Ababhali: Neereja Sundaresan Theodore J. Yoder Youngseok Kim Muyuan Li Edward H. Chen Grace Harper Ted Thorbeck Andrew W. Cross Antonio D. Córcoles Maika Takita Isishwetho I-Quantum error correction inika indlela ethembisayo yokwenza izibalo ze-quantum eziyi-high fidelity. Noma ngabe ukusebenza ngokugcwele okungazinzileyo kwezibalo kuhlala kungakafezekiswa, ukuthuthuka kwakamuva kuziphethe izinto zokulawula izinto zokulawula kanye ne-quantum hardware kuvumela ukwethulwa okuthuthukileyo okudingekayo ukulungiswa kwempazamo. Lapha, senza i-quantum error correction kuma-superconducting qubits axhunywe kwi-heavy-hexagon lattice. Sigoqa i-logical qubit enebanga elingathathu futhi senza imizuliswano eminingana yokulinganisa kwe-syndrome okungazinzileyo okuvumela ukulungiswa kwanoma yimaphi amaphutha ayedwa kwisekethe. Sisebenzisa impendulo yesikhathi sangempela, sibuyekeza i-syndrome nama-qubits wefulegi ngokuya ngokwenziwa ngemva komjikelezo ngamunye wokukhipha i-syndrome. Sibika iphutha le-logical elincike ku-decoder, elinesilinganiso esiphakathi kwe-logical error nge-syndrome measurement ku-Z(X)-basis ye-~0.040 (~0.088) kanye ne-~0.037 (~0.087) yama-decoder afanayo kanye ne-maximum likelihood, ngokulandelana, kudatha ye-leakage post-selected. Isingeniso Imiphumela yezibalo ze-quantum ingaba neziphutha, empeleni, ngenxa yomsindo ku-hardware. Ukususa amaphutha abangelwa, amakhodi okuvikela amaphutha we-quantum (QEC) angasetshenziswa ukugubha ulwazi lwe-quantum ezindaweni ezinganikeziwe, ezinganamandla, bese ngokuqeda amaphutha ngokushesha kunokuba aqoqwwe, kwenziwe izibalo ezingazinzile (FT). Ukusebenza okugcwele kwe-QEC cishe kuzodingeka: ukulungiswa kwezimo zengqondo; ukwenziwa kweqoqo eligcwele lamabhola engqondo, angase adinge ukulungiswa kwezimo zemilingo; izilinganiso eziningi ze-syndromes; kanye nokufundwa kwe-syndromes ukuze kulungiswe amaphutha. Uma kuphumelela, amazinga ephutha engqondo ayoba ngaphansi kunezizinga zamaphutha omzimba, futhi anciphe ngokwanda kwamabanga ekhodi kuze kube amagugu angabaluleki. Ukukhetha ikhodi ye-QEC kudinga ukucatshangelwa kwe-hardware esekelwe kanye nezici zayo zomsindo. Kwi-heavy-hexagon lattice , ye-qubits, amakhodi e-subsystem QEC ayathandeka ngoba afanelana kahle nama-qubits anoxhumano oluncishisiwe. Amakhodi amanye abonise isithembiso ngenxa yomkhawulo wawo ophakeme kakhulu we-FT >6. 1 2 3 4 Endleleni yokufunda, ukulungiswa okuphumelelayo kuncike, hhayi nje ekusebenzeni kwe-quantum hardware, kodwa nangokwenziwa kwezinto zokulawula ezisetshenziselwa ukuqoqa nokucubungula imininingwane ye-classical etholwe kusuka kuzilinganiso ze-syndrome. Kithina, ukulungiswa kwama-qubits we-syndrome nama-flag ngempendulo yesikhathi sangempela phakathi kwemijikelezo yokulinganisa kungasiza ekunciphiseni amaphutha. Ezingeni lokufunda, ngenkathi kukhona amasu atholakalayo okwenza i-QEC ngokungavunyelwanga ngaphakathi komqondo we-FT , , isivinini lapho i-error syndromes itholwa khona kufanele ifane nesikhathi sayo sokucubungula i-classical ukugwema ukwanda kwedatha ye-syndrome. Futhi, amanye amasu, njengokusebenzisa isimo somlingo se-logical -gate , adinga ukwenziwa kwe-feed-forward yesikhathi sangempela. 7 8 T 9 Ngakho-ke, umbono wesenkathi ende we-QEC awuhambi ngomgomo owodwa wokugcina kodwa kufanele ubhekwe njengokuqhubeka kwezinhlelo eziningi ezihlangene kakhulu. Indlela yokuhlola ekuthuthukisweni kwalobu buchwepheshe izobandakanya ukwethulwa kwezinhlelo ezisetshenzisiwe kuqala bese zihlanganiswa kamuva, njalo ngenkathi kuthuthukiswa izilinganiso zazo. Okunye kwalokhu kuqhubeka kubonakala kwinhlangano yezinhlelo ze-quantum ezintsha ezihlukahlukene ezisekelwe kumalungiselelo ahlukahlukene, eziveze noma zafanisa izici eziningana zezifiso ze-FT quantum computing. Ngokukhethekile, ukulungiswa kwe-FT logical state kube yinto eyethulwe kuma-ions , ama-spins enukliya ku-diamond >12. Imijikelezo ejwayelekile yokukhipha i-syndrome iboniswe kuma-superconducting qubits kumakhodi amancane okuthola amaphutha , , kuhlanganise nokulungiswa kwamaphutha okuyingxenye >16. Ukuvezwa kwe-FT kweqoqo eligcwele lamabhola engqondo kuma-qubits amabili ayisibalo kubikwe kamuva kuma-ions . Emkhakheni wokuvikelwa kwamaphutha, kuye kwenzeka izinto eziningi ezisanda kwenzeka zokwenza ikhodi yesurface eyi-distance-3 kuma-superconducting qubits enokufundwa >19, kanye nokwenziwa kwe-FT okuyikhono lemvelo ye-quantum ebonakalayo kusetshenziswa ikhodi yombala >21. 10 11 13 14 15 17 18 20 Lapha sihlanganisa amandla empendulo yesikhathi sangempela kusistimu ye-superconducting qubit enendlela yokufunda ye-maximum likelihood eyayingakaze ihlolwe ngaphambili ukuze kuthuthukiswe ukusinda kwezimo zengqondo. Siveza lezi zixhobo njengengxenye yokusebenza kwe-FT ye-subsystem code , i-heavy-hexagon code , ku-superconducting quantum processor. Okubalulekile ekwenzeni ukwenziwa kwale khodi kungazinzile kungenxa yama-qubits wefulegi, lapho kutholakala ukuthi awanawo amandla, axwayisa i-decoder ngamaphutha ekhethekile. Ngokubuyekeza ngokuhlanganiswa kwama-flag nama-syndrome qubits ngemva komjikelezo ngamunye wokulinganisa we-syndrome, sivikela uhlelo lwethu kumaphutha avela ekungalingani komsindo okufakwe kokuphila. Siphinde sisebenzise izindlela zokufunda ezisanda kwenziwa >24. 22 1 15 Imiphumela I-heavy-hexagon code nemizuliswano eminingi I-heavy-hexagon code esiyicabangayo iyikhodi ye- = 9 qubit eqoka i- = 1 logical qubit enebanga = 3 . Iziqulatho ze- ne- (bona uMfanekiso 1a) namaqembu we-stabilizer akhiqizwa. n k d 1 Z X Amaqembu we-stabilizer amaphakathi kwamaqembu omkhono afaneleke kakhulu . Lokhu kusho ukuthi izibhalo ze-stabilizer, njengemikhiqizo yama-operators omkhono, zingatholwa kusuka kuzilinganiso zama-operators omkhono kuphela. Ama-operators angqondo angakhethwa njenge- = 1 2 3 ne- = 1 3 7. XL X X X ZL Z Z Z Iziqulatho ze- (blue) ne- (red) (izimp. (1) kanye (2)) ezifakwe kuma-qubits angama-23 adingekayo anobude be-distance-3 heavy-hexagon code. Ama-qubits ekhodi ( 1 − 9) abonakala ku-yellow, ama-qubits e-syndrome ( 17, 19, 20, 22) asetshenziselwa izibhalo ze- ku-blue, nama-qubits wefulegi nama-syndromes asetshenziselwa izibhalo ze- ku-white. Uku-oda kanye nesiqondiso lapho amasango e-CX enziwa khona ngaphakathi kwesigaba ngasinye (0 kuye ku-4) kukhonjiswa yimicibisholo enemibhalo. >4 >5. a Z X Q Q Q Q Q Q Z X b Lapha sigxila ku-circuit ethile ye-FT, izindlela zethu eziningi zingasetshenziswa ngokujwayelekile namakhodi nemizuliswano ehlukahlukene. Amasethi amabili emizuliswano, abonakala kuMfanekiso 1b, enziwa ukukala ama-operators omkhono we- ne- . Ukulinganisa kwe- -gauge nakho kuthola ulwazi oluwusizo ngokulinganisa ama-qubits wefulegi. X Z Z Silungisa izimo ze-code kwisimo se-logical () ngokulungisa kuqala ama-qubits ayisishiyagalolunye kwisimo se- () bese silinganisa i- -gauge (i- -gauge). Bese sisebenzisa imizuliswano ye-syndrome measurement ye- , lapho umjikelezo ubandakanya ukulinganisa kwe- -gauge okulandelwa ukulinganisa kwe- -gauge (ngokulandelana, i- -gauge elandelwa yi- -gauge). Ekugcineni, sifunda wonke ama-qubits ayisishiyagalolunye esisekelweni se- ( ). Sisebenzisa izivivinyo ezifanayo zezimo ze-logical ne- njengoba, ngokulungisa ama-qubits ayisishiyagalolunye ku- ne- esikhundleni. X X Z r Z X X Z Z X Izindlela zokufunda Esikhundleni sokubala izibalo ze-quantum eziningazinzile, i-decoder iyindlela eyabela okufakiwe kuzilinganiso ze-syndrome kusuka kukhodi yokulungisa amaphutha ezinto ezibonakalayo bese ivumela ukuthi ibuyele ekulungisweni kwe-qubits noma idatha yokulinganisa. Kulesi sigaba sichaza izindlela ezimbili zokufunda: ukufunda okufanayo okuphelele nokufunda okuningi kakhulu. I-decoding hypergraph >E , okuchaza ukuxhumana phakathi kwemicimbi okubangelwa amaphutha esekhethini. Umfanekiso 1c–f ubheka izingxenye ze-decoding hypergraph yesivivinyo sethu. 15 Ukwakha i-decoding hypergraph yemizuliswano ye-stabilizer enomsindo we-Pauli kungenziwa kusetshenziswa izifanekiso ze-Gottesman-Knill ezijwayelekile >26. Okokuqala, umcimbi okumelwe amaphutha ususwa kuwo wonke umlinganiselo onokwenzeka lapho kuyiqiniso ekhethini elingenalo iphutha. Umlinganiselo onokwenzeka >FM(mod2), okuyinto eyi-zero (ebuye ibizwe ngokuthi i-trivial) lapho kungekho khona amaphutha. Ngakho-ke, ukubona umcimbi okungewona owona (ubuye ubizwe ngokuthi i-non-trivial) kusho ukuthi ikhethe ibe namaphutha angaphezu kweyodwa. Emizuliswaneni yethu, imicimbi okufanele amaphutha iyizilinganiso zama-flag qubit noma umehluko wokulinganisa okulandelanayo kwe-stabilizer efanayo (kwesinye isikhathi obizwa nangokuthi i-difference syndromes). 25 M Okulandelayo, ama-hyperedges angezwa ngokucabangela amaphutha ekhethini. Imodeli yethu iqukethe i-probability ye-fault >I-CX yisango elilawulayo, i-H isango le-Hadamard, futhi i-x, y, z amawuphawu we-Pauli. (bona iMetjhodi “IBM_Peekskill ne-experimental details” ukuthola imininingwane eyengeziwe). Amagugu ezibalo afakwe ohlwini eMetjhodi “IBM_Peekskill ne-experimental details”. pC pC Imodeli yethu yephutha yimishayo ye-depolarizing. Ngamaphutha okuqala kanye nokuphumula, i-Pauli >pinit futhi reset >pC elinye lamawuphawu amathathu angewona awe-identity (i-two-qubit) Pauli errors elandela isango eliyiqiniso. Kukhona ithuba elilinganayo lokuvela kwanoma yimaphi ama-Pauli errors. X p Lapho kwenzeka i-fault eyodwa ekhethini, idala ukuthi ingxenye yemisebenzi okumelwe amaphutha ibe engavamile. Leli qembu lemisebenzi okumelwe amaphutha liba yi-hyperedge. I-set yazo yonke i-hyperedges yi- . Amaphutha amabili ahlukene angakhiqiza i-hyperedge efanayo, ngakho-ke i-hyperedge ngayinye ingase ibhekwe njengokumelela iqoqo lamaphutha, ngalinye lapho leli qembu lingakhiqiza imisebenzi eyenzeka ku-hyperedge ibe yingavamile. Kuhambisana ne-hyperedge ngayinye kukhona i-probability, ezingeni lokuqala, iyisamba sama-probability amaphutha aqoqwe.i- . Sila kithi amabhola omqondo kanye ne-basis ye-2 > >1 kwi-heavy-hexagon code esetshenzisiwe esivivinyweni. Singagcina sibheka ukuthi yimaphi ama-operators omqondo angahambelani ne-error kusetshenziswa i-vector kusuka ku-. Ngakho-ke, i-hyperedge ngayinye > > futhi ingalinganiswa nenye yala ma-vectors , okubizwa ngokuthi i-logical label. Qaphela ukuthi uma ibanga lekhodi linge-3, i-hyperedge ngayinye inombhalo we-logical ongajwayelekile. E XL k k k h h h Ekugcineni, sibona ukuthi i-decoder ingakhetha ukwenza lula i-decoding hypergraph ngezindlela ezahlukene. Indlela eyodwa esiyisebenzisa njalo lapha yinqubo yokuyeka ukudlala. Izilinganiso zama-flag kusuka kuma-qubits 16, 18, 21, 23 zinyatheliswa kalula ngaphandle kokwenziwa kwanoma yikuphi ukulungiswa. Uma i-flag 11 ingavamile futhi i-12 ibuye yajwayeleka, sebenzisa i- >2. Uma i-12 ingavamile futhi i-11 ijwayelekile, sebenzisa i- >6. Uma i-flag 13 ingavamile futhi i-14 ijwayelekile, sebenzisa i- kwi-qubit 4. Uma i-14 ingavamile futhi i-13 ijwayelekile, sebenzisa i- kwi-qubit 8. Bona ireferensi. 15 ngenhloso yokuthi lokhu kwanele ekuzinzeni kwamaphutha. Lokhu kusho ukuthi esikhundleni sokufaka imicimbi okumelwe amaphutha kusuka kuzilinganiso ze-flag qubit ngqo, sigudla idatha ngokusebenzisa imininingwane yefulegi ukusebenzisa izilungiso ze-Pauli >I-Z kwamaphutha ayisibalo. I-hyperedges ye-deflagged hypergraph ingatholwa nge-stabilizer simulation efaka izilungiso ze- . Ake imele inombolo yemijikelezo. Ngemuva kokudlala, usayizi weqoqo >Z (resp. >X ukusekelwa kwedatha) kuyi-∣ ∣ = 6 + 2 (resp. 6 + 4), ngenxa yokulinganisa izibalo zesivikelo ezintandathu ngomjikelezo kanye nokuba nezimbili (resp. ezine) izibalo zokuqala eziyisivikelo ngemuva kokulungiswa kwesimo. Usayizi we- >E >E futhi). Ngokwahlukanisa phakathi kwezimpawu ze- >X >Z ukuqondisa, inkinga yokuthola isilungiso esincane samaphutha sekhodi yesurface ingancishiswa ekutholeni okufanayo okuncane okufanayo kugrafu . Ama-decoder afanayo ahlala etadishwa ngenxa yokuphumelela kwawo >28, . Kulesi sigaba, sichaza i-decoder efanayo ye-khodi yethu ye-heavy-hexagon enebanga elingathathu. Z Z Z Z Z Z r V X V r r E X 4 27 29 Amagrafu okufunda, eyodwa yamaphutha e- (UMfanekiso 1c) nenye yamaphutha e- (UMfanekiso 1d), yokufanayo okuphelele okuncane ayi-subgraph yama-hypergraph okufunda esigabeni esedlule. Ake sigxile lapha kugrafu yokuqondisa ama- -errors, njengoba igrafu ye- -error ingafani. Kulesi simo, kusuka kwi-decoding hypergraph sigcina izindawo >VZ ezilinganayo (noma ngezimpawu ezibhalwe njengama-boundary). Zonke izinduku ku- -error graph zithola ama-probability nama-logical labels kusuka kuma-hyperedges azo afanayo (bona Itafula 1 >Tab1 ye- >X futhi -error edge data yesivivinyo semizuliswano emi-2). X Z X Z VZ X X Z Inqubo yokufanayo ephelele ithatha igrafu enezinduku ezinesisindo kanye neqoqo elilinganisiwe lezindawo ezikhanyisiwe, bese ibuyisa iqoqo lezinduku kugrafu ehlanganisa zonke izindawo ezikhanyisiwe ngamapheya futhi inesisindo esincane sonke phakathi kwawo wonke amakhoqo anjalo ezinduku. Kithina, izindawo ezikhanyisiwe yimicimbi yokuphutha engavamile (uma kukhona inombolo eyinqaba, indawo eyinqala nayo iyakhanyiswa), futhi izisindo zezinduku zikhethwa ukuthi zibe munye zonke (indlela eyi-uniform) noma zibekwe njenge-log-likelihood yalokho qoqo, bese ifanayo encane kakhulu iyazama ukukhuphula lokhu okuthembekayo phezu kwezinduku kugrafu. Kunikezwe ifanayo ephelele encane, umuntu angasebenzisa ama-logical labels ezinduku kufanayo ukunquma isilungiso sesimo sengqondo. Kungenjalo, i- -error (i- -error) graph ye-decoder efanayo ingalungiswa lapho ingaba ihlotshaniswa ne-qubit yekhodi (noma i-measurement error), lapho ukufaka i-edge kufanayo kusho ukuthi i- >(i- ) isilungiso kufanele senziwe ku-qubit ehambelanayo. X Z X Z Ukufunda okuningi kakhulu (MLD) kuyindlela enhle, kodwa enganyakazi, yokufunda amakhodi okuvikela amaphutha we-quantum. Ekuqaleni, i-MLD yasetshenziswa kumamodeli omsindo we-phenomenological lapho amaphutha avame ukuvela ngaphambi nje kokuthi ama-syndromes alinganiswe , . Lokhu, kunjalo, kuyakushiya imbangela yangempela lapho amaphutha angasakazeka ngokusebenzisa izixhobo zokulinganisa ze-syndrome. Muva nje, i-MLD yandiswe ukufaka umsindo we-circuit , . Lapha, sichaza ukuthi i-MLD ilungisa kanjani i-circuit noise kusetshenziswa i-decoding hypergraph. 24 30 23 31 I-MLD ithola isilungiso esingokwengqondo esingokwengqondo esihle kakhulu ngemuva kokubona imicimbi okufanele amaphutha. Lokhu kwenziwa ngokubala ukusatshalaliswa kwamathuba Pr[ , ], lapho imele imicimbi okumelwe amaphutha futhi imele isilungiso sengqondo. β γ Singabala i-Pr[ , ] ngokufaka yonke i-hyperedge kusuka kwi-decoding hypergraph, UMfanekiso 1c–f, siqala ekusabalalisweni kwamaphutha, okungukuthi, Pr[0∣ ∣, 02 ] = 1. Uma i-hyperedge >h ine-probability >ph >h >h >h >h ukwenzeka, ngaphandle kwanoma iyiphi enye i-hyperedge, sifaka >h >h >h >h >h >h >h >h >h >h >h >h >h futhi >h >h kanye >h >h futhi >h >h futhi >h kanye >h futhi >h kanye >h kanye >h kanye >h kanye >h kanye >h kanye >h kanye >h kanye >h kanye >h kanye >h kanye >h >h njengoba >h kanye >h njengoba >h >h >h >h >h >h >h >h >h >h >h >h kanye >h >h futhi >h futhi >h futhi >h futhi >h futhi >h >h futhi >h kanye >h kanye >h futhi >h kanye >h kanye >h >h >h >h >h kanye >h >h futhi >h >h futhi >h >h >h >h >h >h >h >h >h futhi >h >h >h >h >h futhi >h >h β γ V k h ph h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h h
