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 Ikhompyutha ye-Quantum ithembisa ukubonelela ngezona zikhawulezayo phezu kwekhontraparti yayo yeklasikhi kwezinye iingxaki. Nangona kunjalo, isithintelo esikhulu sokufezekisa amandla ayo apheleleyo yingxolo ekhoyo kwezi nkqubo. Isisombululo esamkelekileyo kule ngxaki kukuqaliswa kweesekethe ze-quantum ezinganyangekiyo, ezingafikelelekiyo kwiiphrosessa zangoku. Apha sibika amava kwiphrosessa ye-quantum engama-127 enengxolo kwaye sibonisa imilinganiselo yenani lemidlalo ekujikelezeni ngevolumu yesekethe ngaphezu kokubala kweklasikhi. Siyaphikisa ukuba oku kubonisa ubungqina bokusebenziseka kwekhompyutha ye-quantum kwixesha lokukhusela iimpazamo. Ezi ziphumo zamava zenziwe lula kukuphucuka kokuhambelana kunye noqwalelo lwephrosessa ye-superconducting kule volumu kunye nesakhono sokuqwalasela kunye nokulawula ingxolo kuyo yonke le nkqubo inkulu. Siseka ukuchaneka kwezi ndawo ezilinganiselweyo ngokuzithelekisa neziphumo zezikhokhelo ezichanekileyo. Kwindawo yokuqalelwa okunamandla, ikhompyutha ye-quantum ibonelela ngezona ziphumo, apho iikhontraki zeklasikhi eziphambili ezifana neyona-state-based 1D (matrix product states, MPS) kunye ne-2D (isometric tensor network states, isoTNS) iindlela zenethiwekhi ye-tensor , iyasilela. Ezi nqobo zibonisa isixhobo esisisiseko sokufezekisa usetyenziso lwe-quantum lwesikhathi esiseduze , . 1 2 3 4 5 Iziphumo eziphambili Ngokubanzi kuyavunywa ukuba ii-algorithms ze-quantum eziphambili ezifana nokugcina okanye ukulinganisa izigaba >i>zifuna ukulungiswa kweempazamo ze-quantum. Nangona kunjalo, kubonakala ngathi kunokwenzeka ukuba iiphrosessa ezikhoyo ngoku zenziwe zithembekile ngokwaneleyo ukuba zisebenzise ezinye izikhokelo, ezimfutshane, ngevolumu enokubonelela ngamandla kwiingxaki ezisebenzayo. Ngeli xesha, ulindelo oluqhelekileyo kukuba ukuqaliswa kwezikhokhelo ze-quantum ezilula ezinamathuba okugqitha izakhono zeklasikhi kuya kufuneka kulindele ukufika kweziphrosessa eziphambili, ezinganyangekiyo. Ngaphandle kokuphumelela okukhulu kwe-hardware ye-quantum kwiminyaka yakutshanje, imida yefidelity elula >ibonelela ngesi sikhokelo sobubi; omnye ulinganisa ukuba isikhokelo se-quantum esibanzi nge-qubit eyi-100 kunye no-100 ubunzulu besango elisebenzisa i-0.1% impazamo yesango ibonelela ngefidelity engezantsi kune-5 × 10−4. Nangona kunjalo, umbuzo uhlala uhleli ukuba iimpawu zesimilo esifanelekileyo zinokufikelelwa nokuba ngefidelity ephantsi kangaka. Indlela yokulungiswa kweempazamo , >kwindawo ye-quantum advantage kwizixhobo ezinengxolo ijongana ngqo nalo mbuzo, oko kukuthi, inokubonelela ngenani lezabelo ezichanekileyo kwiingqungquthela ezininzi ezingafaniyo zesikhokhelo esinengxolo kusetyenziswa i-post-processing yeklasikhi. 6 7 8 9 10 Ukunqoba kwe-Quantum kunokufikelelwa ngamanyathelo amabini: Okokuqala, ngokubonisa isakhono sezixhobo ezikhoyo ukwenza imisebenzi yokubala enchanekileyo ngevolumu engaphezu kokulinganisa iklasikhi, kwaye okwesibini, ngokufumana iingxaki ezinobunxibelelwano obunobunxibelelwano obubonelela ngamandla kwiizixhobo ezi. Apha sigxila ekuthathweni kwelo nyathelo lokuqala kwaye asijolanga ukuqaliswa kwezikhokhelo ze-quantum kwiingxaki ezineziphumo zokugqwesa ezibonisiweyo. Sisebenzisa i-superconducting quantum processor enama-qubits ayi-127 ukuqhuba izikhokhelo ze-quantum ezineentswelo ezingama-60 zezango ezingama-2-qubit, iyonke ii-CNOT gates ezingama-2,880. Izikhokhelo ze-quantum ezibanzi zaloo mvulane zingaphezulu kokuphumelelayo ngeendlela zokubala zokugqitha. Ngoko ke sigxila kuqala kwiimeko zovavanyo ezithile zezikhokhelo ezivumela ukuqinisekiswa kweklasikhi ngokuchanekileyo kwezi ndawo ezilinganiselweyo. Emva koko sijika kwizikhokhelo kunye neminye imizekelo apho ukulinganisa iklasikhi kuba nzima kwaye sithelekise neziziphumo ezivela kwiindidi zeklasikhi zokulinganisa. Isikhokhelo sethu esiyinkonzo yinguquko yexesha le-Trotterized yomkhethe we-2D transverse-field Ising, esabelana ngomfanekiso wephrosessa ye-qubit (Umfanekiso. ). Imkhethe ye-Ising ibonakala kakhulu kwiindawo ezahlukeneyo zefiziksi kwaye ifumene ukwandiswa okusungulayo kwimilinganiselo yakutshanje ejonga iziphumo ezininzi ze-quantum, ezifana ne-time crystals , , quantum scars >kunye ne-Majorana edge modes . Njengovavanyo lokusebenziseka kwekhompyutha ye-quantum, nangona kunjalo, ingqungquthela yexesha ye-2D transverse-field Ising model ifanelekile kumda wokukhula okumandla kokungathembani apho ii-approximations zeklasikhi ezinyibilikayo zinzima. 1a 11 12 13 14 , Inyathelo ngalinye le-Trotter lomyalezo we-Ising libandakanya ii-rotations ze-single-qubit >kunye nezingama-2-qubit . Ii-Pauli gates ezichanekileyo ziyafana nokudibanisa (izinti) kunye nokulawula ingxolo yomgca ngamnye we-CNOT. Idijini ibonisa ukufaniswa ngesiko elililo lomgca. , Ii-layers ezintathu zokuqala ze-CNOT gates zanele ukufezekisa ubudlelwane phakathi kwazo zonke izibini ezikufutshane kwi-ibm_kyiv. , Amava okuchaza ngokuchanekileyo afumana iinqanaba zempazamo ye-Pauli ye-local , >(izikali zombala) ezakha ijelo le-Pauli lipheleleyo Λ >eboniswa kumgca we- th twirled CNOT. (Umfanekiso wandiswa kwiNxalenye Engaphezulu. ). , Iimpazamo zePauli ezongezwe kwiinqanaba ezilinganayo zingasetyenziswa ukucima (PEC) okanye ukomeleza (ZNE) ingxolo yangaphakathi. a X ZZ b c λl i l l IV.A d Ngokukodwa, siqwalasela ubudlelwane bexesha leHamiltonian, apho > 0 yiyo i-coupling ye-nearest-neighbour spins kunye < >kunye >liluhlobo lwesayibhile. Ubume beSpin ukusuka kwisimo sokuqala bunokulinganiswa ngokusebenzisa i-Trotter decomposition yokuqala yomsebenzi wokujikeleza kwexesha, J i j h apho ixesha lokujikeleza >lahlulwe lube / >amanyathelo e-Trotter kunye kunye zizango >kunye >zomjikelo, ngokulandelanayo. Asizikhathali ngeempazamo zemodeli ezibangelwa yi-Trotterization kwaye ngoko sithatha isikhokhelo se-Trotterized njengesifanelekileyo kulo lonke uthelekiso lweklasikhi. Ukulula kwamava, sigxila kwimeko = −2 = −π/2 ukuze ijiko le- >lidinge i-CNOT enye kuphela, T T δt ZZ X θJ Jδt ZZ apho ukulingana kubanjwa ngaphandle kwesigaba esibanzi. Kwisikhokhelo esiveliswayo (Umfanekiso. ), inyathelo ngalinye le-Trotter libandakanya ibala le-single-qubit rotations, R ( h), elandelwa ngamaqhina asebenzisanayo angama-parallelized two-qubit rotations, R ( ). 1a X θ ZZ θJ Ukusebenza kwamava, sisebenzise kakhulu i-IBM Eagle processor ibm_kyiv, equkethe ama-qubits angama-127 afriqquency fixed transmon >kunye ne-heavy-hex connectivity kunye ne-T1 kunye ne-T2 times ezingama-288 μs kunye ne-127 μs, ngokulandelanayo. Ezi thuba zokuhambelana azikaze zibonwe kwiiphrosessa ze-superconducting zale volumu kwaye zivumela ubunzulu besikhokhelo obufikelelwe kulo msebenzi. Ii-CNOT gates ezimbini ze-qubit phakathi kwezibini ezikufutshane ziqaliswa ngokusebenzisa uhlobo lokudibanisa lokudibanisa . Njengoko i-qubit nganye inama-neighbours angama-3 ubuninzi, zonke ii-ZZ interactions zingenziwa kwiingqayi ezintathu zezango ze-parallelized ze-CNOT (Umfanekiso. ). Ii-CNOT gates kwiqhina ngalinye ziqwalaselwa ukusebenza okufanayo (bona >ngolwazi olungaphezulu). 15 16 1b Iindlela Ngoku sibona ukuba le nqaku lenkqubo ye-hardware luvumela iingxaki ezinkulu ukuba ziphunyezwe ngempumelelo ngolungiso lweempazamo, xa kuthelekiswa nemisebenzi yakutshanje , >kwesi sikhokhelo. Ukucinywa kweempazamo ngeprobabliti (PEC) >ibonisiwe >ukuba isebenza kakhulu ekuboneleleni ngeziphumo ezingekho phambili kwee-observables. Kwi-PEC, imodeli yengxolo emele yenziwa kwaye ingasebenzi ngempumelelo ngokuchukumisa ukusuka kumdlalo wezikhokhelo ezingafaniyo ezixhumene nemodeli efundisiweyo. Nangona kunjalo, kwiinqanaba zempazamo zangoku kwisixhobo sethu, i-sampling overhead kwiivolumu zesikhokhelo ezithathelwe ingqalelo kulo msebenzi isasele iyimida, njengoko kuchazwe ngokuqhubekayo. 1 17 9 1 Ngoko ke sijika kwi-zero-noise extrapolation (ZNE) , , , , ebonelela ngomlinganisi we-bias kwiindleko ezincinci zokuchukumisa. I-ZNE yindlela ye-polynomial , >okanye exponential >indlela yokwandisa kwii-expectation values ezingafaniyo njengomsebenzi womlinganisi wengxolo. Oku kufuna ukomelezwa okucwangcisiweyo kwengxolo yangaphakathi ye-hardware ngenani lofumano olwaziwayo >ukuze kuqhubekwe kwisiphumo esifanelekileyo = 0. I-ZNE iye yafunyanwa ngokubanzi ngokuphunyezwa kwezikimu zokomeleza ingxolo ngokusebenzisa ukolula okubuyiselweyo , , >okanye ukubuyiselwa kwesikhokhelo , , >iye kwacetyiswa isidingo sokufunda ingxolo ngokuchanekileyo, ngelixa kuxhomekeke kwiingcinga ezilula malunga nengxolo yesixhobo. Nangona kunjalo, ukomeleza ingxolo okunchanekileyo kunokubonelela ngokuphunyezwa okukhulu kwi-bias yesimilo esiqhubekayo, njengoko sibonisa apha. 9 10 17 18 9 10 19 G G 9 17 18 20 21 22 Imodeli yengxolo ye-sparse Pauli–Lindblad ecetywe kwi-ref. >iyabonakala ilungele kakhulu ukubunjwa kwengxolo kwi-ZNE. Imbanelelo inefomu , apho liyilo le-Lindbladian eliqulunqwe ngemisebenzi yokutsiba kwe-Pauli >ebotshelelwe kwiinqanaba . Kwabonakaliswa kwi-ref. >ukuba ukuthintelwa kwimisebenzi yokutsiba esebenza kwii-qubits ezikufutshane kwenza imodeli yengxolo ye-sparse enokufundwa ngokukhawuleza kwaye ibambe ngokuchanekileyo ingxolo enxulumene nee-layers zezango ze-Clifford ze-2-qubit, kubandakanya i-crosstalk, xa idibene nee-Pauli twirls ezingachanekanga , . Ibala leengozi ezidibanisayo liboniswa njengeseti yeenongo ezilunge ngaphambili kwijelo lengxolo Λ. Ngoko ke, ukusebenzisa i-Λ >phambi kwebhala yenongo kuvelisa ijelo lengxolo lipheleleyo Λ >kunye nofumano = + 1. Ngenxa yefomu ye-exponential yemodeli ye-Pauli–Lindblad, i-mapu ifumaneka ngokucofa nje iinqanaba ze-Pauli >ngu . Umbanelelo we-Pauli ovelisiweyo ungachothelwa ukufumana imizekelo yesikhokhelo efanelekileyo; kwi ≥ 0, i-mapu yijelo le-Pauli elinokuchothelwa ngqo, ngelixa kwi < 0, ukuchothelwa okufana neprobabliti kuyafuneka kunye ne-sampling overhead −2 >kwi-model-specific . Kwi-PEC, sikhetha = −1 ukuze sifumane inqanaba lengxolo elingathathi cala. Kwi-ZNE, endaweni yoko, siyayandisa ingxolo , , , >kwiinqanaba ezahlukeneyo zefumano kwaye siqikelele umda we-zero-noise ngokusebenzisa i-extrapolation. Kwiisicelo ezisebenzayo, kufuneka siqwalasele uqeqesho lwemodeli yengxolo efundiweyo ngokuhamba kwexesha (Icandelo Elihlanganisiweyo ), umzekelo, ngenxa yobudlelwane be-qubit kunye neengozi eziguquguqukayo ezincinci ezaziwa njengee-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 Iisikhokhelo zeClifford zisetyenziswa njengee-benchmarks eziluncedo zezilinganiso eziveliswa bubungqina bempazamo, njengoko zinokulinganiswa nge-classical . Ngokukodwa, yonke imodeli ye-Ising Trotter iba yi-Clifford xa h >ikhethwa ukuba ibe yinkulumbuso ye-π/2. Njengomzekelo wokuqala, ngoko ke sibeka inkunzi yombane kwi-zero (R (0) = ) kwaye sijikelezisa isimo sokuqala |0⟩⊗127 (Umfanekiso. ). Ii-CNOT gates ziyayigcina le mveli ingatshintshi, ngoko ke i-observables yobukhulu obu-1 ilinde ixabiso le-1; ngenxa ye-Pauli twirling yomgca ngamnye, ii-CNOTs ezicacileyo ziyayichaphazela imeko. Kwinqobo nganye ye-Trotter, siqala sasebenzisa imodeli yengxolo Λ >yezi-CNOT gates ezintathu ze-Pauli-twirled (Umfanekiso. ) >kwaye emva koko sisebenzise ezi modeli ukuqala imizila ye-Trotter eneenqanaba zokomeleza ingxolo ∈ {1, 1.2, 1.6}. Umfanekiso. >ubonisa ukulinganisa kwe ⟨ 106⟩ >emva kwamanyathelo amane e-Trotter (iigates ezingama-12 ze-CNOT). Kwi >nganye, sivelise imizekelo yesikhokhelo eyi-2,000 apho, phambi komgca , sifake iimveliso ze-Pauli ze-one-qubit kunye ne-two-qubit >ukusuka ezidweliswe ngamanqanaba kwaye saqhuba imizekelo nganye amaxesha angama-64, ngoku konke kwenziwa amaxesha angama-384,000. Njengoko iingqungquthela zesikhokhelo ziqokelelwa, izilinganiso ze ⟨ 106⟩ , ezihambelana neemfuno ezahlukeneyo , ziyafunyanwa kwiindawo ezahlukeneyo. Izilinganiso ezahlukeneyo emva koko zifakwa yifungtion yokuqhubela phambili >ukuqikelela ixabiso elifanelekileyo ⟨ 106⟩0. Iziziphumo kumfanekiso. >zigxininisa i-bias encitshisiweyo ukusuka kwi-exponential extrapolation >xa kuthelekiswa ne-linear extrapolation. Oko kwathiwa, i-exponential extrapolation ingabonisa ukungazinzisi, umzekelo, xa izinto ezilindelekileyo zikufutshane kakhulu ne-zero, kwaye-kwiimeko ezinjalo-siphanda sinciphisa ubuchule bembali yokuqhubela phambili (bona ICandelo Elihlanganisiweyo ). Inkqubo echazwe kumfanekiso. >yasetyenziswa kwiimiphumo zemilinganiselo ukusuka kwi-qubit nganye >ukuqikelela zonke = 127 i-Pauli expectations ⟨ ⟩0. Ukutshintshana kwezinto ezilindelekileyo ezingalungisiweyo nezilungisiweyo kumfanekiso. >ibonisa ukungafani kweenqanaba leempazamo kuyo yonke iphrosessa. Sibika i-global magnetization kwisisekelo , , ngokunyuka kobunzulu kumfanekiso. . Nangona isiphumo esingalungisiweyo sibonisa ukwehla okuthe ngcembe ukusuka ku-1 kunye nokwanda kokwehluka 29 θ X I 1a l 1c G 2a Z G l i Z G G G Z 2a 19 II.B 2a q N Zq 2b 2c
