```html Ababhali: UBravyi UAndrew W. Cross UJamo M. Gambetta UDmitri Maslov UPatrick Rall UTheodore J. Yoder Isishwankathelo Ukuhlangana kweempazamo zomzimba , , kuthintela ukwenziwa kwezixilongo ezinkulu kwiikhompyutha zangoku ze-quantum. Ukulungiswa kweempazamo ze-Quantum iyathembisa isisombululo ngokubeka i- ye-logical qubits kwisamba esikhulu esingu- ye-physical qubits, ukuze iimpazamo zomzimba zincitshiswe ngokwaneleyo ukuze uvumele ukusebenza kobalo olufunwayo ngobuchule obunokholo. Ukulungiswa kweempazamo ze-Quantum kuyenzeka ngokwenene xa ireyidi ye-physical error ingaphantsi kwexabiso lemida elixhomekeke kukhetho lwekhowudi ye-quantum, isekethe yokulinganisa ye-syndrome kunye ne-algorithm yokuchonga iimpazamo . Sikwazisa iprotocol yokulungiswa kweempazamo ze-quantum ukusuka ekugqibeleni kuye ekugqibeleni enika inkqubo yokugcina inqobo ye-fault-tolerant ngokusekelwe kusapho lwekhowudi ephantsi-density parity-check (LDPC) . Indlela yethu ifumana umda weempazamo we-0.7% kwisisekelo semodeli ye-noise esekelwe kwisetingelwa, efana ne-surface code , , , eyeyona khowudi iphambili kwiminyaka eyi-20 malunga nomda weempazamo. Isiyingi sokulinganisa i-syndrome kwikhawudi yobude kwiintsapho zethu ifuna ii-ancillary qubits ezingama- kunye nesekethe yobunzulu be-8 ene-CNOT gates, ukuqaliswa kwe-qubit kunye nemilinganiselo. Ukuqhagamshelwa kwe-qubit okufunekayo yi-graph enobunzulu be-6 equka ii-subgraphs ezimbini ezingena kwi-planar. Ngokukodwa, sibonisa ukuba i-logical qubits ezili-12 zingagcinwa phantse izihlandlo ezili-1 zokulinganisa i-syndrome kusetyenziswa ii-qubits ezingama-288 kumntla, ukuba ireyidi ye-physical error yi-0.1%, ngelixa i-surface code ingafuna ii-qubits ezingama-3,000 ukufezekisa le nkqubo. Iziphumo zethu zibeka ubungqina bokugcina i-quantum memory ye-fault-tolerant enesibonelelo esiphantsi ngaphakathi kwesantya samaqonga okwangoku e-quantum. 1 2 3 4 k n 5 6 7 8 9 10 6 6 n n Into Ebalulekileyo Ukubala nge-Quantum kudonsela ingqalelo ngenxa yomthamo walo wokubonelela ngezisombululo ezikhawulezayo kwiingxaki ezithile zokubala xa kuthelekiswa neyona algorithm yakudala eyaziwayo . Kukholelwa ukuba i-computer ye-quantum esebenza kakuhle kwaye inokujikwa inganceda ukusombulula iingxaki zokubala kwiindawo ezinjengokufunyanwa kwenzululwazi, uphando lwezinto eziphathekayo, ikhemistri kunye noyilo lwemithi, ukukhankanya ezimbalwa , , , . 5 11 12 13 14 Isithintelo esiphambili ekwakheni i-computer ye-quantum kukuthotywa kolwazi lwe-quantum, ngenxa yeendlela ezahlukeneyo zengxolo ezichaphazela yona. Njengoko ukwahlula i-computer ye-quantum kwiziphumo zangaphandle kunye nokuyilawula ukwenza ubalele kufana nokungqubana, ingxolo ibonakala ingaphepheki. Imithombo yengxolo ibandakanya ukungagqibeleli kwi-qubits, izinto eziphathekayo ezisetyenzisiweyo, izixhobo zokulawula, ukulungiswa kwesigaba kunye nemilinganiselo kunye neendlela ezahlukeneyo zangaphandle ukusuka kwimishini yasekhaya eyenziweyo, njengemimandla ye-electromagnetic echithekileyo, ukuya kwezo zipheleleyo kwiNdalo iphela, njengeenkwenkwezi zekhosi. Jonga kwi-ref. yesishwankathelo. Ngelixa imithombo yengxolo ingasuswa ngolawulo olungcono , izinto eziphathekayo kunye nokhuselo , , , imithombo emininzi eyahlukileyo ibonakala inzima ukuba ingasuswa. Uhlobo lokugqibela lungabandakanya ukukhutshwa okuzenzekelayo kunye nokukhuthazwa kwi-trapped ions , , kunye nokunxibelelana nebhafu (i-Purcell effect) kwiisekethe ze-superconducting—ezimboza zombini iiteknoloji ze-quantum eziphambili. Ngoko ke, ukulungiswa kweempazamo kubangumfuneko ongundoqo wokwakha i-computer ye-quantum esebenza kakuhle enokujikwa. 15 16 17 18 19 20 1 2 3 Ubunokwenzeka be-quantum fault tolerance bumiselwe kakuhle . Ukubeka i-logical qubit ngokugqithiseleyo kwii-qubits ezininzi zomzimba kwenza kube lula ukuxilonga kunye nokulungisa iimpazamo ngokulinganisa rhoqo i-syndromes ze-parity-check operators. Nangona kunjalo, ukulungiswa kweempazamo kunenzuzo kuphela ukuba ireyidi ye-physical hardware error ingaphantsi kwexabiso elithile lemida elixhomekeke kwiprotocol ethile yokulungisa impazamo. Iziphakamiso zokuqala zokulungiswa kweempazamo ze-quantum, ezinje ngeekhowudi ezi-concatenated , , , zigxile ekubonisaneni ngamandla ethoretically okunciphisa impazamo. Njengoko ukuqonda i-quantum error correction kunye namandla eeteknoloji ze-quantum zavuthwa, ingqalelo yafudukela ekufumaneni iiprotocol ezisebenzayo zokulungisa impazamo ze-quantum. Oku kwakhokelela kuphuhliso lwe-surface code , , , enikezela ngomda omkhulu wempazamo osondela kwi-1%, iialgorithms zokuchonga iimpazamo ezikhawulezayo kunye nokuhambelana kunye namaqonga e-quantum ekhoyo asebenzisa ukuqhagamshelana kwe-two-dimensional (2D) square lattice qubit. Izigqibelelo ezincinci ze-surface code kunye ne-logical qubit enye sele zibonisiwe ngokwezobuchwepheshe ngamaqela amaninzi , , , , . Nangona kunjalo, ukwandisa i-surface code ukuya kuma-logical qubits ayi-100 okanye ngaphezulu kungabiza kakhulu ngenxa yobuchule bayo obungasebenziyo bokubeka. Oku kwandise umdla kwiikhowudi eziphakamileyo ezibizwa ngokuba yi-low-density parity-check (LDPC) codes . Ukuqhubela phambili kutshanje kufundo lweekhowudi ze-LDPC kubonisa ukuba zingafumana i-quantum fault tolerance enobuchule obuphezulu bokubeka . Apha, sigxila kufundo lweekhowudi ze-LDPC, njengoko injongo yethu kukufumana iikhowudi zokulungiswa kweempazamo ze-quantum kunye neeprotocol ezingasebenziyo kwaye zinokubonakaliswa ngokwenyani, kuthathwa ukuba kukho imida yeeteknoloji ze-quantum computing. 4 21 22 23 7 8 9 10 24 25 26 27 28 6 29 Ikhowudi yokulungisa impazamo ye-Quantum ingohlobo lwe-LDPC ukuba nganye kwi-check operator yekhowudi isebenza kwii-qubits ezimbalwa kuphela kwaye i-qubit nganye ithatha inxaxheba kwii-checks ezimbalwa. Iinguqulelo ezininzi zeekhowudi ze-LDPC ziye zaphethwe kutshanje kuquka ii-hyperbolic surface codes , , , hypergraph product , balanced product codes , two-block codes based on finite groups , , , kunye ne-quantum Tanner codes , . Le yokugqibela ibonisiwe , ukuba ingene 'ngokulungileyo' ngokubhekiselele ekuboneleleni ngesantya esingaguqukiyo sokubeka kunye nomgama olungileyo: iparameter ebalelayo inani leempazamo ezingalungiswa. Ngokuchaseneyo, i-surface code inesantya sokubeka esincipha ngokungapheliyo kunye nomgama ongu-square-root kuphela. Ukutshintsha i-surface code ngekhowudi ye-LDPC enesantya esiphezulu kunye nomgama omkhulu kungaba neziphumo ezinkulu kakhudlwana. Okokuqala, i-overhead ye-fault-tolerance (ubudlelwane phakathi kwenani le-physical kunye ne-logical qubits) ingancitshiswa ngokucacileyo. Okwesibini, iikhowudi ezinomgama omkhulu zibonisa ukuncipha okunamandla kwireyidi yeempazamo ze-logical: njengoko ubuchule beempazamo zomzimba budlula ixabiso lemida, inqanaba lokuncitshiswa kwempazamo elifunyenwe yikhawudi linganda ngama-oda obukhulu nokuba kunye nokuncipha okuncinci kakhubuchule beempazamo zomzimba. Le nto yenza iikhowudi ze-LDPC ezinomgama omkhulu zikhangela ukubonakaliswa okufanayo okungenokwenzeka ukuba kusebenze kwindawo yokusondeza i-threshold. Nangona kunjalo, kwakukholelwa ngaphambili ukuba ukwenza ngcono i-surface code yeemodeli zengxolo ezisebenzayo ezibandakanya imemori, igate kunye nokulungiswa kwesigaba kunye nemilinganiselo yepazulo ingafuna ii-LDPC codes ezinkulu kakhulu ezinemilinganiselo engaphezu kwe-10,000 ye-physical qubits . 30 31 32 33 34 35 36 37 38 39 40 39 40 31 Apha sikwazisa imizekelo ethile yeekhowudi ze-LDPC eziphakamileyo ezinama-hundreds ambalwa e-physical qubits axhotyiswe ngesiseko esiphantsi sokulinganisa i-syndrome, i-algorithm yokuchonga iimpazamo esebenzayo kunye ne-protocol ye-fault-tolerant yokujongana nee-logical qubits zodwa. Ezi khowudi zibonisa umda weempazamo osondela kwi-0.7%, zibonisa ukusebenza okugqwesileyo kwindawo esondeleyo kwi-threshold kwaye zinikezela ngokuphindeka kwe-10 kunciphiso lwe-overhead yokubeka xa kuthelekiswa ne-surface code. Iimfuno zehlabathi zokwenza iiprotocol zethu zokulungiswa kweempazamo azikho nzima, njengoko i-physical qubit nganye idityaniswe nge-two-qubit gates kunye ne-qubits ezintandathu kuphela. Nangona i-qubit connectivity graph ayifakwanga kwi-2D grid, ingahlulwa ibe yii-subgraphs ezimbini ezingena kwi-planar. Njengoko sibonisa ngezantsi, ezi qubit connectivity zihambelana neziqulunqo eziyisisekelo kwi-qubits ze-superconducting. Iikhowudi zethu ziyimfuneko yeekhowudi ezithile ezibizwa ngokuba yi-bicycle codes ezaphethwe nguMacKay et al. kwaye zafundwa nzulu kwi-refs. , , . Siyibize imikhowudi yethu nge-bivariate bicycle (BB) kuba isekelwe kwi-polynomials ezimbini, njengoko kuchaziwe kwi-Methods. Ezi yikhowudi ze-stabilizer ze-Calderbank–Shor–Steane (CSS) type , ezingachazwa ngumqokeleli we-six-qubit check (stabilizer) operators equka i-Pauli kunye ne- . Kwinqanaba eliphezulu, i-BB code ifana ne-toric code ye-two-dimensional. Ngokukodwa, ii-qubits zomzimba ze-BB code zingabekwa kwi-grid ye-two-dimensional kunye nemida ye-periodic ukuze bonke oobhodi bokujonga bafunyanwe kwisibini esinye see-checks ze- kunye ne- ngokusebenzisa ii-shifts ezithe tye nezithe nkqo zegridi. Nangona kunjalo, ngokungafani ne-plaquette kunye ne-vertex stabilizers ezichaza i-toric code, oobhodi bokujonga beekhowudi ze-BB abangaboniswa ngokwembonakalo. Ngaphezu koko, umyelezo ngamnye usebenza kwii-qubits ezintandathu endaweni yee-qubits ezine. Siza kuchaza ikhowudi nge-Tanner graph ukuze ilungu ngalinye le- limele i-qubit yedatha okanye i-check operator. I-check vertex kunye nelungu ledatha ziqhagamshelwe kunye nomphetho ukuba i- th check operator isebenza kwi-qubit yedatha ye- th (ngokusebenzisa i-Pauli okanye i- ). Jonga i-Fig. imizekelo yeTanner graphs ye-surface kunye neekhowudi ze-BB, ngokulandelanayo. I-Tanner graph yayo nayiphi na ikhowudi ye-BB inobunzulu be-vertex eyi-six kunye nobukhulu be-graph elingana no-two, okuthetha ukuba ingahlulwa ibe yii-subgraphs ezimbini ezingena kwi-planar ( ). Ubunzulu be-2 qubit connectivity ihambelana neziqulunqo ze-superconducting qubits ezidibaniswe nge-microwave resonators. Ngokomzekelo, imimandla emibini ye-couplers kunye nemigca yayo yokulawula ingafakwe phezulu nasemva kwi-chip ebanjisiweyo ii-qubits, kwaye imigca emibini idityaniswe. 41 35 36 42 43 44 X Z 7 X Z G G i j i j X Z 1a,b 29 Methods , Tanner graph ye-surface code, ukuthelekisa. , Tanner graph yekhowudi ye-BB eneparameter [[144, 12, 12]] efakwe kwi-torus. Umphetho ngamnye weTanner graph uqhagamshela idatha kunye ne-check vertex. Ii-qubits zedatha ezihambelana neerejista ( ) kunye ne- ( ) iboniswa ngama-ringi aluhlaza nomthubi. Ilungu ngalinye linemiphetho eyi-six kuquka imiphetho emine emfutshane (ejonge ngasentla, ngasezantsi, ngasekunene nasekunxele) kunye nemiphetho emibini emide. Sibonisa kuphela imiphetho emide yokuthintela ukuxakeka. Imiphetho enqamlezileyo kunye nemigca emitshelileyo ibonisa ii-subgraphs ezimbini ezingena kwi-Tanner graph, jonga i-Methods. , Isiqinisekiso se-Tanner graph extension yokulinganisa kunye ne- landela i-ref. , ukudibanisa kwi-surface code. I-ancilla ehambelana ne- measurement ingadityaniswa kwi-surface code, ivumela ukusebenza kwe-load-store kuzo zonke ii-logical qubits ngokusebenzisa i-quantum teleportation kunye nee-unitaries zolwimi ezithile. Le Tanner graph enwetshiweyo nayo inenkqubo yokusebenza kwi-thickness-2 architecture ngokusebenzisa imiphetho ye- kunye ne- >( ). a b q L q R c 50 A B Methods Ikhowudi ye-BB eneparameter [[ , , ]] ibeka ii-logical qubits ezingama- kwi-data qubits ezingama- inikezela ngomgama wekhowudi , oko kuthetha ukuba nakuphi na impazamo yobulwimi ihlala phakathi kwama-data qubits angama- . Sahlula i-data qubits ezingama- kwii-registers ( ) kunye ne- ( ) ezinomlinganiselo ongu- /2 nganye. Umyelezo ngamnye usebenza kwii-qubits ezintathu ukusuka kwi- ( ) kunye nee-qubits ezintathu ukusuka kwi- ( ). Ikhowudi ixhomekeke kwi-ancillary check qubits ezingama- ukulinganisa i-syndrome yeempazamo. Sihlula ii-check qubits ezingama- kwiirejista ( ) kunye ne- ( ) ezinomlinganiselo ongu- /2 eziqokelela ii-syndromes ze- kunye ne- types, ngokulandelanayo. Zizonke, ukubekwa kufuna ii-qubits ezingama-2 ezomzimba. Ngoko ke, isantya sokubeka net ngu = /(2 ). Ngokomzekelo, i-standard surface code architecture ibeka i-logical qubit enye = 1 kwi-data qubits ezingama- = 2 yomgama we-d code kwaye isebenzisa ii-check qubits ezingama- − 1 ukulinganisa i-syndromes. Isantya sokubeka net ngu ≈ 1/(2 2), nto leyo eba nzima ngokukhawuleza njengoko siyinyanzeliswa ukuba sikhethe umgama omkhulu wekhowudi, ngenxa, ngokomzekelo, iimpazamo zomzimba zisondele kwixabiso lemida. Ngokuchaseneyo, iikhowudi ze-BB zine-encoding rate ≫ 1/ 2, jonga iTafile imizekelo yekhowudi. Kwi-bawo lethu, zonke iikhowudi eziboniswe kwiTafile zintsha. Ikhowudi ye-distance-12 [[144, 12, 12]] ingaba yona ithembisa kakhulu ekubonakalisweni okufanayo, njengoko idibanisa umgama omkhulu kunye nesantya esiphezulu net = 1/24. Ukuthelekisa, i-distance-11 surface code inesantya net n k d k n d d n q L q R n q L q R n n q X q Z n X Z n 1 r k n k n d n 1 r d r d 1 1 1 r
