```html Ababhungqongi: Sergey Bravyi Andrew W. Cross Jay M. Gambetta Dmitri Maslov Patrick Rall Theodore J. Yoder Isishwankathelo Ubuninzi beempazamo zomzimba , , buyathintela ukwenziwa kwezifundo ezinkulu kwii-quantum computers zangoku. Ukulungiswa kweempazamo ze-quantum iyathembisa isisombululo ngokufaka iikhowudi yezibalo kumnani omkhulu yee-qubits zomzimba, ukuze iimpazamo zomzimba zicinywe ngokwaneleyo ukuvumela ukwenziwa kobalo olufunwayo ngobunyaniso obunokwamkelwa. Ukulungiswa kweempazamo ze-quantum kufikeleleka ngokupheleleyo xa izinga lempazamo yomzimba lingaphantsi kwexabiso lomda elixhomekeke kukhetho lwe-quantum code, isekethe yokulinganisa i-syndrome kunye ne-algorithm yokuchaza . Siyazisa inkqubo epheleleyo yokulungiswa kweempazamo ze-quantum esebenzisa imemori enokubuyisela impazamo esekelwe kusapho lwee-low-density parity-check (LDPC) codes . Indlela yethu ifikelela kumda weempazamo we-0.7% kwimodeli yemveliso yesekethe, efana ne-surface code , , , ebiyeyona khowudi iphambili kwiminyaka eyi-20 ngokubhekiselele kumda weempazamo. Isibonelelo sokulinganisa i-syndrome sebude be- code kwintsapho yethu sifuna i- qubits ezongezelekileyo kunye nesekethe yobunzulu be-8 ene-CNOT gates, ukubuyisela ngokutsha kwe-qubit kunye nemilinganiselo. Ukuxhunywa kwe-qubit okufunekayo yi-degree-6 graph equka ii-planar subgraphs ezimbini ezingadibanelaniyo. Ngokukodwa, sibonisa ukuba i-12 qubits ezifanelekileyo zinokugcinwa kangangezigidi ezi-1 zamaxesha okulinganisa i-syndrome kusetyenziswa ii-qubits ezingama-288 zomzimba, ngokuchasene ne-surface code iya kufuna ii-qubits ezingama-3,000 zomzimba ukuze ifikelele le nkqubo. Iziphumo zethu zizisa iinkcukacha ze-quantum memory enokubuyisela impazamo kwisibonelelo esiphantsi esifikelelekayo kwiiprocessors ze-quantum ezizayo. 1 2 3 4 k n 5 6 7 8 9 10 n n Ukuntywila I-Quantum computing itsale umdla ngenxa yokukwazi kwayo ukubonelela ngezisombululo ezikhawulezileyo kwiingxaki ezithile zokubala xa zithelekiswa nezona algorithms zaziwayo zakwa-classical . Kukholelwa ukuba i-quantum computer enokusebenza kwaye iyakwazi ukunceda ukusombulula iingxaki zokubala kwiindawo ezinjengophando lwesayensi, uphando lwezinto eziphathekayo, ikhemistri kunye noyilo lweziyobisi, phakathi kwezinye , , , . 5 11 12 13 14 Ubunzima obukhulu ekwakheni i-quantum computer bubuthathaka bolwazi lwe-quantum, ngenxa yezizathu ezahlukeneyo zemveliso ebuchaphazela yona. Njengoko ukwahlula i-quantum computer kwiimpembelelo zangaphandle kunye nokuyilawula ukuze yenze ubalo olufunwayo kunokungangqinelani, imveliso ibonakala ingaphepheki. Izizathu zemveliso zibandakanya ukungagqibeleli kwi-qubits, izinto eziphathekayo ezisetyenzisiweyo, izixhobo zokulawula, ukulungiswa kwesigaba kunye neempazamo zokulinganisa kunye neentlobo ezahlukeneyo zezinto zangaphandle ukusuka kwezobuntu, ezifana nemiqolo yombane, ukuya kwezo zingeyona nto ipheleleyo yeNdalo iphela, ezinje nge-cosmic rays. Bona i-ref. ngokufingqwa. Ngelixa ezinye izizathu zemveliso zinokupheliswa ngolawulo olungcono , izinto eziphathekayo kunye nokukhusela , , , ezinye izizathu ezininzi zibonakala kunzima, ukuba kunokwenzeka, ukuzisusa. Uhlobo lokugqibela lungabandakanya ukukhutshwa ngokuzenzekelayo nokukhutshwa okwenziweyo kwi-trapped ions , , kunye nokunxibelelana ne-bath (Purcell effect) kwiiseti zesekethe —ezifaka zombini iitekknoloji ze-quantum ezihamba phambili. Ngoko ke, ukulungiswa kweempazamo kufika ekubeni kufuneke kube yinto ephambili ekwakheni i-quantum computer enokusebenza kwaye ibeyinkulu. 15 16 17 18 19 20 1 2 3 3 Ubuninzi bokubuyisela impazamo ye-quantum buye babekwa kakuhle . Ukufaka i-logical qubit ngokugqithisileyo kwi-qubits ezininzi zomzimba kuvumela ukuxilonga kunye nokulungisa iimpazamo ngokulinganisa rhoqo i-syndromes yee-parity-check operators. Nangona kunjalo, ukulungiswa kweempazamo kunenzuzo kuphela ukuba izinga lempazamo yehardware lingaphantsi kwexabiso elithile lomda elixhomekeke kwinkqubo ethile yokulungiswa kweempazamo. Izindululo zokuqala zokulungiswa kweempazamo ze-quantum, ezinje ngeekhowudi ezidibeneyo , , , bagxile ekuboniseni ububunzulu bokucima impazamo. Njengoko ukuqonda ukulungiswa kweempazamo ze-quantum kunye namandla eeteknoloji ze-quantum aqala ukukhula, ingqalelo yajika ekufumaneni iinkqubo zokulungiswa kweempazamo ze-quantum ezinokwenzeka. Oku kwakhokelela kuphuhliso lwe-surface code , , , ebonelela ngomda omkhulu weempazamo obungange-1%, ii-algorithms zokuchaza ezikhawulezileyo kunye nokuhambelana nee-quantum processors ezikhoyo ezisekelwe kubudibaniso be-2D (2D) square lattice qubit. Imizekelo emincinci ye-surface code ene-logical qubit enye sele ibonisiwe ngokwenza experiments ziiqela ezininzi , , , , . Nangona kunjalo, ukwanda kwe-surface code ukuya kutsho kwii-logical qubits ezili-100 okanye nangaphezulu kuya kubiza kakhulu ngenxa yokungasebenzi kwayo kokubeka. Oku kukhuthaze umdla kwiikhowudi ze-quantum ezibanzi ezaziwa njenge-low-density parity-check (LDPC) codes . Ukuqhubela phambili kwangoku kwisifundo see-LDPC codes kubonisa ukuba zingafikelela i-quantum fault tolerance ngomsebenzi omkhulu wokubeka . Apha, sigxile kwisifundo see-LDPC codes, njengoko injongo yethu kukufumana iikhowudi kunye neenkhqubo zokulungiswa kweempazamo ze-quantum ezisebenza kakuhle kwaye zinokubonisa ngokwezibalo, ngenxa yezithintelo zeteknoloji ze-quantum computing. 4 21 22 23 7 8 9 10 24 25 26 27 28 6 29 I-quantum error correcting code ingohlobo lwe-LDPC ukuba bonke abaqhubi bokujonga be-code bathatha nje ii-qubits ezimbalwa kwaye i-qubit nganye ithatha inxaxheba kwimijongizo embalwa. Iinguqulelo ezininzi zee-LDPC codes ziye zaziswa kutshanje kuquka ii-hyperbolic surface codes , , , hypergraph product , balanced product codes , two-block codes based on finite groups , , , kunye nee-quantum Tanner codes , . Le yokugqibela yabonakaliswa , njenge-asymptotically ‘good’ ngokuthetha ukubonelela nge-encoding rate engaguqukiyo kunye ne-distance linear: iparameter elinganisayo inani leempazamo ezingalungiswa. Ngokuchaseneyo, i-surface code inereyithi yokubeka ethandabuzekayo engapheliyo kwaye kuphela yi-square-root distance. Ukubuyisela i-surface code nge-LDPC code enereyithi ephezulu, enomgama omkhulu kungaba neziphumo ezinkulu. Okokuqala, i-fault-tolerance overhead (umlinganiselo phakathi kwenani le-physical kunye ne-logical qubits) ingancipha kakhulu. Okwesibini, iikhowudi ezinomgama omkhulu zibonisa ukwehla okunamandla kwizinga lempazamo engokwezibalo: njengoko uxinizelelo lweempazamo zomzimba ludlula ixabiso lomda, ubungakanani bokucima impazamo obufikelelwe yikhowudi bunganda ngemiyalelo emikhulu nakuba nokuncipha okuncinci koxinizelelo lweempazamo zomzimba. Le nto yenza i-LDPC codes ezinomgama omkhulu zinomtsalane kwiziboniso ezizayo ezinokuthi zisebenze kwindawo ekufuphi nomda. Nangona kunjalo, kwakukholelwa ngaphambili ukuba ukudlula i-surface code kwii-models zemveliso ezisebenzayo ezibandakanya imemori, i-gate kunye nokulungiswa kwesigaba kunye neempazamo zokulinganisa kungafuna ii-LDPC codes ezinkulu kakhulu ezine-qubits zomzimba ezingaphezu kwe-10,000 . 30 31 32 33 34 35 36 37 38 39 40 39 40 31 Apha sivelisa imizekelo emininzi ecacileyo yee-LDPC codes ezinereyithi ephezulu ezine-qubits zomzimba ezimbalwa ezixhotyiswe ngesekethe yokulinganisa i-syndrome enobunzulu obuphantsi, i-algorithm yokuchaza esebenzayo kunye nenkqubo yokubuyisela impazamo yokujongana nee-logical qubits nganye. Ezi khowudi zibonisa umda weempazamo ongange-0.7%, zibonisa ukusebenza okugqwesileyo kwindawo ekufuphi nomda kwaye zinikezela ngokusasazeka kwe-10 yokunciphisa i-overhead yokubeka xa kuthelekiswa ne-surface code. Iimfuno zehardware ukuze senziwe iinkqubo zethu zokulungiswa kweempazamo azibanga ngqongqo, njengoko i-qubit yomzimba ngamnye idibaniswe nge-two-qubit gates kunye nee-qubits ezintandathu kuphela. Nangona i-qubit connectivity graph ayifakwanga kwilattice ye-2D, ingahlulwa ibe zii-planar subgraphs ezimbini. Njengoko sixoxa ngezantsi, ubudibaniso obunjalo be-qubit bulungele imiqolo esekelwe kwi-superconducting qubits. Iikhowudi zethu ziyingcaciso yee-bicycle codes ezaziswa nguMacKay et al. kwaye zachazwa kabanzi kwiiref. , , . Saziimbiza iikhowudi zethu njenge-bivariate bicycle (BB) kuba zisekelwe kwi-bivariate polynomials, njengoko zichaziwe kwi-Methods. Ezi zizi-stabilizer codes zohlobo lweCalderbank–Shor–Steane (CSS) , ezingachazwa liqokelelo lee-operators ezisithoba ze-qubit (stabilizer) ezibandakanya iPauli kunye . Ngokubanzi, i-BB code ifana ne-two-dimensional toric code . Ngokukodwa, ii-qubits zomzimba ze-BB code zinokulungiswa kwi-grid enobukhulu obubini enemida ejikelezayo ukuze bonke abaqhubi bokujonga bafumaneke kwi-pair enye ye- kunye ne- checks ngokusebenzisa ukuhambisa okuqulunqweyo nokuthe tye kwigridi. Nangona kunjalo, ngokungafaniyo nee-stabilizers ze-plaquette kunye ne-vertex ezichaza i-toric code, abaqhubi bokujonga be-BB codes abanobubanzi bokuma. Ngaphezu koko, njalo isijongiso sihlala kwii-qubits ezintandathu endaweni yezine. Siza kuchaza ikhowudi nge-Tanner graph ukuze zonke i-vertex ze-G zimele i-qubit yedata okanye umqhubi wokujonga. I-vertex yokujonga kunye ne-vertex yedata ziqhagamshelwe ngomda ukuba umqhubi wokujonga we-i usebenza ngokungacacanga kwi-qubit yedata ye-j (ngokusebenzisa iPauli okanye ). Bona iFig. 1a,b imizekelo yeetanner graphs ye-surface kunye ne-BB codes, ngokulandelelana. I-Tanner graph yayo nayiphi na i-BB code inobunzulu be-vertex obuyi-six kunye nobubanzi begrafu obuthe-thetha ngokuba bungahlulwa bubelii-planar subgraphs ezimbini ezizimeleyo ngokomda (Methods). Ububanzi-2 ubudibaniso be-qubit bulungele ii-superconducting qubits ezidibene ngee-microwave resonators. Ngokomzekelo, imigangatho emibini ye-planar yama-couplers kunye nemigca yayo yolawulo ingafakwa phezulu naphantsi kwesiphafu esi ngee-qubits, kwaye imigangatho emibini idityaniswe. 41 35 36 42 43 44 X Z 7 X Z G i j X Z 29 , I-Tanner graph ye-surface code, ukuze kuthelekiswe. , I-Tanner graph ye-BB code eneenkcukacha [[144, 12, 12]] efakwe kwi-torus. Nawuphi na umda we-Tanner graph uqhagamshela i-qubit yedata kunye ne-vertex yokujonga. Ii-qubits zedatha ezinxulumene neerejista ( ) kunye ( ) ziboniswa ngeenxawele eziluhlaza kunye nombala omfusa. Sonke i-vertex sinee-edges ezintandathu ezikhoyo ezibandakanya imida emine emfutshane (ejonge ngase ntla, ngasezantsi, ngasekunene nasekunxele) kunye nemida emibini emide. Sibonisa kuphela imida emininzi emide ukunqanda ukudideka. Imida enobude obufutshane kunye nemida eqinileyo ibonisa ii-planar subgraphs ezimbini ezisasazeka kwi-Tanner graph, bona iMethods. , Umzekelo we-Tanner graph extension yokulinganisa kunye ilandelwa yi-ref. , isongezwa kwi-surface code. I-ancilla ehambelana nokulinganisa ingafakwa kwi-surface code, ivumela imisebenzi yokulayisha-gcina yazo zonke ii-logical qubits ngokusebenzisa i-quantum teleportation kunye nee-unitaries ezingokwezibalo. Eli Tanner graph elongeziweyo likwanayo nenkcazelo kwisigqobho esinobubanzi obuyi-2 ngokusebenzisa i-A kunye ne-B edges (Methods). a b q L q R c 50 I-BB code eneenkcukacha [[ , , ]] ibeka ii-logical qubits kwi-data qubits inikezela ngobubanzi bekhowudi , oko kuthetha ukuba nayiphi na impazamo yobubalo idlula ubuncinci ii-data qubits . Sikwahlula ii-data qubits kwiirejista ( ) kunye ( ) zobungakanani obuyi- /2 nganye. Lonke ujongiso lusebenza kwi-qubits ezintathu ukusuka ( ) kunye nee-qubits ezintathu ukusuka ( ). Ikhowudi ixhomekeke kwii-ancillary check qubits ukulinganisa i-syndrome yempazamo. Sikwahlula ii-check qubits kwiirejista ( ) kunye ( ) zobungakanani obuyi- /2 ezibamba ii-syndromes ze-X kunye ne-Z zohlobo, ngokulandelelana. Ngokupheleleyo, ukubeka kufuna ii-qubits ezingama-2 ezomzimba. Ngoko ke, irayithi yokubeka net i-r = /(2 ). Ngokomzekelo, i-standard surface code architecture ibeka i-logical qubit = 1 kwi-data qubits = 2 kwikhowudi yobubanzi be-d kwaye isebenzisa ii-check qubits ze- -1 kumilinganiselo ye-syndrome. Irhafu yokubeka net i-r ≈ 1/(2 2), ekhawuleza ibe yinto engenakwenzeka njengoko sixinizelelwa kukhetha ububanzi obukhulu bekhowudi, ngenxa, ngokomzekelo, iimpazamo zomzimba ezikufutshane nexabiso lomda. Ngokuchaseneyo, i-BB codes inereyithi yokubeka ≫ 1/ 2, bona itheyibhile 1 imizekelo yeekhowudi. Ngokwazi kwethu, zonke iikhowudi eziboniswe kwiThebula 1 zintsha. Ikhowudi yobubanzi obu-12 [[144, 12, 12]] ingaba yeyona inokubangela iziboniso ezizayo, njengoko idibanisa ububanzi obukhulu kunye nereyithi ephezulu yokubeka net = 1/24. Ukuze kuthelekiswe, i-surface code yobubanzi obu-11 inereyithi yokubeka net = 1/241. Ngaphantsi, sibonisa ukuba i-BB code yobubanzi obu-12 idlula i-surface code yobubanzi obu-11 kuluhlu olufanelekileyo lweempazamo lokwenza experiments ngezinga leempazamo. n k d k n d d n q L q R n q L q R n n q X q Z n n k n k n d n d r d r r Ukuthintela ukuqokelela kweempazamo kufuneka kukwazi ukulinganisa i-syndrome yempazamo rhoqo ngokwaneleyo. Oku kungenziwa yisiseko semilinganiselo ye-syndrome esijonga ii-qubits zedatha kwindawo yomqhubi ngamnye wokujonga kunye ne-qubit eyongezelekileyo ngokusebenzisa uthotho lwee-CNOT gates. Ii-qubits zokujonga ke zilinganiswa zibonisa ixabiso le-syndrome yempazamo. Ixesha elithathayo ukwenza isiseko sokulinganisa i-syndrome lixhomekeke kubunzulu bayo: inani lemigangatho ye-gate equka ii-CNOTs ezingadibanelaniyo. Njengoko iimpazamo ezintsha zisiya zenzeka ngelixa isiseko sokulinganisa i-syndrome senziwa, ubunzulu bayo kufuneka bancitshiswe. Umjikelo opheleleyo wokulinganisa i-syndrome kwi-BB code uchazwe kwiFig. 2. Umjikelo we-syndrome ufuna kuphela imigangatho esixhenxe yee-CNOTs kungakhathaliseki ubude bekhowudi. Ii-qubits zokujonga zibuyiselwa kwasekuqaleni kwaye zilinganiswe ekuqaleni nasekuphumeni komjikelo we-syndrome ngokulandelelana (bona iMethods
