```html Ababhali: Sergey Bravyi Andrew W. Cross Jay M. Gambetta Dmitri Maslov Patrick Rall Theodore J. Yoder Isishwankathelo Ukunqwabelana kweempazamo zomzimba , , kuthintela ukwenziwa kwezikhangayo ezinkulu kwikhompyutha zamaxesha ethu ezikhompyutha. Ukulungiswa kweempazamo zeQuantum iyathembisa isisombululo ngokufaka iikhowudi yezibhalo kwiqela elikhulu yeekhuphethi zomzimba, ukuze iimpazamo zomzimba zicuthwe ngokwaneleyo ukuze kuvunyelwe ukwenziwa kokubala okufunekayo ngesizotha esinyamezelekayo. Ukulungiswa kweempazamo zeQuantum kufikeleleka ngokusebenza xa izinga lempazamo yomzimba lingaphantsi kwexabiso lomda elixhomekeke kukhetho lwekhowudi yequantum, isekethe yokulinganisa isignali kunye ne algorithm yokuchaza . Siyazisa inkqubo yokulungisa impazamo yequantum esuka ekupheleni ukuya ekupheleni eyenza inkumbulo evulekileyo yeempazamo esekelwe kusapho lweekhowudi zeparity-check ezisezantsi . Indlela yethu ifikelela kumda weempazamo we-0.7% ngenxa yenkqubo eqhelekileyo ye-circuit-based noise model, ifana nekhowudi engumgangatho , , , ebeyikhowudi ephambili kwiminyaka eyi-20 malunga nomda weempazamo. Isiketi somlinganiso wesignali kwikhowudi enobude obungu-n kusapho lwethu ifuna ii-qubits ezingama-n ezongezelelweyo kunye ne-circuit enobunzulu obuyi-8 ene-CNOT gates, ukubuyiselwa kwe-qubit kunye nemilinganiso. Ukuqhagamshelwa kwe-qubit okufunekayo yi-graph enobubanzi obuyi-6 equka ii-subgraphs ezimbini ezihlukileyo zemizobo. Ngokukodwa, sibonisa ukuba ii-qubits ezili-12 ezibhaliweyo zingagcinwa malunga ne-1 yezigidi zesiketi zesignali kusetyenziswa ii-qubits ezingama-288 zizonke, kulungiselelo ukuba izinga lempazamo yomzimba li-0.1%, ngelixa ikhowudi engumgangatho ingafuna ii-qubits ezingaphezu kwama-3,000 ukuze ifikelele kule nkqubo. Izinto esizifumeneyo zizisa imbonakalo yenkumbulo ye-quantum evulekileyo yeempazamo ngendleko ezantsi phantsi kokufikelela kwiikhompyutha ze-quantum ezizayo ezizayo. 1 2 3 4 k n 5 6 7 8 9 10 Umyalezo Ukubala ngeQuantum kuye kwatsala umdla ngenxa yamandla ayo okubonelela ngezisombululo ezikhawulezayo kwiingxaki ezithile zokubala xa kuthelekiswa ne-algorithms ezaziwayo kakhulu zakudala . Kukholelwa ukuba ikhompyutha ye-quantum ephantsi-phantsi enokusebenza inganceda ekusombululeni iingxaki zokubala kwizinto ezinjengokufumanisa inkcubeko, uphononongo lwezinto, amayeza kunye noyilo lwamayeza, ukubala nje ezimbalwa , , , . 5 11 12 13 14 Umqobo omkhulu ekwakheni ikhompyutha ye-quantum luthando lolwazi lwe-quantum, ngenxa yezizathu ezahlukeneyo zengxolo eziluchaphazelayo. Njengoko ukugocagocwa kwekhompyutha ye-quantum kwimiphumo yangaphandle kunye nokuyilawula ukuze kubangwe inkqubo yokubala efunekayo kungqubana, ingxolo ibonakala ingaphetshukiyo. Izizathu zengxolo zibandakanya ukungagqibeleli kwiikhuphethi, izinto ezisetyenzisiweyo, izixhobo zokulawula, ukulungiswa kwesimo kunye neziphumo zemilinganiso kunye nezizathu ezahlukenyo zangaphandle ukusuka kwizinto ezenziwe ngabantu, ezinje ngeemidibaniso zombane, ukuya kwezo ziphantsi kwiNdalo iphela, ezinje nge-cosmic rays. Bona i-ref. ngenjongo yokugqibezela. Ngelixa ezinye izizathu zengxolo zinokupheliswa ngolawulo olungcono , izinto kunye nokukhusela , , , ezinye izizathu ezininzi zibonakala zinzima ukuba zingapheliswa. Uhlobo lokugqibela lunokubandakanya ukukhutshwa kwenzululwazi kunye nokukhutshwa okukhuthazwayo kwi-ions ezibanjisiweyo , , kunye nokudibana kunye ne-bath (Purcell effect) kwiisekethe ze-superconducting—ezicatshulwe zombini ubuchwepheshe obuphambili be-quantum. Ngoko ke, ukulungiswa kweempazamo kufuna isidingo esibalulekileyo sokwakha ikhompyutha ye-quantum ephantsi-phantsi enokusebenza. 15 16 17 18 19 20 1 2 3 Ubume bokungaqhubeki kweempazamo zeQuantum buzinzile . Ukufaka i-qubit yombhalo ngokungafunekiyo kwiikhuphethi zomzimba ezininzi kwenza kube lula ukuxilonga kunye nokulungisa iimpazamo ngokulinganisa rhoqo imiqondiso yee-operator zokuhlola i-parity. Nangona kunjalo, ukulungiswa kweempazamo kunenzuzo kuphela ukuba izinga lempazamo yehardware lingaphantsi kwexabiso elithile elixhomekeke kwinkqubo ethile yokulungisa impazamo. Izindululo zokuqala zokulungiswa kweempazamo ze-quantum, ezinje ngeekhowudi ezicatshulweyo , , , zibeke ingqalelo ekubonakaliseni ubume benzululwazi bokunciphisa impazamo. Njengoko ukuqonda malunga nokulungiswa kweempazamo ze-quantum kunye namandla ezobuchwepheshe ze-quantum kuvele, ingqalelo yajika ekufumaneni iinkqubo zokulungiswa kweempazamo ze-quantum. Oku kuye kwakhokelela kuphuhliso lwekhowudi engumgangatho , , , ebonelela ngomda omkhulu weempazamo obufutshane ne-1%, i-algorithms ezikhawulezayo zokuchaza kunye nokuhambelana nezikhompyutha ze-quantum ezikhoyo ezisekelwe kuqhagamshelwano lwe-qubit lwe-2D yeenkalo. Iimveki ezincinci zekhowudi engumgangatho enye i-qubit enye yombhalo sele ibonakaliswe ngovavanyo ngamaqela amaninzi , , , , . Nangona kunjalo, ukwandisa ikhowudi engumgangatho ukuya kwi-qubits ezili-100 okanye ngaphezulu kungabizi kakhulu ngenxa yokungasebenzi kwayo kakuhle. Oku kuye kwabangela umdla kwiikhowudi ze-quantum ezaziwa ngokubanzi njengeekhowudi zeparity-check ezisezantsi (LDPC) . Ukuqhubeka kwangoku kufundo lweekhowudi ze-LDPC kubonisa ukuba zingafumana ukungaqhubeki kweempazamo ze-quantum ngendleko yokufaka ephezulu kakhulu . Apha, sigxila kufundo lweekhowudi ze-LDPC, njengoko injongo yethu kukufumana iikhowudi kunye neenkqubo zokulungisa impazamo ze-quantum ezisebenza kakuhle kwaye zinokubonakaliswa ngokusebenza, ngenxa yemida yezobuchwepheshe ze-quantum computing. 4 21 22 23 7 8 9 10 24 25 26 27 28 6 29 Ikhowudi ye-quantum eqhubekayo impazamo ye-LDPC type ukuba nganye yee-operator zokuhlola isebenza kwiikhuphethi ezimbalwa kuphela kwaye i-qubit ngayinye ithatha inxaxheba kwiimvavanyo ezimbalwa. Izinto ezahlukeneyo zeeqhowudi ze-LDPC ziye zasolulwa kutshanje kubandakanya iikhodi ze-hyperbolic surface , , , i-hypergraph product , iikhowudi ezivunyelanisiweyo , iikhowudi ezimbini zeebhloko ezisekwe kulaqela emathethe , , , kunye nekhowudi ze-quantum Tanner , . Ezi zimva zibonakaliswe , njenge ‘ezilungileyo’ ngokugqithisileyo ngokokuphathelele ukubonelela ngereyidi yokufaka engaguqukiyo kunye nomgama olungelelanayo: iparameter echaza inani leempazamo ezingalungiswa. Ngokungafaniyo, ikhowudi engumgangatho inereyidi yokufaka ethintelweyo kunye nomgama we-square-root kuphela. Ukubuyisela ikhowudi engumgangatho ngekhowudi ye-LDPC enereyidi ephezulu, umgama omkhulu kungaba nemiphumo emikhulu. Okokuqala, ubuninzi bokungaqhubeki kweempazamo (umlinganiso phakathi kwee-qubits zomzimba kunye nezombhalo) bungancitshiswa kakhulu. Okwesibini, iikhowudi ezinomgama omkhulu zibonisa ukuncipha okukhawulezileyo kwinqanaba leempazamo zombhalo: njengoko ubude bempazamo yomzimba budlula ixabiso lomda, ubungakanani bokunciphiswa kwempazamo obufumaneka yikhowudi bunganda ngokuhamba kwamakhulu. Eli nqaku lenza iikhowudi ze-LDPC ezinomgama omkhulu zithandeka kwiinkcukacha zesizukulwana esilandelayo ezinokuthi zisebenze kwindawo ekufuphi nomda. Nangona kunjalo, ngaphambili kwakukholelwa ukuba ukugqitha kwikhawudi engumgangatho kwiimodeli zengxolo ezisebenzayo ezibandakanya inkumbulo, iingalo, ukulungiswa kwesimo kunye nemilinganiso yeempazamo kungafuna iikhodi ezinkulu kakhulu ze-LDPC ezinemikhuphethi yomzimba engaphezu kwe-10,000 . 30 31 32 33 34 35 36 37 38 39 40 39 40 31 Apha siyazisa imizekelo emininzi eqingqwelekileyo yeekhowudi ze-LDPC eziphezulu-reyidi kunye nekhuphethi zomzimba ezimbalwa ezixhotyiswe ngesekethe yokulinganisa isignali enzulu, i-algorithm yokuchaza esebenza kakuhle kunye nenkqubo evulekileyo yeempazamo yokujongana nee-qubits ezibhalwe ngokunye. Ezi khowudi zibonisa umda weempazamo osondeleyo kwi-0.7%, zibonisa ukusebenza okugqwesileyo kwindawo ekufutshane nomda kwaye zinika ukuncitshiswa okuphindaphindwe ka-10 kwindleko yokufaka xa kuthelekiswa nekhowudi engumgangatho. Iimfuno zehardware ukuze zenziwe iinkqubo zethu zokulungisa impazamo zithambile, njengoko i-qubit yomzimba nganye idibene nee-gates ezimbini-qubit kunye nezinye ii-qubits ezintandathu. Nangona ukudibanisa kwe-qubit akufakwanga kwi-grid ye-2D, kunokwahlulwa kwiimbombo ezimbini ezihlukileyo zemizobo. Njengoko sixoxa ngoku, uqhagamshelwano olunjalo lwe-qubit lufanelekile kwimicenyeni esekelwe kwi-superconducting qubits. Iikhowudi zethu zisisiphelo saphula iikhowudi ezibhalwe nguMacKay et al. kwaye sifundwe kakhulu kwi-refs. , , . Siyibize iikhowudi zethu ze-bivariate bicycle (BB) kuba zisekelwe kwiipolynomials ezimbini, njengoko kuchaziwe kwi . Le yikhodi ze-stabilizer zohlobo lweCalderbank–Shor–Steane (CSS) , ezingachazwa liqela lee-operator ze-check ezisithoba-qubit eziquka u-Pauli kunye . Kwinqanaba eliphezulu, ikhowudi ye-BB ifana nekhowudi ye-toric eyi-dimensional . Ngokukodwa, ii-qubits zomzimba zekhowudi ye-BB zingabatyalwa kwigridi eneenkalo ezimbini kunye nemida yokubuyela emva ukuze zonke ii-operator zokuhlola zifunyaniswe kwisibini esinye se- kunye zikhangela ngokudluliselwa komgangatho kunye nowomnyele. Nangona kunjalo, ngokungafaniyo ne-stabilizers zepalquette kunye ne-vertex ezichaza ikhowudi ye-toric, ii-operator zokuhlola zeekhowudi ze-BB azilungelelananga ngokwemizobo. Ngapha, isiqinisekiso ngasinye sixhomekeke kwiikhuphethi ezithandathu endaweni yezine. Siza kuchaza ikhowudi nge-Tanner graph ukuze nganye inqaku le- limele i-qubit yedatha okanye i-operator yokuhlola. Isiqinisekiso sokuhlola kunye nenqaku ledatha zidityaniswe ngenqaku ukuba i- th check operator isebenza ngokungathanga ngqo kwi- th data qubit (ngokwenza u-Pauli okanye ). Bona iFig. imizobo ye-Tanner eyimzekelo yeekhowudi ze-surface kunye ne-BB, ngokulandelanayo. I-Tanner graph yayo nayiphi na ikhowudi ye-BB inobubanzi besiqintsi esiyi-6 kunye nobunzima begeji obuyi-2, oko kuthetha ukuba ingahlulwa kwiimbombo ezimbini ezihlukileyo zemizobo (iindlela. ). Uqhagamshelwano lwekhuphethi lobubanzi obuyi-2 lufanelekile kwii-superconducting qubits ezidibene ngama-resonators e-microwave. Ngokomzekelo, imibhalo emibini yemizobo yama-coupler kunye nemigca yayo yokulawula ingafakelwa kwicala eliphezulu kunye nelasezantsi lesiqwengana esibamba ii-qubits, kwaye ii-cala ezimbini zidibene. 41 35 36 42 Methods 43 44 X Z 7 X Z G G i j i j X Z 1a,b 29 Methods , I-Tanner graph yekhowudi engumgangatho, ukuthelekisa. , I-Tanner graph yekhowudi ye-BB enee-parameters [[144, 12, 12]] efakwe kwi-torus. Naluphi na unqambothi lwe-Tanner graph ludibanisa inqaku ledatha kunye neyokuhlola. Ii-qubits zedatha ezihambelana nerejista ( ) kunye ( ) iboniswa ngamangqengqe aluhlaza kunye ne-orange. Unqambothi ngalunye luneenqamlezo ezintandathu kubandakanya iinqamlezo ezine-short-range (ezikhombisa umntla, umzantsi, umntla-mpuma kunye nomntla-ntshona) kunye neenqamlezo ezimbini ezide-range. Sibonisa kuphela iinqamlezo ezimbalwa ezide-range ukuthintela ukudibanisa. Iinqamlezo ezichaziweyo nezicacileyo zibonisa iimbombo ezimbini zemizobo ezisasazekileyo kwi-Tanner graph, bona iindlela. . , Isigcawu sesandiso se-Tanner graph sokulinganisa kunye emva kwe-ref. , kufakwe kwikhodi engumgangatho. I-ancilla ehambelana nomlinganiso ingadityaniswa kwikhodi engumgangatho, ivumela imisebenzi yokulayisha-yogcino kuzo zonke ii-qubits zombhalo ngokusebenzisa i-teleportation ye-quantum kunye neeyunithi ezithile zombhalo. Le-Tanner graph eyandisiweyo ikwanayo nenkcazo kwi-architecture enobubanzi obuyi-2 ngokusebenzisa iinqamlezo kunye (iindlela. ). a b q L q R Methods c 50 A B Methods Ikhowudi ye-BB enee-parameters [[ , , ]] ifaka ii-qubits ezibhaliweyo ezili- kwii-qubits zedatha ezili- ezibonelela ngomgama wekhowudi , okuthetha ukuba nakuphi na impazamo yombhalo idlula ubuncinane ii-qubits ezili- . Sahlula ii-qubits zedatha ezili- kwiirejista ( ) kunye ( ) yobungakanani obuzi- /2 nganye. Ngokwahlukileyo, nganye ijongana nee-qubits ezintathu ezivela kwi- ( ) kunye nezintathu ezivela kwi- ( ). Ikhowudi ixhomekeke kwi-qubits zokuhlola ezingama-n ukulinganisa imiqondiso yeempazamo. Sahlula ii-qubits zokuhlola ezili- kwii-rejista ( ) kunye ( ) yobungakanani obuyi- /2 ezibamba imiqondiso ye- kunye uhlobo, ngokulandelanayo. Zizonke, ukufakwa kuquka ii-qubits zomzimba ezingama-2 . Ngoko ke, ireyidi yokufaka eyongeziweyo yi = /(2 ). Ngokomzekelo, inkqubo eqhelekileyo yekhowudi engumgangatho ifaka i- = 1 i-qubit yombhalo kwi- = 2 data qubits kumgama-d code kwaye isebenzisa ii-qubits zokuhlola ezili- − 1 ukuze kulungiswe imiqondiso. Irhasi yokufaka eyongeziweyo yi ≈ 1/(2 2), ekhawuleza ingasebenzi njengoko sifuna ukukhetha umgama omkhulu wekhowudi, ngenxa, umzekelo, iimpazamo zomzimba zisondele kumda. Ngokungafaniyo, iikhowudi ze-BB zinereyidi yokufaka ≫ 1/ 2, bona Itheyibhile imizekelo yekhowudi. Kangangoko siyaziyo, zonke iikhowudi eziboniswe kwiTeyibhile zintsha. Ikhowudi ye-distance-12 [[144, 12, 12]] ingaba yona inokubakho kakhulu kubonakaliswa kwixesha el n k d k n d d n q L q R n q L q R n q X q Z n X Z n r k n k n d n r d r d 1 1
