
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Abaholo: 
 
 
 
 
 
 
 
 
 
 
 Neereja Sundaresan Theodore J. Yoder Youngseok Kim Muyuan Li Edward H. Chen Grace Harper Ted Thorbeck Andrew W. Cross Antonio D. Córcoles Maika Takita Peahenelo Quantum error correction imbola yendlela eyimbalwa yokwenza imisebenzi ye-quantum ephezulu. Nangona ukwenziwa ngokupheleleyo kwe-algorithm enganyelwanga ziimpazamo kusekhona, ukuphucuka kwamva nje kulawulo lwe-elektroniki kunye ne-quantum hardware kuvumela imiboniso ephucukileyo yezi msebenzi ziyafuneka kulungiso lweempazamo. Apha, senza i-quantum error correction kwi-superconducting qubits edibene kwi-heavy-hexagon lattice. Siguqula i-logical qubit ngobude obuthathu kwaye sisebenzisa imijikelo emininzi ye-syndrome measurement measurements evumela ukulungiswa kulo naluphi na uhlobo olulodwa lweempazamo kwisifundo. Ngokusebenzisa impendulo yexesha langempela, sibuyisela i-syndrome kunye ne-flag qubits ngokungafaniyo emva komjikelo ngamnye wokukhutshwa kwe-syndrome. Siyichaza impazamo ye-logical exhomekeke kwi-decoder, kunye nempazamo ye-logical ephakathi komlinganiselo womlinganiselo we-syndrome kwi-Z(X)-basis ye ~0.040 (~0.088) kunye ne ~0.037 (~0.087) yezokufanisa kunye ne-maximum likelihood decoders, ngokulandelanayo, kwidatha ye-leakage post-selected. Intshayelelo Iziphumo zemisebenzi ye-quantum zingaba neziphazamiso, ngokwenyani, ngenxa yengxolo kwi-hardware. Ukuphelisa iimpazamo ezivelayo, iikhowudi zokulungisa iimpazamo ze-quantum (QEC) zingasetyenziselwa ukuguqula ulwazi lwe-quantum kwii-degrees ezikhuselekileyo, ezingengombutho, kwaye emva koko ngokulungisa iimpazamo ngokukhawuleza kunokuba ziqokelele ukuvumela imisebenzi engenamkhethe (FT). Ukufezekiswa okupheleleyo kwe-QEC kuya kufuna: ukulungiselela iimeko zengqondo; ukufezekiswa kweqela elipheleleyo leegate ezingengombutho, ezingafuna ukulungiselela imeko yomlingo; imilinganiselo ephindaphindwayo ye-syndromes; kunye nokuchazwa kwe-syndromes zokulungisa iimpazamo. Ukuba iyaphumelela, iireyithi zempazamo ye-logical ezivelayo kufuneka zibe ngaphantsi kweekhorayithi zempazamo zefizikali ezikuyo, kwaye zincitshiswe ngokunyuka kwebude bekhowudi ukuya kut Hinton ethile. Ukukhetha ikhowudi ye-QEC kufuna ukuqwalaselwa kwe-hardware ezantsi kunye neempawu zayo zengxolo. Kwilattice le-heavy-hexagon ,  ye-qubits, iikhowudi ze-subsystem QEC  zithandwa kakhulu njengoko zilungele ii-qubits ezine-connectivity encitshisiweyo. Ezinye iikhowudi zibonise isithembiso ngenxa yenqanaba lazo eliphezulu le-FT  okanye inani elikhulu leegate ezingengombutho ezisebenzayo . Nangona ubungqala babo kunye nexesha elikhoyo lingenokubangela umqobo omkhulu wokwanda, kukho iindlela ezikhuthazayo zokunciphisa izixhobo ezibiza kakhulu ngokusebenzisa uhlobo oluthile lokuqiniswa kwempazamo . 1 2 3 4 5 6 Kwindlela yokuchaza, impumelelo yokulungisa ixhomekeke kungekuphela nje ekusebenzeni kwe-hardware ye-quantum, kodwa kunye nasekusebenziseni i-elektroniki yolawulo esetyenziselwa ukufumana kunye nokucwangcisa ulwazi lwe-classical olufunyenwe kwi-syndrome measurements. Kwimeko yethu, ukulungiselela zombini i-syndrome kunye ne-flag qubits nge-real-time feedback phakathi kwemijikelo yokulinganisa kunokunceda ukunciphisa iimpazamo. Kwinqanaba lokuchaza, nangona iiprothokholi ezithile zikhona zokwenza i-QEC asynchronously ngaphakathi kwe-FT formalism , , izinga apho ii-syndromes zempazamo zifunyenwe khona kufuneka zihambelane ne-time yokucwangcisa kwe-classical yazo ukuze kuthintelwe i-backlog eyandayo yedatha ye-syndrome. Kwakhona, iiprothokholi ezithile, njengokusebenzisa imeko yomlingo kwi-logical  -gate , zifuna ukusetyenziswa kwe-real-time feed-forward. 7 8 T 9 Ngoko ke, umbono wokude we-QEC awugxili kumgomo omnye wokugqibela kodwa kufuneka ubukwe njengokuqhubeka kwezabelo ezininzi ezinxibelelanayo. Indlela yovavanyo kuphuhliso lwesi sibonelelo sobuchwepheshe iya kubandakanya ukubonisa ezi zabelo ngokwahlukeneyo kuqala kunye nokudibanisa kwazo okunyuka kamva, ngelixa uphucula rhoqo im metric zazo. Eminye yale nkqubela ivezwa kwiimpumelelo ezininzi zamva nje kwiinkqubo ze-quantum kwi-platforms ezahlukeneyo zefizikali, ezibonise okanye zafikisana neminye imiba ye-desiderata ye-FT quantum computing. Ngokukodwa, ukulungiswa kwe-FT logical state kubonisiwe kwi-ions , i-nuclear spins edayimani  kunye ne-superconducting qubits . Immijiko ephindaphindwayo yokukhutshwa kwe-syndrome ibonisiwe kwi-superconducting qubits kwiikhowudi ezincinci zokufumanisa impazamo , , kuquka ukulungiswa kwempazamo okuyingxenye  kunye neqela elipheleleyo (nangona lingengombutho) leegate ezingabunye ze-qubit . Umboniso we-FT weqela elipheleleyo leegate kwi-logical qubits ezimbini ubonisiwe kutshanje kwi-ions . Kwi-realm yokulungiswa kweempazamo, kube khona iimpumelelo zamva nje ze-surface code enobude obuthathu kwi-superconducting qubits kunye nokuchazwa  kunye ne-post-selection , kunye nokusetyenziswa kwe-FT kwe-quantum memory ekhuselweyo ngokuzenzekelayo kusetyenziswa i-color code  kunye ne-FT state preparation, operation, kunye nomlinganiselo, kuquka ne-stabilizers zayo, yindlela ye-logical kwi-Bacon-Shor code kwi-ions , . 10 11 12 13 14 15 16 17 18 19 20 20 21 Apha sidibanisa ubuchule be-real-time feedback kwi-superconducting qubit system kunye ne-maximum likelihood decoding protocol engafakwanga mazingqisho kuvavanyo ukuze kuphuculwe ukusinda kweemeko zengqondo. Sibonisa ezi zixhobo njengenxalenye yokusebenza kwe-FT ye-subsystem code , ikhowudi ye-heavy-hexagon , kwi-superconducting quantum processor. Kubalulekile ukwenza ukusetyenziswa kwethu kule khowudi kungabi naziphumo ezibi yii-flag qubits ezithi, xa zifunyenwe zingekho zero, zitsalele umnqweno kumbonisi kwisifundo se-circuit errors. Ngokubeka ngokungafaniyo i-flag kunye ne-syndrome qubits emva komjikelo ngamnye wokulinganisa kwe-syndrome, sikhusela inkqubo yethu kwiimpazamo ezivelayo kumngeni wobungcwele wobungcwele obuyimfuneko. Siphinde sisebenzise amasu okuchaza achazwe kutshanje  kwaye sandise izimvo zokuchaza ukubandakanya iingcamango zengqiqo engaphezulu , , . 22 1 15 4 23 24 Iziphumo Ikhodi ye-heavy-hexagon kunye nemijikelo emininzi Ikhodi ye-heavy-hexagon esiyiqwalayo yi-  = 9 qubit code equlunqa i-  = 1 logical qubit ngobude obuyi-  = 3 . Ii-  kunye ne-  gauge (bona uMfanekiso. a) kunye namaqela ezizinzileyo athatyathwa yi n k d 1 Z X 1 AmaQela ezizinzileyo  yiziko lamaqela ezibambiso . Oku kuthetha ukuba izizinzileyo, njengeemveliso zokusebenza kwe-gauge, zinokuqondwa ngokulinganisa ii-gauge operators. Ii-operators zengqondo zingakhethwa ukuba zibe yi-  =  1 2 3 kunye ne-  =  1 3 7. 2 XL X X X ZL Z Z Z  Ii-  (blue) kunye ne-  (red) gauge operators (eqs. ( ) kunye ( )) zibekwe kwii-qubits ezingama-23 ezifunwa yi-distance-3 heavy-hexagon code. Ii-qubits zekhowudi ( 1 −  9) ziboniswa tyheli, ii-syndrome qubits ( 17,  19,  20,  22) ezisetyenziselwa ii-  stabilizers ngeluhlaza, kunye ne-flag qubits kunye nee-syndromes ezisetyenziselwa ii-  stabilizers ngomhlophe. Ubume kunye nolwazi apho ii-CX gates zisetyenziswa ngaphakathi kwicandelo ngalinye (0 ukuya ku-4) lubonisiwe ngotolo olunombolo.   Umzobo wesifundo somjikelo omnye we-syndrome measurement, kubandakanywa zombini ii-  kunye nee-  stabilizers. Umzobo wesifundo ubonisa ukuba kunokwenzeka ukuba i-gate operations ihambisane, ezo zingaphakathi kwemida emiselweyo yemigca ebhetyebhetye (emide eluhlaza okwesibhakabhaka). Njengoko ixesha le-two-qubit gate nganye liyahluka, ukucwangciswa kokugqibela kugqityiwe ngomdlalo oqhelekileyo wokucwangciswa kwesifundo; emva koko i-dynamical decoupling yongezwa kwi-data qubits apho ixesha livumela khona. Imilinganiselo kunye ne-reset operations zihlukile kwi-gate operations ukuze kuvunyelwe i-dynamical decoupling efanayo ukuba yongezwe kwi-data qubits ezimele. Imizobo yokuchaza imijikelo emithathu ye- ( )   kunye ( )   stabilizer measurements kunye ne-circuit-level noise ivumela ukulungiswa kwe-  kunye ne-  errors, ngokulandelanayo. Ii-nodes eziluhlaza kunye nezibomvu kwi-graphs zihambelana ne-syndromes ezahlukileyo, ngelixa ii-nodes ezimnyama ziyimida. Ii-edges ziqulunqa iindlela ezahlukeneyo iimpazamo ezinokwenzeka kwi-circuit njengoko kuchaziwe kwisicatshulwa. Ii-nodes zibhalwe ngohlobo lwe-stabilizer measurement (  okanye  ), kunye nenkcazelo yesixhasi, kunye ne-superscripts echaza umjikelo.   Ii-edges ezimnyama, ezivelayo kwi-Pauli   errors kwi-qubits zekhowudi (kwaye ngoko ke zii-size-2 kuphela), ziqhagamshela ii-graphs ezimbini kwi- ( ) kunye ( ), kodwa azisetyenziswa kwi-matching decoder. F Ii-hyperedges zii-size-4, ezingasetyenziswa yi-matching, kodwa zisetyenziswa kwi-maximum likelihood decoder. Imibala yeyokucaca kuphela. Ukuguqulela nganye kwixesha elinye ngomjikelo kunika i-hyperedge esebenza nayo (kunye nolunye utshintsho kwimida yexesha). Kwakhona ayiboniswanga yi-hyperedges zii-size-3. a Z X 1 2 Q Q Q Q Q Q Z X b X Z c Z d X X Z Z X e Y c d Apha sigxila kwi-FT circuit ethile, uninzi lweendlela zethu zingasetyenziswa ngokubanzi kunye neekhowudi kunye nemijikelo eyahlukeneyo. Ii-circuits ezimbini ezincinci, ezibonisiweyo kuMfanekiso. b, zakhiwe ukulinganisa ii- - kunye ne- -gauge operators. Isifundo se- -gauge nawo sifumana ulwazi oluyimfuneko ngokulinganisa ii-flag qubits. 1 X Z Z Silungiselela imeko ye-code kwimeko ye-logical  () isimo ngokulungisa kuqala ii-qubits ezilithoba kwisimo  () kwaye silinganiswe ii- -gauge ( -gauge). Emva koko senza   imijikelo yokulinganisa kwe-syndrome, apho umjikelo ubandakanya umlinganiselo we- -gauge okulandelwa ngumlalinganiselo we- -gauge (ngokulandelanayo, umlinganiselo we- -gauge okulandelwa ngumlalinganiselo we- -gauge). Okokugqibela, sifunda zonke ii-qubits ezilithoba kwisiseko se-  ( ). Sisebenzisa imisebenzi efanayo yeemvavanyo zezi-logical states  kunye  njengoko, ngokulula ngokulungisa ii-qubits ezilithoba kwisimo  kunye  endaweni yoko. X Z r Z X X Z Z X Iindidi zeDecoding Kwindawo ye-FT quantum computing, i-decoder li-algorithm elithatha njengesiphumo i-syndrome measurements ukusuka kwikhodi yokulungisa impazamo kwaye libuyisele ukulungiswa kwi-qubits okanye idatha yokulinganisa. Kwesi sigaba sichaza ii-algorithms ezimbini zokuchaza: perfect matching decoding kunye ne-maximum likelihood decoding. I-decoding hypergraph  yinkcazo efutshane yolwazi oluqokelelwe yi-FT circuit kwaye yenziwe yafumaneka kumbonisi wegama. Inezikhethi, okanye iziganeko ezibonisa ingozi, , kunye nezikhethi ze-hyperedge , eziqulunqa ubudlelwane phakathi kweziganeko ezibangelwa ziimpazamo kwi-circuit. Umfanekiso. c–f ubonisa amacandelo e-decoding hypergraph yovavanyo lwethu. 15 V E 1 Ukwakha i-decoding hypergraph ye-stabilizer circuits kunye ne-Pauli noise kunokufezekiswa kusetyenziswa i-Gottesman-Knill simulations eqhelekileyo  okanye iindlela ezifanayo ze-Pauli tracing . Okokuqala, isiganeko esibonisa ingozi sidalwa kuyo yonke imilinganiselo echanekileyo kwisifundo esingenampazamo. Umlinganiselo ochanekileyo  ngumlinganiselo wokulinganisa wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqubo wenkqu 25 26 M

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