambili emsebenzini wethu kukwenza iigeyimu zokwenyani kunye ne-LOCC, sibonisa indlela yokwenza ii-cut Bell pairs ezifunekayo kunye nee-local operations. Apha, ii-cut Bell pairs ezininzi zenziwa ngee-parametric quantum circuits, 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 ezingadibaniyo, sibeka i-subcircuit ngalunye kufutshane nee-qubits ezinezibonda ezinde. Isixhobo esivelayo siyasetyenziswa kwiseti ye-teleportation. Ngokomzekelo, kwi-Fig. , ii-cut Bell pairs zisetyenziselwa ukwenza ii-CNOT gates kwi-qubit pairs (0, 1) kunye (2, 3) (bona isebe ' '). 1b,c 17 1b Cut Bell pair factories , Umboniso wesicwangciso se-IBM Quantum System Two. Apha, ii-Eagle QPUs ezili-127 ze-qubit ziqhagamshelwe kunye nolungelelwano lwe-classical ngexesha lokwenyani. QPU nganye ilawulwa zizixhobo zayo zegesi kwirak yakho. Siyavumelanisa ii-racks zombini ukuze sisebenzise zombini ii-QPU njengeyona enye. , Template quantum circuit yokwenza iigeyimu zokwenyani ze-CNOT kwi-qubit pairs ( 0, 1) kunye ( 2, 3) kunye ne-LOCC ngokusebenzisa ii-cut Bell pairs kwiseti ye-teleportation. Imigca emibini emnyama ibonisa ulungelelwano lwe-classical ngexesha lokwenyani. , Cut Bell pair factories 2( ) ezimbini ii-cut Bell pairs ezisebenza ngaxeshanye. I-QPD ineqokelela ezahlukeneyo ezingama-27 zeeparameter . Apha, . a b q q q q c C θ i θ i Imibandela yomda we-Periodic Siyakha i-graph state | ⟩ kunye nemibandela yomda we-periodic kwi-ibm_kyiv, i-Eagle processor , ngaphaya kwemida ebangelwa yindlela yokuyiqhagamshela kwisicwangciso (bona isebe ' '). Apha, inama-nodes eingu-∣ ∣ = 103 kwaye ifuna imiphetho emine ende lr = {(1, 95), (2, 98), (6, 102), (7, 97)} phakathi kwama-qubits aphezulu kunye naphantsi e-Eagle processor (Fig. ). Silinganisa ii-node stabilizers kwilona naliphi na i-node ∈ kunye nee-edge stabilizers eziveliswe yi-product kuyo yonke i-edge ( , ) ∈ . Kwezi stabilizers, sakha i-entanglement witness , engu negative ukuba kukho entanglement ye-bipartite kuyo yonke i-edge ( , ) ∈ (ref. ) (bona isebe ' '). Sigxila kwi-entanglement ye-bipartite kuba yiyo leyo isixhobo esifuna ukuyenza ngemisebenzi yokwenyani. Ukulinganisa izibhengezo zenqaku elingaphezu kwama-two kuya kulayila kuphela umgangatho wee-gates ezingezizo ezokwenyani kunye nemilinganiselo eyenza ubuchule bemiSebenzi yokwenyani bube ngaphantsi. G 1 Graph states G 1 V E 2a Si i V SiSj i j E i j E 27 Entanglement witness , I-graph ye-heavy-hexagonal igotyiwe yodwa ibe yimilo yetyhubhu ngemiphetho (1, 95), (2, 98), (6, 102) kunye (7, 97) eboniswe ngombala oluhlaza okwesibhakabhaka. Sikhethe le miphetho. , Ii-node stabilizers (phezulu) kunye nobume obungqonge ubume , (phantsi), kunye ne-standard deviation enye yee-nodes kunye nemiphetho kufutshane nemiphetho ende. Imigca eqhekekileyo ethe tye ihlanganisa ii-stabilizers kunye nezibhengezo ngokude kwazo kwimiphetho esikiweyo. , Umsebenzi wokusasazwa odityanisweyo wama-error e-stabilizer. Iinkwenkwezi zibonisa ii-node stabilizers ezine-edge eyenziwe yigeyimu ende. Kwi-dropped edge benchmark (dash-dotted red line), ii-gates ezinde azifezekiswanga kwaye ii-stabilizers eziboniswe ngeenkwenkwezi zine-error enye. Indawo engwevu yindlela yamandla ehambelana nee-node stabilizers ezichaphazelekayo kukusikwa. – , Kwizicwangciso ze-2D, ii-nodes eziluhlaza ziphinda ii-nodes 95, 98, 102 kunye 97 ukubonisa imiphetho esikiweyo. Ii-nodes eziluhlaza okwesibhakabhaka kwi zii-qubits resources zokudala ii-cut Bell pairs. Umbala we-node ngowona usahlukileyo | − 1∣ ye-stabilizer elinganiweyo, njengoko ibonisiwe kwibar yombala. I-edge imnyama ukuba iinkcukacha zokubambana zifunyenwe kwinqanaba lolwazi lwama-99% kwaye i-violet ukuba akunjalo. Kwi , ii-gates ezinde zenziwa ngee-SWAP gates. Kwi , ii-gates ezifanayo zenziwa nge-LOCC. Kwi , azifezekiswanga konke konke. a b Sj c Sj d f e i 1 Si d e f Silungiselela i-| ⟩ kusetyenziswa iindlela ezintathu ezahlukeneyo. Ii-edges ezifaniswa ne-hardware zisetyenziswa nge-CNOT gates kodwa imibandela yomda we-periodic yenziwa nge- (1) SWAP gates, (2) LOCC kunye (3) LO ukudibanisa ii-qubits kuyo yonke i-lattice. Umahluko omkhulu phakathi kwe-LOCC kunye ne-LO yindawo yokudlulisela phambili equka ii-single-qubit gates ezixhomekeke kwimiphumo emi-2 yokulinganisa, apho ngamanani ezisiki. Isimo ngasinye sezimo ezingama-22 sibangela indibaniselwano eyahlukileyo ye- kunye/okanye ii-Z gates kwi-qubits ezifanelekileyo. Ukufumana iziphumo zokulinganisa, ukumisela isimo esifanelekileyo kunye nokwenza ngokusekelwe kuso kwenziwa ngexesha lokwenyani yi-hardware yolawulo, ngeendleko zokulibaziseka okongeziweyo. Silungisa kwaye sithintele ii-error ezivela kolu lubalaziso kunye ne-zero-noise extrapolation kunye ne-staggered dynamical decoupling , (bona isebe ' '). G n n X 22 21 28 Error-mitigated quantum circuit switch instructions Silinganisa ii-SWAP, LOCC kunye ne-LO implementations ze-| ⟩ kunye ne-hardware-native graph state kwi- ′ = ( , ′) efunyenweyo ngokukhupha imiphetho ende, oko kukuthi, ′ = lr. I-circuit yokulungiselela i-| ′⟩ ngoko ifuna ii-CNOT gates ezingama-112 ezicwangciswe kwii-layers ezintathu zilandelwa yi-heavy-hexagonal topology ye-Eagle processor. Le circuit izakubika ii-error ezinkulu xa ilinganiswa ii-node kunye nee-edge stabilizers ze-| ⟩ yee-nodes kwi-cut gate kuba yenzelwe ukwenza i-| ′⟩. Sibhekisa kule benchmark ye-hardware-native njenge-dropped edge benchmark. I-circuit esekelwe kwi-SWAP ifuna ii-CNOT gates ezingama-262 ezongezelelweyo ukudala imiphetho ende lr, nto leyo enciphisa kakhulu ixabiso lee-stabilizers ezilinganiweyo (Fig. ). Ngokuchaseneyo, i-LOCC kunye ne-LO implementation yemiphetho kwi- lr ayifuni i-SWAP gates. Ii-error zayo ii-node kunye nee-edge stabilizers zama-nodes angachaphazeleki yi-cut gate zilandela ngokufanayo i-dropped edge benchmark (Fig. ). Ngokuchaseneyo, ii-stabilizers ezibandakanya i-virtual gate zinendawo encinci yempazamo kunokuba yi-dropped edge benchmark kunye ne-SWAP implementation (Fig. , iinkwenkwezi ezibonisa). Njengomlinganiselo wobulunga obupheleleyo, siphakathi kweendawo zokubala ii-errors ezichanekileyo kwi-node stabilizers, oko kukuthi, ∑ ∈ ∣ − 1∣ (Extended Data Table ). I-SWAP overhead enkulu iyimbangela ye-44.3 sum absolute error. I-13.1 error kwi-dropped edge benchmark ibangelwa kakhulu yii-nodes ezisibhozo kwimiphetho emine esikiweyo (Fig. , iinkwenkwezi ezibonisa). Ngokuchaseneyo, ii-LO kunye ne-LOCC errors zichaphazeleka yi-MCMs. Sifaka impazamo eyongezelelweyo ye-1.9 ye-LOCC phezu kwe-LO kubulali kunye nee-CNOT gates kwiseti ye-teleportation kunye nee-cut Bell pairs. Kwiziphumo ze-SWAP-based, ayikwazi ukufumana entanglement kwi-35 kuma-116 edges kwinqanaba lolwazi lama-99% (Fig. ). Ngokuphathelele i-LO kunye ne-LOCC implementation, izibhengezo zobume bezibini bokubambana kuzo zonke izibonda kwi kwinqanaba lolwazi lama-99% (Fig. ). Ezi zilinganiso zibonisa ukuba ii-gates ezibonakalayo ezinde zivelisa ii-stabilizers ezinemiyalo encinci yempazamo kune-decompositions zazo kwii-SWAPs. Ngaphezu koko, zigcina i-variance iphantsi ngokwaneleyo ukuqinisekisa iinkcukacha zokubambana. 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 Ukusebenza kwama-QPU amabini njengeyona enye Ngoku sidibanisa ii-Eagle QPUs ezimbini kunye nee-qubits ezili-127 nganye kwisixhobo esinye se-QPU ngolungelelwano lwe-classical ngexesha lokwenyani. Ukusebenza kwezixhobo njengeprocessor enye enkulu kubandakanya ukwenza ii-circuits ze-quantum ezijikeleze irejista enkulu ye-qubit. Ngaphandle kweegates ze-unitary kunye nemilinganiselo esebenza ngaxeshanye kwi-QPU ed
