```html Ababhali: Youngseok Kim Andrew Eddins Sajant Anand Ken Xuan Wei Ewout van den Berg Sami Rosenblatt Hasan Nayfeh Yantao Wu Michael Zaletel Kristan Temme Abhinav Kandala Isishwankathelo I-quantum computing itsingathembisa ukunika izibonelelo ezinkulu phezu kwezakhiwo zayo zakudala kwezinye iingxaki. Nangona kunjalo, esona sithintelo sikhulu ekuzalisekiseni ubuchule bayo bubushushu obukho kwezi nkqubo. Isisombululo esamkelweyo ngokubanzi kule ngxaki kukuphunyezwa kwezixokelelwano ze-quantum ezinganyangekiyo, ezingekabikho kwiiprosesa zangoku. Apha sinikezela ngamava kwi-processor ye-quantum ye-127-qubit enobushushu kwaye sibonise umlinganiselo weexabiso ezichanekileyo zemisebenzi yomjikelo ngobukhulu obudlula kubalo olugqithisileyo lwangoku. Sibanga ukuba oku kubonisa ubungqina bokusetyenziswa kwe-quantum computing kwixesha lokungabikho kobuchule. Ezi ziphumo zamava zenziwa yimpumelelo ekukhutshelweni nasekulungisweni kwe-superconducting processor ngale mlinganiselo kunye nekhono lokuchaza kwaye zilawule ubushushu kuso sonke isixhobo esikhulu kangaka. Sikumisela ukuchaneka kweexabiso ezilinganisiweyo ngokuzithelekisa nemiphumo yeemijikelo efuna ukuqinisekiswa ngokuchanekileyo. Kwindawo yokuhlala enkulu, i-quantum computer ibonelela ngeziphumo ezichanekileyo apho iziqhelo zangoku zokulinganisa ezifana ne-pure-state-based 1D (matrix product states, MPS) kunye ne-2D (isometric tensor network states, isoTNS) tensor network methods , ziphazamiseka. Ezi zixhaphazo zibonisa isixhobo esisisiseko sokwenziwa kwezicelo ze-quantum ezithathayo. , . 1 2 3 4 5 Icandelo eliphambili Kwamkelwa ngokubanzi ukuba iialgoritma ze-quantum eziphuculweyo ezifana nokubala okanye ukumisela ubuchule zifuna ukulungiswa kwempazamo ye-quantum. Nangona kunjalo, kudala kubangiswa kakhulu ukuba ii-processors ezikhoyo ngoku zinokwenziwa zibe neenqanaba elaneleyo lokusebenza imijikelo ye-quantum emfutshane kakhulu ngobukhulu obunokubonelela ngomvuzo kwiingxaki ezisebenzayo. Ngeli xesha, ulindelo oluqhelekileyo kukuba ukuphunyezwa kwemijikelo ye-quantum elula enokubakho ukugqitha kumandla e-classical kuya kufuneka kulindele ukuba ii-processors eziphuculweyo, ezinganyangekiyo zifiké. Ngaphandle kokuphumelela okukhulu kwehadiwe ye-quantum kwiminyaka yakutshanje, imida yobuchule nje ixhasa le ngcaphephe yemibono emnyama; omnye ubale ukuba umjikelo we-quantum owenza ama-qubits ayi-100 ububanzi nama-gate layers ayi-100 ubunzulu osebenza nge-0.1% ye-gate error ubangela ubuchule obungaphantsi kwe-5 × 10−4. Nangona kunjalo, umbuzo uhlala usenokufunyanwa iimpawu zesimo esifanelekileyo nokuba lunobuchule obuphantsi kangaka. Indlela yokunciphisa impazamo , ukuya kumvuzo we-quantum ongasondelanga kwizixhobo ezinobushushu ibandakanya ngqo lo mbuzo, oko kukuthi, enye ingavelisa iimpendulo ezichanekileyo kwiinqanaba ezininzi ezahlukeneyo zomjikelo we-quantum onobushushu usebenzisa i-post-processing ye-classical. 6 7 8 9 10 Umvuzo we-quantum unokufikelelwa kwiinyathelo ezimbini: okokuqala, ngokubonisa ikhono lezixhobo ezikhoyo ukwenza imisebenzi echanekileyo ngobukhulu obudlula ubungakanani bokulinganisa kwe-classical, kwaye okwesibini, ngokufumana iingxaki ezineemijikelo ye-quantum ehambelanayo ebizifumanela umvuzo kwiindawo zokusebenza ezivela kwezi zixhobo. Apha sigxila ekuthathweni kwenyathelo lokuqala kwaye asijolanga ukuphunyezwa kweemijikelo ye-quantum kwiingxaki ezinezigonyo eziqinisekisiweyo. Sisebenzisa i-superconducting quantum processor ene-127 qubits ukusebenzisa imijikelo ye-quantum eneengxowa ezingama-60 ze-two-qubit gates, kwiingqokelelo ezingama-2,880 ze-CNOT gates. Iimijikelo ezibanzi ze-quantum zolu buchopho ziyakwazi ukugqitha kwizindlela ezidala ze-classical. Ngoko ke siqala sigxile kwiimeko zokuvavanya ezithile zemijikelo evumela ukuqinisekiswa kwe-classical okuchanekileyo kweempendulo ezilinganisiweyo. Emva koko sijolisa kwiindawo zemijikelo kunye neziqulunqi ezenza ubungakanani obuchazwa yi-classical bube nzima kwaye sithelekise nemiphumo yeendlela zokulinganisa zangoku. Isixhobo sethu sobunqulo yi-Trotterized time evolution ye-2D transverse-field Ising model, esabelana ngomumo womodeli we-qubit processor (Fig. ). Imibono ye-Ising iveka kakhulu kwiindawo ezahlukeneyo kwifiziksi kwaye ifumene ulwandiso oluyilayo kuluhlu lwamva nje oluphanda iziphumo ze-quantum many-body, ezinje nge-time crystals , , ii-quantum scars kunye ne-Majorana edge modes . Njengovavanyo lobuchule be-quantum computation, nangona kunjalo, ubuhlobo be-time evolution ye-2D transverse-field Ising model bubaluleke kakhulu kumda wobushushu obukhulu bokudibanisa apho iziqhelo ze-classical ezikhulayo zibandezela. 1a 11 12 13 14 , Inyathelo ngalinye le-Trotter yokuqikelelwa kwe-Ising libandakanya ukujikeleza kwe-single-qubit kunye ne-two-qubit . Izinto zikaPauli ezingahleliyo zingena ukujikeleza (izangqa) kunye nokulinganisa ngokulawulwayo kobushushu banqanaba ngalinye le-CNOT. U-dagger ubhekisa ku-conjugation ngunqanaba olufanelekileyo. , Iinqanaba ezintathu zobunzulu-1 ze-CNOT gates zanele ukwenziwa kwezinto phakathi kwawo wonke amasango omlingani kwi-ibm_kyiv. , Izixhaphazo zokuchaza zifunda ngokufanelekileyo ii-local Pauli error rates , (izikali zombala) ezakha isiphithiphithi sikaPauli esipheleleyo Λ ehambelana nenqanaba le-CNOT elijikelezayo th. (Umboniso wongezwa kwiNkcukacha eNgakumbi ). , Iimpazamo zikaPauli ezifakwe kwiinqanaba ezilinganisiweyo zinokusetyenziselwa ukukhansela (PEC) okanye ukunyusa (ZNE) ubushushu obuyimfuneko. a X ZZ b c λl i l l IV.A d Ngokukodwa, siqwalasele ubuhlobo bexesha leHamiltonian, apho > 0 yiyo indibaniselwano yeespini ezikufutshane > > kunye yiyo igunya elibanzi. Ubudlalwano besipini ukusuka kwisimo sokuqala bunokulinganiswa ngokusebenzisa ukwahlulwa kwe-Trotter yohlobo loku-1 komsebenzi wobuhlobo bexesha, J 2 j h apho ixesha lobuhlobo lihlulwe zizinyathelo ze-Trotter ze / kunye kunye yi- kunye rotation gates, ngokulandelanayo. Asizikhathaleli impazamo yomzekelo ebangelwa yi-Trotterization kwaye ngoko sithatha umjikelo we-Trotterized njengowona ufanelekileyo kulo naluphi na uthelekiso lwe-classical. Ngokulula kokuphunyezwa, sigxila kwimeko = −2 = −π/2 ukuze i-rotation ye- ifune i-CNOT enye kuphela, T T δt ZZ X θJ Jδt ZZ apho ukulingana kuhambelana ngeqondo eligqithisileyo. Kumjikelo osiphumo (Fig. ), inyathelo ngalinye le-Trotter libandakanya inqanaba lokujikeleza kwe-single-qubit, R ( h), elandelwa ziinqanaba ezihambelanayo zodlalwano ezijikelezayo ze-two-qubit, R ( ). 1a X θ ZZ θJ Ngokuphunyezwa kokuphunyezwa, sidla ngokusebenzisa i-IBM Eagle processor ibm_kyiv, equkethe ii-transmon qubits ezizi-127 ezimileyo >ne-heavy-hex connectivity kunye ne-median 1 kunye 2 times ye-288 μs kunye ne-127 μs, ngokulandelanayo. Ezi xesha zokukhutshelwa aziqhelekanga kwiiprosesa ze-superconducting zolu buchopho kwaye ziyavumela ubunzulu bemijikelo obufikelelwe kulo msebenzi. I-two-qubit CNOT gates phakathi kwabalingani ziyenziwa ngokulungisa ukudibanisa kwe-cross-resonance . Njengoko i-qubit nganye inamaqabane angadluliyo amathathu, zonke izinto zika- >ezingena kuzo zinokwenziwa kwiinqanaba ezintathu zodlalwano lwe-CNOT gates (Fig. ). I-CNOT gates ngaphakathi kwinqanaba ngalinye zilungiswa ukuze zisebenze ngaxeshanye (bona >ngolwazi oluthe kratya). 15 T T 16 ZZ 1b Methods Ngoku sibona ukuba ezi mpembelelo zokusebenza kwehadiwe zenze iingxaki ezinkulu zingaqhubeka zisebenza ngempumelelo ngokusetyenziswa kwempazamo, xa kuthelekiswa nemisebenzi yakutshanje , kwesi siseko. Ukukhanselwa kwempazamo ye-probabilistic (PEC) kubonisiwe ukuba yeyona iyasebenza ekuboneleleni ngeemilinganiselo ezingagungqiyo zezinto eziqwalaselweyo. Kwi-PEC, imodeli yempazamo emele yenziwa isingqisho ize ize ngokuphindwa ngokuphindwa kweemijikelo ye-quantum enobushushu ehambelana nemodeli efundwayo. Nangona kunjalo, kwiinqanaba zempazamo zangoku kwisixhobo sethu, umsebenzi wokulinganisa ukhathaza imijikelo eqwalaselweyo kulo msebenzi usalindelekile, njengoko kuchaziwe ngakumbi ngaphantsi. 1 17 9 1 Ngoko ke sijolisa ku-zero-noise extrapolation (ZNE) , , , , ebonelela nge-estimator ye-biased ngexabiso eliphantsi lokulinganisa njengomsebenzi wobukhulu bempazamo. Oku kufuna ukunyusa ngokulawulwa kobushushu behadiwe ngomyinge owaziwayo >ukubuyisela isiphumo esifanelekileyo = 0. I-ZNE isetyenziswa kakhulu ngokuyinxenye kuba iindlela zokunyusa ubushushu ezisekelwe kukugqithisa komqhubekeko , , >okanye ukubuyisela kwakhona umjikelo ongaphantsi , , >iye yaqeqesha imfuneko yokuchaza ngokuchanekileyo impazamo, ngelixa ixhomekeke kwizinto ezilula malunga nemvutho yesixhobo. Nangona kunjalo, ukunyusa ubushushu okuchaneke ngakumbi kunokubonelela ngokuphuculwa okukhulu kwi-bias ye-estimator eyenziweyo, njengoko sibonisa apha. 9 10 17 18 G G 9 17 18 20 21 22 Imodeli yempazamo ye-sparse Pauli–Lindblad ecetywayo kwi-ref. >iyabonakala iyilungele kakuhle ukubunjwa kobushushu kwi-ZNE. Imbali ithatha ifomu . Apho yiyo i-Lindbladian equka ii-Pauli jump operators >ezingumyinge . Kwabonakala kwi-ref. >ukuba ukunciphisa kwii-jump operators ezisebenza kwii-pairs zemvutho zenza imodeli yempazamo ye-sparse enokufundwa ngokufanelekileyo kuma-qubits amaninzi kwaye ibambe ngokuchanekileyo impazamo ehambelana neenqanaba ze-two-qubit Clifford gates, kubandakanya i-crosstalk, xa idityaniswe ne-Pauli twirls engahleliyo , . Inqanaba elineempazamo lee gates liboniswa njengeqoqo lee gates ezifanelekileyo ezandulelwe yinjubuso ethile yempazamo Λ. Ngoko ke, ukusebenzisa i-Λ phambi kwenqanaba elineempazamo kubangela i-injubiso yempazamo epheleleyo Λ ngomyinge = + 1. Ngenxa yefomu ye-exponential yomzekelo wePauli–Lindblad, i-map iyifunyanwa ngokukhuphela nje ii-Pauli rates >nge . Isiphithiphithi sikaPauli esiphumelayo sinokulinganiswa ukuze sifumane imijikelo efanelekileyo; kwi- ≥ 0, i-map yiyo i-Pauli channel enokulinganiswa ngokuthe ngqo, ngelixa kwi- < 0, i-quasi-probabilistic sampling ifuneka kunye nomsebenzi wokulinganisa −2 kwi-model-specific . Kwi-PEC, sikhetha = −1 ukuze sifumane inqanaba lobushushu lobungakanani obulinganayo. Kwi-ZNE, endaweni yoko sixhophe ubushushu , , , >kwimilinganiselo eyahlukeneyo yomyinge kwaye silinge umda wobushushu obungubulolweyo usebenzisa i-extrapolation. Kwiinkonzo ezisebenzayo, kufuneka siqwalasele ugunyiso lwemodeli yempazamo efundiweyo ngokuhamba kwexesha (Supplementary Information ), umzekelo, ngenxa yokudibanisa kwe-qubit kunye neengxaki eziguquguqukayo ezincinci ezaziwa njengezi-two-level systems . 1 Pi λi 1 23 24 α G G α λi α α α γ α γ α 10 25 26 27 III.A 28 Imijikelo ye-Clifford isetyenziselwa njengee-benchmarks eziluncedo zezimilo ezenziwa kukuphathwa kwempazamo, njengoko zinokulinganiswa ngokufanelekileyo kwi-classical . Ngokukodwa, umjikelo opheleleyo we-Ising Trotter uba yi-Clifford xa h >ikhethwe njengonobungakanani obuyi-π/2. Njengesibonelo sokuqala, ngoko ke sibeka igunya eliqhelekileyo libe zero (R (0) = ) kwaye siphembelela isimo sokuqala |0⟩⊗127 (Fig. ). I-CNOT gates zishiya esi simo singatshintshi, ngoko ke ii-observables zokuqala eziyimfuneko ubunzulu obuyi-1 >zonke zinexabiso elilindelekileyo eli-1; ngenxa ye-Pauli twirling yenqanaba ngalinye, ii-CNOTs ezibonwayo ziyakuchaphazela isimo. Kukuphunyezwa ngakunye kwe-Trotter, siqala sibe nobuchule kwiimodeli zempazamo Λ yeenqanaba ezintathu ze-CNOT ezijikelezwe yi-Pauli (Fig. ) >emva koko sisebenzise ezi modeli ukuphunyezwa kweemijikelo ye-Trotter eneenqanaba zomlinganiso wobushushu ∈ {1, 1.2, 1.6}. Umfanekiso >ubhekisa kwisilingo ⟨ 106⟩ >emva kweenqanaba ezine ze-Trotter (iinqanaba ezingama-12 ze-CNOT). Kwi- >nganye, sivunye imijikelo engama-2,000 apho, phambi kwenqanaba ngalinye , sifake ii-products zee-Pauli errors ze-one-qubit kunye ne-two-qubit >ezivela ku ezidonswe ngezabelo kwaye sasebenzisa umjikelo ngamnye amaxesha angama-64, kwandisa iziqulunqo ezili-384,000. Njengoko izigcineli zemijikelo zisanda, izilinganiso ze ⟨ 106⟩ , ezihambelana nemilinganiso eyahlukileyo ye , ziyafana neziphumo ezahlukeneyo. Izilinganiso ezahlukeneyo zize zifakwe ngokwe-extrapolating function kwi >ukulinganisa ixabiso elifanelekileyo ⟨ 106⟩0. Iziphumo kumfanekiso >zigxininisa ukuncitshiswa kwebias ukusuka kwi-exponential extrapolation >xa kuthelekiswa ne-linear extrapolation. Nangona kunjalo, i-exponential extrapolation ingabonisa ukungazinzisi, umzekelo, xa amaxabiso alindelekileyo engakwazi ukwahlulwa kwi-zero, kwaye—kwiimeko ezinjalo—siyayehlisa inqanaba lobuchopho bemodeli yokucoca ngokuthe ngaphandle (bona Supplementary Information ). Inkqubo echazwe kumfanekiso >yasebenza kuzo zonke iziphumo zemilinganiselo ezivela kwi-qubit nganye >ukulinganisa zonke ii-N = 127 ze-Pauli expectations ⟨ ⟩0. Ukwahluka kwi-observables engachukumiswanga kwaye ilungisiwe kumfanekiso >kubonisa ukungalingani kwiinqanaba zempazamo kuyo yonke iprosesa. Sibika i-global magnetization malunga no , , ngenxa yobunzulu obunyukayo kumfanekiso . Nangona isiphumo esingachukumiswanga sibonisa ukwehla okuphawulekayo ukusuka ku-1 kunye nokwandisa ukwahluka kwiimijikelo ezibunzulu, i-ZNE iphucula kakhulu ukuhambelana, nangona kune-bias encinci, nexabiso elifanelekileyo nkqu ukuya kwiinqanaba ezili-20 ze-Trotter, okanye ubunzulu obu-60 be-CNOT. Ngokukodwa, inani leziphumo ezisetyenzisiweyo apha lincinci kakhulu kunobungakanani besampulu obungafuneka kwi-PEC implementational elula (bona Supplementary Information ). Ngokomga 29 θ X I 1a Zq l 1c G 2a Z G l i Z G G G Z 2a 19 II.B 2a q Zq 2b 2c IV.B
