Ababhali: Sergey Bravyi Andrew W. Cross Jay M. Gambetta Dmitri Maslov Patrick Rall Theodore J. Yoder Isishwankathelo Ukubuthaneka kweziphoso zomzimba , , kuthintela ukwenziwa kwezisombululo ezinkulu kwiikhompyutha zangoku ze-quantum. Ukulungiswa kwempazamo ye-Quantum iyathembisa isisombululo ngokufaka iil ogical qubits kwinani elikhulu ookudumisa ngokwasemzimbeni, ukuze iziphumo zomzimba zichithwe ngokwaneleyo ukuvumela ukubaleka kokubala okufunwayo ngokunyaniseka okubekekayo. Ukulungiswa kweziphoso ze-Quantum kubonakala kulungile xa izinga lokungaphumeleli komzimba lingaphantsi komda wokubaleka othembela kukhetho lekhowudi ye-quantum, umjikelo wokulinganisa we-syndrome, kunye nomgaqo wokuchonga . Siyazisa inkqubo epheleleyo yokulungiswa kweziphoso ze-quantum eyenza imemori eyenziwe ngezicwangciso isebenzise usapho lweekhowudi ezininzi zokupakisha iziqu (low-density parity-check codes) . Indlela yethu ifumana umda weziphoso we-0.7% kumnikezo weqabane lesekethe elisekelwe kwisiqu, elilingana nekhowudi ye-surface code , , , ekudala iminyaka engama-20 yayiyeyona khowudi iphambili ngokungathelekanga kwimida yeziphoso. Umjikelo wokulinganisa we-syndrome kwiqela le-n elinye kwintsapho yethu lifuna i-n ancillary qubits kunye nesekethe enobunzulu bama-8 enee-CNOT gates, ukuqala kweqabane, kunye nemilinganiselo. Ukuqhagamshelwa kweQubit okufunekayo yileyo yegraphi enomlinganiselo om-6 enee-subgraphs ezimbini ezingeyomdibaniso. Ngokukodwa, sibonisa ukuba iil ogical qubits ezili-12 zinokugcinwa kangangezihlandlo ezisi-1 yezigidi zemijikelo ye-syndrome kusetyenziswa i-288 qubits zomzimba, ngokuchasene nekhowudi ye-surface code iya kufuna i-3,000 yeekubiti zomzimba ukufezekisa le njongo. Iziphumo zethu zibeka ubungqina bokugcinwa kwe-quantum fault-tolerant memory ngesiphoso esiphantsi ngaphakathi kwamaqabane e-quantum asebenzayo. 1 2 3 4 k n 5 6 7 8 9 10 k Into Ebalulekileyo Ukubala kwe-Quantum kuye kwatsala umdla ngenxa yamandla ayo okubonelela ngezisombululo ezikhawulezileyo kwezinye iingxaki zokubala xa kuthelekiswa neziphakamileyo ezaziwayo zesikolo . Kukholelwa ukuba ikhompyutha ye-quantum eyenziweyo enokubaleka inganceda ekusonjululeni iingxaki zokubala kwiindawo ezinjengophando lwesayensi, uphendlo lwezinto eziphathekayo, amachiza kunye noyilo lwamayeza, ukuze kubekho ezininzi , , , . 5 11 12 13 14 Umqobo omkhulu ekwakheni ikhompyutha ye-quantum kukutshatyalaliswa kolwazi lwe-quantum, ngenxa yeendidi zeziphumo ezichaphazela zona. Njengoko ukugquma ikhompyutha ye-quantum kwiziphumo zangaphandle kunye nokuyilawula ukuba ibe kukubala okufunwayo kuyachasana, iziphumo zibonakala zingaphepheki. Izizathu zeziphumo zibandakanya ukungapheleli kwee-qubits, izinto eziphathekayo ezisetyenzisiweyo, izixhobo zokulawula, ukulungiswa kwesitayile kunye nemilinganiselo, kunye neendidi zeziphumo zangaphandle ukusuka kwizinto zenziwe ngumntu, ezinjengezinto zombane, ukuya kwezo ziphuhliswe yindawo yonke, ezinjengezikhanyiso zobuso. Jonga iref. ngesishwankathelo. Ngelixa ezinye izizathu zeziphumo zinokupheliswa ngolawulo olungcono , izinto eziphathekayo kunye nokugquma , , , ezinye izizathu ezininzi zibonakala zinzima ukuba zingapheliswa. Uhlobo lokugqibela lungabandakanya ukukhutshwa kwe-spontaneous kunye ne-stimulated kwii-ions ezibanjisiweyo , , kunye nokudibana nebhafu (Purcell effect) kwii-circuits ezisekelwe kwi-superconducting—ezibandakanya zombini ubuchwepheshe obukhokhelayo be-quantum. Ngokunjalo, ukulungiswa kweziphoso kuba yimfuneko ephambili ekwakheni ikhompyutha ye-quantum eyenziweyo enokubaleka. 15 16 17 18 19 20 1 2 3 Ubume be-quantum fault tolerance busekwe kakuhle . Ukufaka i-logical qubit ngokuchanekileyo kwiqabane elininzi le-qubits zomzimba kuvumela ukuxilonga kunye nokulungisa iziphoso ngokulinganisa rhoqo izigwebo ze-syndrome. Nangona kunjalo, ukulungiswa kweziphoso kuyanceda kuphela ukuba izinga leziphoso zehardware lingaphantsi komda othile wokubaleka othembela kwinkqubo ethile yokulungiswa kweziphoso. Izicwangciso zokuqala zokulungiswa kweziphoso ze-quantum, ezinje ngeekhowudi ezidibanisiweyo , , , zazijolise ekubonakaliseni ubume be-theoretical bokunciphisa iziphoso. Njengoko ukuqonda ukulungiswa kweziphoso ze-quantum kunye namandla ezobuchwepheshe ze-quantum zivuthiwe, ingqwalasela yaguqukela ekufumaneni iinkqubo ezisebenzayo zokulungiswa kweziphoso ze-quantum. Oku kukhokelele ekudalweni kwekhowudi ye-surface code , , , ezibonelela ngomda weziphoso omkhulu osondele ku-1%, iinkqubo zokuchonga ezikhawulezileyo kunye nokuhambelana namaqabane e-quantum asebenzayo asebenzisa ubuchwepheshe be-two-dimensional (2D) square lattice qubit. Imizekelo emincinci yekhowudi ye-surface code enye i-logical qubit sele iboniswe ngabavavanyi ziingqokelele ezininzi , , , , . Nangona kunjalo, ukwandisa ikhowudi ye-surface code ukuya kwi-100 okanye nangaphezulu i-logical qubits kungaba yindleko kakhulu ngenxa yokungaphumeleli kwayo okungafanelekanga. Oku kuye kwadala umdla kwiikhowudi ze-quantum ezibanzi ezaziwa ngokuba ziziqu ezichanekileyo (LDPC) zeekhowudi . Uphuhliso olutsha kwisifundo see-LDPC codes lubonisa ukuba zingafumana i-quantum fault tolerance ngokusetyenziswa okungafanelekanga okukwanda kakhulu . Apha, sigxila kwisifundo see-LDPC codes, njengoko injongo yethu kukufumana iikhowudi ze-quantum error correction kunye neenqubo ezisebenzayo 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 error correcting ingohlobo lwe-LDPC ukuba umsebenzi ngamnye wokujonga wekhowudi usebenza kwi-qubits ezimbalwa kwaye i-qubit nganye ithatha inxaxheba kumanani ambalwa okujonga. Iintlobo ezininzi zee-LDPC codes ziye zavela kutshanje kuquka iikhowudi ze-hyperbolic surface codes , , , i-hypergraph product , iikhowudi ezifanelekileyo zomkhiqizo , iikhowudi ezimbini zesikwele ezisekelwe kumaqela ezifana namaqela , , , kunye neekhowudi ze-quantum Tanner , . Ezi zokugqibela zibonakaliswe , ukuba zihlala zilungile ngokubhekisele ekuboneleleni ngereyidi yokubeka engenamda kunye nomgama olungelelaneyo: iparameter echaza inani leziphoso ezinokulungiswa. Ngokungafaniyo, ikhowudi ye-surface code inereyidi yokubeka engafanelekanga kwaye kuphela umgama wesikweri. Ukubuyisela ikhowudi ye-surface code ngekhowudi ye-LDPC enomgama omkhulu kunye nomgangatho ophezulu kungaba neziphumo ezibalulekileyo. Okokuqala, isiphoso sokulungisa iziphoso (umlinganiselo phakathi kwenani le-qubits zomzimba kunye neye-logical) ingancitshiswa kakhulu. Okwesibini, iikhowudi ezinomgama omkhulu zibonisa ukuhla okukhulu kwinqanaba leziphoso zolwimi: njengoko ubumongola besiphoso somzimba bugqitha kumda wokubaleka, ubungakanani bokunciphisa iziphoso obufumanwa yikhowudi bunganda ngama-oda amakhulu nakwizisombululo ezincinci zesiphoso somzimba. Le ngcaciso yenza iikhowudi ze-LDPC ezinomgama omkhulu zibhenele imiboniso esele ikho, ejonge ukusebenza kwimida yokubaleka. Nangona kunjalo, ngaphambili kwakukholelwa ukuba ukugqitha kwikhawudi ye-surface code yeenkqubo ezingafanelekanga ezinje ngeziphoso zememori, iingcali kunye nokulungiswa kwesitayile kunye nemilinganiselo kungafuna iikhowudi ezinkulu ze-LDPC ezinezi-qubits zomzimba ezingaphezu kwe-10,000 . 30 31 32 33 34 35 36 37 38 39 40 39 40 31 Apha siyazisa imizekelo emininzi ethile yee-LDPC codes eziqala ngokuphakathi, ezine-hundreds yeekubiti zomzimba ezixhotyiswe ngomjikelezo wokulinganisa we-syndrome onobunzulu obuncinci, umgaqo wokuchonga osebeneleyo, kunye nenkqubo yokulungisa iziphoso yokujongana nee-logical qubits ezizodwa. Ezi khowudi zibonisa umda weziphoso osondele ku-0.7%, zibonisa ukusebenza okugqwesileyo kumda wokubaleka kunye nokunciphisa isiphoso esiphindwe ka-10 xa kuthelekiswa nekhowudi ye-surface code. Iimfuno zehardware zokubonelela ngeenqubo zethu zokulungisa iziphoso zilingane, njengoko i-qubit nganye yomzimba idityaniswe nge-two-qubit gates kunye nezinye iikubiti ezintandathu. Nangona ukudibanisa kwe-qubit graph ayifakwanga kwi-2D grid, ingahlulwa ibe zii-subgraphs ezimbini ze-planar. Njengoko sibonisa ngezantsi, ukudibanisa okunjalo kwe-qubit kufanelekile kwimiyalezo esekelwe kwi-superconducting qubits. Iikhowudi zethu ziyilapho ye-bicycle codes eyavulwa nguMacKay et al. kwaye yafundwa ngokunzulu kwiirefs. , , . Siyibiza iikhowudi zethu zibini zebhayisekile (BB) kuba zisekelwe kwi-polynomials ezimbini, njengoko zichazwe kwi-Methods. Ezi yii-stabilizer codes zohlobo lweCalderbank–Shor–Steane (CSS) , ezinokuchazwa ngoluhlu lwamaqabane okujonga ayisithandathu-qubit (stabilizer) aquka i-Pauli kunye . Ngokubanzi, i-BB code ifana ne-toric code ye-two-dimensional . Ngokukodwa, i-qubits zomzimba zekhowudi ye-BB zingafakwa kwigridi ye-two-dimensional enee-boundary conditions eziphindaphindwayo ukuze zonke izigwebo zokujonga zifunyanwe kwisibini esinye kunye zigwebo ngokujikeleza okuthe tye nokuthe nkqo kwegridi. Nangona kunjalo, ngokungafaniyo ne-stabilizers ze-plaquette kunye ne-vertex ezichaza i-toric code, izigwebo zokujonga ze-BB codes azikho kwi-geometrically local. Ngaphezu koko, isigwebo ngasinye senza kwi-qubits ezithandathu endaweni yezi-4. Siza kuchaza ikhowudi nge-Tanner graph ukuze i-vertex nganye ye imele i-data qubit okanye i-check operator. I-check vertex kunye ne-data vertex zidityaniswe ngomda ukuba isigwebo sokujonga th sisebenza ngokungathanga ngqo kwi-data qubit th (ngokusebenzisa i-Pauli okanye ). Jonga i-Fig. yemizekelo ye-Tanner graphs yee-surface kunye nee-BB codes, ngokulandelelana. I-Tanner graph yayo nayiphi na i-BB code inobunzulu be-vertex obuzi-6 kunye nobukhulu begrafu obulingana no-2, nto leyo ethetha ukuba ingahlulwa ibe zii-subgraphs ezimbini ze-planar ezingadibaniyo ( ). Ubunzulu-2 ubuchwepheshe be-qubit bufanelekile kwii-superconducting qubits ezidibene ngama-resonators ombane. Ngokomzekelo, imicengezi emibini yeenqaba zabaxhumi kunye nemigca yabo yokulawula ingadityaniswa phezulu nangaphantsi kwesikhahlulo esibamba i-qubits, kwaye zombini iziphelo zidityaniswe. 41 35 36 42 43 44 X Z 7 X Z G G i j i j X Z 1a,b 29 Methods , I-Tanner graph yekhowudi ye-surface, ukuthelekisa. , I-Tanner graph yekhowudi ye-BB eneeparameter [] efakwe kwi-torus. Nawuphi na umda we-Tanner graph udibanisa i-data kunye ne-check vertex. I-qubits zedata ezinxulumene nerejista ( ) kunye ( ) boniswa ngamajikolo aluhlaza nombala wewolofi. Inqaku ngalinye lineemida emithandathu efaka imida emine emfutshane (ebheke entla, ezantsi, empuma nasentshona) kunye nemida emibini emide. Sibonisa kuphela imida emide ukuze singabi ngumkhuhlane. Iimida ezibhalwe ngemigca emdaka kunye nemigca eyomeleleyo zibonisa ii-subgraphs ezimbini ze-planar ezibala i-Tanner graph, jonga i-Methods. , Isikiti se-Tanner graph extension yokulinganisa kunye elandela iref. , idibanisa kwikhawudi ye-surface. I-ancilla ehambelana nomlinganiselo we- ingadibaniswa kwikhawudi ye-surface, ivumela ukusebenza kokulayisha-gcina kuzo zonke iil ogical qubits ngokusebenzisa i-quantum teleportation kunye nee-unitaries zolwimi ezithile. Le Tanner graph eyandisiweyo ikwanayo nenkcazelo kwi-thickness-2 architecture ngokusebenzisa i- kunye ne- edges ( ). a b q L q R c 50 k A B Methods I-BB code eneeparameter [[ , , ]] ifaka iil ogical qubits kwi- data qubits ebonelela ngomgama wekhowudi , nto leyo ethetha ukuba nasiphi na isiphoso solwimi sisasazeka ubuncinci kwi- data qubits. Sahlula i- data qubits kwii-registers ( ) kunye ( ) yobungakanani /2 nganye. Isigwebo ngasinye sisebenza kwi-qubits ezintathu ukusuka kwi- ( ) kunye nezi-3 ukusuka kwi- ( ). Ikhowudi ithembela kwi- ancillary check qubits ukulinganisa i-syndrome yesiphoso. Sahlula i- check qubits kwii-registers ( ) kunye ( ) yobungakanani /2 eqokelela i-syndromes zeentlobo kunye , ngokulandelelana. Ngokubanzi, ukubeka kufuna ii-qubits zomzimba ezili-2 . Ireyidi yokubeka net is therefore = /(2 ). Ngokomzekelo, umzekelo owaziwayo wekhowudi ye-surface code ubeka = 1 i-logical qubit kwi- = 2 data qubits yomgama wekhowudi kwaye isebenzisa − 1 check qubits kwi-syndrome measurements. Ireyidi yokubeka net is ≈ 1/(2 2), eba yinto engekho praktikal njengoko sifuna ukukhetha umgama omkhulu wekhowudi, ngenxa, umzekelo, iziphoso zomzimba zisondele kumda wokubaleka. Ngokungafaniyo, iikhowudi ze-BB zinereyidi yokubeka ≫ 1/ 2, jonga iThebula ngeemizekelo zeekhowudi. Ngokwazi kwethu, zonke iikhowudi eziboniswe kwiThebula zintsha. Ikhowudi ye-distance-12 [] ingaba yeyona ithembisa kakhulu kwimiboniso esele ikho, njengoko idibanisa umgama omkhulu kunye nereyidi yokubeka net ephakame kakhulu = 1/24. Ukuthelekisa, ikhowudi ye-distance-11 surface code inereyidi yokubeka net = 1/241. Ngaphantsi, sibonisa ukuba ikhowudi ye-distance-12 BB igqitha ikhowudi ye-distance-11 surface code kuluhlu olufanelekileyo lokujonga kweziphoso. 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 r k n k n d d n r d r d 1 1 r r Ukuthintela ukubuthaneka kweziphoso kufuneka ukwazi ukulinganisa i-syndrome yephoso rhoqo. Oku kufezekiswa ngomjikelezo wokulinganisa we-syndrome odibanisa i-data qubits kwinkxaso yomsebenzi ngamnye wokujonga kunye ne-ancillary qubit ehambelanayo ngoluhlu lwee-CNOT gates. Ii-qubits zokujonga ziq
