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 Ubukhompyutha be-Quantum uthembisa ukunika inkqubela enkulu ngaphezu kweklasikhi yayo kwizinto ezithile. Nangona kunjalo, isithintelo esikhulu ekuzalisekiseni ubuchule bayo obupheleleyo bubutyala obungokwemvelo kwezi nkqubo. Isisombululo esamkelekileyo ngokubanzi kule ngxaki kukuphunyezwa kwezangqa ze-quantum ezichasayo, ezingekho ngoku kwiiprosessa zangoku. Apha sibika amava kwiprosessa ye-127-qubit enengxolo kwaye sibonisa imilinganiselo yamaxabiso okulindelekileyo kwivolumu zesangqa ngobungakanani obudlula ubalo-nxaxheba lwekhompyutha yakudala. Siyavuma ukuba oku kubonisa ubungqina bokusetyenziswa kobukhompyutha be-quantum ngexesha langaphambi kokuchasana ne-fault-tolerant. Ezi ziphumo zamava zenziwa kukuphucuka kobuchule kunye nokuhlelwa kweprosessa ye-superconducting ngobu bungakanani kunye nokukwazi ukuchaza kunye nokulawula ingxolo ngokuchanekileyo kwisixhobo esikhulu kangaka. Siseka ukuchaneka kwamaxabiso okulindelekileyo emilinganiselo ngokuthi siwathelekise nemiphumo yeengqokelela ezivunywe ngokuchanekileyo. Kwindawo yokuqina okunamandla, ikhompyutha ye-quantum ibonelela ngezona ziphumo zichanekileyo apho iingcaciso zekhompyutha ezihamba phambili ezifana ne-pure-state-based 1D (matrix product states, MPS) kunye ne-2D (isometric tensor network states, isoTNS) iindlela ze-tensor network , ziyasilela. Ezi nqaku zibonisa isixhobo esisisiseko sokuphunyezwa kwezicelo ze-quantum ezithathayo. , . 1 2 3 4 5 Ubizwe Kakhulu Kwaziwa phantse kuwo wonke umntu ukuba iialgorithem ze-quantum eziphucukileyo njengokwenza inani okanye ukucacisa kweziseko ziza kufuna unyango lwempazamo ye-quantum. Nangona kunjalo, kubalulekile ukuba kuphikiswane ngakumbi ukuba iiprosessa ezikhoyo ngoku zinokwenziwa zithembeke ngokwaneleyo ukuba zisebenzise ezinye, izangqa ze-quantum ezimfutshane kwiinqanaba ezingadala inzuzo kwiingxaki ezisebenzayo. Ngeli xesha, ulindelo oluqhelekileyo kukuba ukuphunyezwa kwezangqa ze-quantum ezilula ezinekhono lokudlula amandla ekhompyutha kuya kufuneka kulinde de kuvele iiprosessa eziphucukileyo, ezichasayo. Ngaphandle kophuculo olukhulu lwehardware ye-quantum kule minyaka ingaphambili, imida ethembekileyo yobuninzi ixhasa lo mbono mnyama; umntu uqikelela ukuba isangqa se-quantum esingama-100 qubits ububanzi yi-gate-layers eli-100 ubunzulu esenziwe nge-0.1% ye-gate error ibonelela ngombutho olungelelanisiweyo ongaphantsi kwe-5 × 10−4. Nangona kunjalo, umbuzo uhlala ukuba ngaba iimpawu zeswele eyiyo zinokufikeleleka nokuba kunengxolo enjalo. Indlela yokunciphisa impazamo , ukuya kwimbalelwano ye-quantum ethathayo kwizixhobo ezinengxolo iphendula ngqo lo mbuzo, oko kukuthi, umntu unokuvelisa amaxabiso okulindelekileyo achanekileyo ukusuka kwimpatho ezininzi ezahlukeneyo zesangqa se-quantum esinengxolo usebenzisa ukucwangcisa kwakhona kwekhompyutha. 6 7 8 9 10 Inzuzo ye-Quantum ingafikelelwa ngezigaba ezimbini: okokuqala, ngokubonisa amandla ezixhobo ezikhoyo ukwenza imibalo echanekileyo ngobungakanani obudlula ubalo-nxaxheba oluqhelekileyo lwekhompyutha, kwaye okwesibini ngokufumana iingxaki ezinezikangqa ze-quantum ezixhamla kwezi zixhobo. Apha sigxile ekuthathweni kwesigaba sokuqala kwaye asijolanga ukuphumeza izangqa ze-quantum kwiingxaki ezinempembelelo ephuculweyo. Sisebenzisa iprosessa ye-quantum ye-superconducting enee-qubits ezili-127 ukusebenzisa izangqa ze-quantum ukuya kuthi ga kwiingqimba ezingama-60 zezangqa ze-two-qubit, zizonke ii-CNOT gates ezingama-2,880. Iisangqa ezibanzi zalo bungakanani ziyadlula kwisipho esingafikelelekiyo ngeendlela zokubala-nxaxheba ezipheleleyo. Ngoko ke, siqala sigxile kwiimeko zovavanyo ezikhethekileyo zezangqa ezivumela ukuqinisekiswa kwangoko kwekhompyutha kwamaxabiso okulindelekileyo. Emva koko sijike kwiimeko zesangqa kunye nee-observables apho ukubala-nxaxheba kwekhompyutha kubangela umngeni kwaye sithelekise nemiphumo yeendlela zokubala-nxaxheba zangoku ezikufutshane. Isangqa sethu se-benchmark yindlela ye-Trotter yokuziqhelanisa nemodeli ye-Ising ye-2D ye-transverse-field, esabelana ngendlela ye-qubit processor (iFig. ). Imodeli ye-Ising ivela kakhulu kwiindawo ezininzi zefiziksi kwaye ifumene izandiso zokuyila kwiimbalalelo zangoku zophononongo lwezinto ezininzi ze-quantum, ezinje ngeekristale zexesha , , izihlobo ze-quantum kunye neempawu ezisemngceleni ze-Majorana . Njengovavanyo lobuchule bolwelo lwe-quantum, nangona kunjalo, ukuziqhelanisa kwexesha lembali ye-Ising ye-transverse-field ye-2D kubaluleke kakhulu kumda wokuqokeleleka okubanzi apho iingcaciso ezikhangayo ze-classical zingene. 1a 11 12 13 14 , Unyathelo ngalunye lwe-Trotter lwembalelwano ye-Ising lubandakanya i-qubit enye X kunye nee-rotations ezimbini ze-qubit ZZ. Iigati zePauli ezingahleliyo zifakwa ukutshiza (i-spirals) kunye nokubala ngokulawulwayo ingxolo yomjikelo ngamnye we-CNOT. Idagi ibonisa ukudibanisa kwesigaba se-CNOT esililo. , Izigaba ezintathu ze-depth-1 zeegati ze-CNOT zanele ukwenza unxibelelwano phakathi kwamapheya onke omakhelwane kwi-ibm_kyiv. , Amava okuchaza acwangcisa ngokufanelekileyo ukufunda imilinganiselo ye-Pauli error yendawo il,i (izikali zemibala) ezakha itshaneli yePauli iphela Λl ehambelana nomjikelo we-CNOT ochazwe kwicandelo le-l. (Umhlalaphantsi wandisiwe kulwazi oluNcedisayo ). , Iimpazamo zePauli ezifakwe kwiinqanaba ezilinganayo zinokusetyenziswa ukucima (PEC) okanye ukukhulisa (ZNE) ingxolo eyona. a b c IV.A d Ngokukodwa, siqwalasela ubume benzama beHamiltonian, apho J > 0 ingunxibelelwano lwezibini ezikufutshane kunye no i < j kwaye h yintsimi eyindibaniso. Ubume beSpin ukusuka kwiswele sokuqala bunokubaliswa ngokusebenzisa ukucalulwa kokuqala kukaTrotter komsebenzi wokuziqhelanisa nexesha, apho ixesha lokuziqhelanisa nexesha T lihlelwa kwizinyathelo zeTrotter ezili-T/δt kwaye kunye no ziingqokelela zokujikeleza zeZZ kunye neX, ngokulandelanayo. Asikhathali ngempazamo yomzekelo ngenxa yeTrotterization kwaye ngoko sithatha isangqa seTrotter njengesililo ngenxa yayo naluphi na uthelekiso lwekhompyutha. Ngobulula bamava, sigxila kwisimo esithile uθJ = −2Jδt = −π/2 ukuze ukujikeleza kwe-ZZ kufune i-CNOT enye kuphela, apho ukulingana kusebenza kude kube yinto eqhelekileyo. Kwisangqa esivelayo (iFig. ), unyathelo ngalunye lwe-Trotter lubalela kwisigaba sokujikeleza kwe-qubit enye, RX(θh), kulandelwa yizigaba ezidibanayo zogqabantshi ezijikelezayo, RZZ(θJ). 1a Ngokwenza ngamava, sisebenzise iprosessa ye-quantum ye-IBM Eagle ibhaliweyo ibhaliweyo, eyakhiwe nge-127 ye-transmon qubits ezikhawulezayo ene-heavy-hex connectivity kunye ne-T1 kunye ne-T2 yexesha lama-288 μs kunye nama-127 μs, ngokulandelanayo. Ezi nqanaba zokuphila zazingazange zibekho kwiiprosessa ze-superconducting zobungakanani obunjalo kwaye zivumela ubunzulu besangqa obufikelelwe kulo msebenzi. I-CNOT gates ezimbini ze-qubit phakathi kwamagagaba zenzeka ngokuhlanganisa unxibelelwano lwe-cross-resonance . Njengoko i-qubit nganye inamakatye angathathu ubuninzi, zonke iinkqubela ze-ZZ zinokwenziwa ngezigaba ezintathu ze-CNOT gates ezihambelanayo (iFig. ). I-CNOT gates ngaphakathi kwisigaba ngasinye zilungele ukusebenza okungalingani ngaxeshanye (bona ngolwazi oluthe kratya). 15 16 1b Iindlela Ngoku sibona ukuba olu phucuko lwemisebenzi yehardware luvumela iingxaki ezinkulu ukuba zenziwe ngempumelelo ngokuNciphisa impazamo, xa kuthelekiswa nemisebenzi yakutshanje , kwesi siseko. Ukucima impazamo ngokwamanani (PEC) kubonisiwe ukuba kusebenza kakhulu ekuboneleleni ngemilinganiselo engenaphantsi ye-observables. Kwi-PEC, imodeli yengxolo emele igcina i-inverted ngokukhetha iimpathe ezinengxolo ezihambelana nemodeli egciniweyo. Nangona kunjalo, kwiinqanaba zangoku zempazamo kwisixhobo sethu, i-overhead yokukhetha imijikelezo ye-circuit volumes equlethwe kulo msebenzi ihlala ikhawulelwe, njengoko kuchaziwe ngakumbi ngaphantsi. 1 17 9 1 Ngoko ke, sijika kwi-zero-noise extrapolation (ZNE) , , , , ebonelela ngomlinganiselo onaphantsi ngendleko yokukhetha enokwenzeka ibe ngaphantsi. I-ZNE yindlela yokwandisa eyenziwa yi-polynomial , okanye eyokubaleka yexabiso lokulindela elinengxolo njengomsebenzi womlinganiselo wengxolo. Oku kufuna ukukhuliswa okulawulwayo kwengxolo ye-hardware eyona ngokwezixhobo zokukhulisa eziqhelekileyo G ukuze zifunyaniswe kumda we-ideal G=0. I-ZNE iye yamkelwa ngokubanzi ngenxalenye ngenxa yezi zicwangciso zokwandisa ingxolo ngokusebenzisa ulwandiso lwemiyalezo , , okanye ukubuyiselwa kwisangqa esingaphantsi , , ziye zaphelisa imfuneko yokuchaza ngokuchanekileyo ingxolo, ngelixa zixhomekeke kwiingcamango ezilula malunga nengxolo yesixhobo. Nangona kunjalo, ukukhula kwengxolo okuchanekileyo ngakumbi kungakhokelela kuncitshiswa okubonakalayo kwingxaki yomlinganisi owandisiweyo, njengoko sibonisa apha. 9 10 17 18 9 10 19 9 17 18 20 21 22 Imodeli yengxolo ye-Pauli–Lindblad emxinwa enikelwe kwi-ref. ibonakala ifaneleke kakhulu kumsebenzi wokubumba ingxolo kwi-ZNE. Imbanelelo inobume be , apho kuhlanganiswa ii-Pauli jump operators Pi zixhonywe kwiinqanaba λi. Kwaboniswa kwi-ref. ukuba ukunqongophala kwemisebenzi yokutsiba ebonisa imibini yee-qubits ezikufutshane kubonelela ngemodeli yengxolo emxinwa enokufundwa ngempumelelo kubuninzi beee-qubits kwaye ngokuchanekileyo ichaza ingxolo ehambelana nezigaba zezangqa ezimbini ze-Clifford, kubandakanya i-crosstalk, xa zidibaniswe ne-Pauli twirls engahleliyo , . Umjikelo weengqokelela ezinengxolo ubekelwe njengeseti yeengqokelela ezililo ezandulelwe ngumatshini wokubumba ongxakayo Λ. Ngoko ke, ukusebenzisa Λα phambi komjikelo onengxolo kubonelela ngomatshini wokubumba obandakanya ingxolo u-ΛG owobunzulu obungafaniyo no G=α+1. Ngenxa yobume obubalekayo bemandelelo yePauli–Lindblad, igrafu ifunyenwa ngokumandla izixa zePauli λi nge α. Isikhundla sePauli esivelisiweyo sinokukhethwa ukuze sifumane imizekelo efanelekileyo yesangqa; nge α ≥ 0, igrafu yitshaneli yePauli enokukhethwa ngokuthe ngqo, ngelixa nge α < 0, ukukhetha okungafaniyo kuyimfuneko kunye ne-overhead yokukhetha γ−2α yamodeli ethile eyenzelwe imodeli. Kwi-PEC, sikhetha α=−1 ukuze sifumane umphumo wengxolo ongufana no-zero. Kwi-ZNE, sijika ingxolo , , , kwimilinganiselo yobunzulu eyahlukileyo kwaye sixabise umda wengxolo enguziro usebenzisa ukubaleka. Kwiisicelo ezisebenzayo, kufuneka siqwalasele ukuzinza kwemodeli yengxolo egciniweyo ngokuhamba kwexesha (ulwazi oluNcedisayo ), umzekelo, ngenxa yobudlelwane be-qubit kunye ne-microscopic defects eguquguqukayo ezaziwa njenge-two-level systems . 1 1 23 24 10 25 26 27 III.A 28 Iisangqa ze-Clifford zisebenza njengee-benchmarks eziluncedo zezixabiso eziveliswa kukuNciphisa impazamo, njengoko zinokubaliswa ngempumelelo ngamandla ekhompyutha . Ngokukodwa, isangqa sonke se-Ising Trotter sibangumjikelo we-Clifford xa θh ikhethwa ukuba ibe ngumphindaphindi we π/2. Njengomzekelo wokuqala, ngoko ke sibeka intsimi yentsimbi ibe zero (RX(0)=I) kwaye siziqungqise iswele sokuqala |0⟩⊗127 (iFig. ). Iigati ze-CNOT zingashukumisa esi swele, ngoko ke i-observables enobunzima obu-1 eyona nto iphela ikufuneka ibenexabiso le-1; ngenxa yokudutyulwa kwePauli kwesigaba ngasinye, i-CNOTs ezisiseko ziyawuchaphazela umsebenzi. Ngovavanyo ngalunye lwe-Trotter, siqale sachaza iimibhalo yengxolo Λl yezi ngqokelela ezintathu ze-CNOT ezidutyulwe yiPauli (iFig. ) kwaye sasisebenzisa ezi mibhalo ukuze siphumeze izangqa ze-Trotter kunye nemilinganiselo yobunzulu bengxolo G∈{1, 1.2, 1.6}. Umhlalaphantsi. ibonisa ukubalwa kwe⟨Z106⟩ emva kweenyathelo ezine zeTrotter (izigaba ezingama-12 ze-CNOT). Ngayo yonke i-G, sakha iimf Hofmann ezili-2,000 apho, phambi komjikelo ngamnye l, sifakele ii-Pauli errors ezimbini-qubit kunye nenye-qubit i-Pauli errors i ukusuka ku ekhethwe ngeenqanaba kwaye sasebenzisa imf Hofmann nganye ka-64, zizonke ii-executions ezingama-384,000. Njengoko imf Hofmann ezininzi ziqokelelwa, imilinganiselo ye⟨Z106⟩G, ehambelana nobunzulu obuhlukeneyo G, ifikelela kumaxabiso ahlukeneyo. Emva koko imilinganiselo eyahlukeneyo ifakwe kwi-function yokubaleka kwi-G ukuze kuqikelelwe ixabiso le-ideal ⟨Z106⟩0. Imiphumo kumhlalaphantsi. ibonisa ukuncitshiswa kwengxaki yokubaleka kwe-exponential xa kuthelekiswa nokubaleka okuthe ngqo. Kunjalo, ukubaleka kwe-exponential kungabonakalisa ukungazinzi, umzekelo, xa amaxabiso okulindelekileyo angabonakali ukuba asondele kakhulu kwi-zero, kwaye—kwiimeko ezinjalo—sihambisa ngokuphindaphindiweyo ubunzulu bembala yokubaleka (bona ulwazi oluNcedisayo ). Inkqubo echazwe kumhlalaphantsi. yasetyenziswa kwimiphumo yokulinganisa ukusuka kwi-qubit nganye q ukubala zonke i-N=127 ye-Pauli expectations ⟨Zq⟩0. Ukwahluka kumazinga acacileyo kunye namazinga acacisiweyo kumhlalaphantsi. ibonisa ukungafani kwezinto zempazamo kulo lonke iprosessa. Siyazisa i-magnetization eyindibaniso kwi-, , ngokunyuka kobunzulu kumhlalaphantsi. . Nangona isiphumo esingacaciswanga sibonisa ukwehla okuthe ngqambileyo ukusuka ku-1 ngokwenyuka kwezinto ezingafaniyo kwizangqa ezinzulu, i-ZNE iphucula kakhulu ukuthelelana, nangona inomlinganiselo omncinci, kunye nexabiso le-ideal nasekuqheleni okungama-20 amanyathelo e-Trotter, okanye ubunzulu obungama-60 be-CNOT. Ngokukodwa, inani leem samples ezisetyenzisiweyo apha lingaphantsi kunelo likalulo eliphantsi eliya kufuneka kwisicelo esilula se-PEC (bona ulwazi oluNcedisayo ). Ngokwaso, le nkqubela phambili ingancitshiswa kakhulu ngeengcaciso ze-PEC eziphuculweyo ezisebenzisa i-light-cone tracing okanye ngokuphuculwa kwezinto zempazamo zehardware. Njengoko i-hardware yekamva kunye nophuhliso lwe-software lunciphisa iindle 29 1a 1c 2a 2a 19 II.B 2a 2b 2c IV.B 30
