Ababhali: USirhayi Bravyi UMnumzana Andrew W. Cross UMnumzana Jay M. Gambetta UMnumzana Dmitri Maslov UMnumzana Patrick Rall UMnumzana Theodore J. Yoder Isishwankathelo Ukuhlanganiswa kweempazamo zomzimba , , kuthintela ukusetyenziswa kwezicwangciso ezinkulu kwiikhompyutha zangoku zequantum. Ukulungiswa kweempazamo zeQuantum idala isisombululo ngokugqithisa i- yee-qubits ezingokwemimiselo kwilixa elikhulu . Ukulungiswa kweempazamo zeQuantum kufikeleleka ngokupheleleyo xa izinga lempazamo yomzimba lingaphantsi kwexabiso lemida elixhomekeke kukhetho lwekhowudi yequantum, isekethe yokulinganisa i-syndrome kunye ne-algorithm yokudeka . Sibonisa inkqubo yokulungisa impazamo yequantum yokugqibezela kunye nokulungisa imemori eqinisekileyo ngokusekelwe kusapho lweekhowudi ezithile zokugqibezela i-low-density parity-check (LDPC). Indlela yethu ifikelela kumda we-0.7% weempazamo ze-syndrome , , , ekuyona khowudi ekhokelayo malunga ne-1% yomda weempazamo iminyaka eyi-20. Isiphaluka sokulinganisa i-syndrome sekhowudi yobude kulo sapho lwethu sifuna ama-qubits ancedisayo kunye nesekethe yobunzulu obuyi-8 kunye neengcambu ze-CNOT, ukubekwa kwe-qubit kunye nemilinganiselo. Ukuqhagamshelwa kwe-qubit okufunekayo yi-degree-6 graph equka iigraffiti ezimbini ezingaphandle kwe-planar. Ngokukodwa, sibonisa ukuba i-12 ye-qubits ezingokwemimiselo ingagcinwa kangangee-cycles ezingama-1 million ze-syndrome kusetyenziswa ii-qubits ezingama-288 zomzimba, ukuba i-rate yempazamo yomzimba yi-0.1%, ngelixa ikhowudi ye-surface ingafuna ii-qubits ezingama-3,000 zomzimba ukufezekisa le nto. Izinto esizifumanisileyo zizisa imiboniso yezinto ezingenayo zokulungisa impazamo ye-quantum kwiziphanje zee-processors zangoku zequantum. 1 2 3 4 k 5 6 7 8 9 10 11 n Okubalulekileyo Ukubala kweQuantum kuye kwafumana ingqalelo ngenxa yobuchule bayo bokubonelela ngezisombululo ezikhawulezayo kwiingxaki zokubala xa kuthelekiswa neyona algorithm ye-classical eyaziwayo . Kukholelwa ukuba ikhompyutha yequantum esebenzayo enokubala inganceda ukusombulula iingxaki zokubala kwiindawo ezinjengokufumanisa isayensi, uphando lwezinto, amayeza kunye nokuyilwa kwamayeza, ukuze kubalulwe ezimbalwa , , , . 5 11 12 13 14 Ukuqhekeka okuyintloko ekwakheni ikhompyutha yequantum kukuthotywa kwemلوماتiki yequantum, ngenxa yezizathu ezahlukeneyo zengxaki ezichaphazela yona. Njengoko ukwahlula ikhompyutha yequantum kwiimpawu zangaphandle kunye nokuyilawula ukuba yenze ucwangciso olufunekayo ingqubana omnye komnye, ingxaki ibonakala ingaphepheki. Izizathu zengxaki zibandakanya ukungapheleli kwi-qubits, izinto ezisetyenzisiweyo, izixhobo zolawulo, ukulungiswa kwesigaba kunye neziphumo zokulinganisa kunye neendidi ezahlukeneyo zezinto zangaphandle ukusuka kwizinto ezenziweyo zasekuhlaleni, ezinje ngemiba yombane etyelelayo, ukuya kwezo zingaphakathi zeNdalo iphela, ezinje ngeekhowudi zekhosi. Jonga i-ref. ngesishwankathelo. Ngelixa ezinye izizathu zengxaki zinokupheliswa ngolawulo olungcono , izinto kunye nokukhusela , , , ezinye izizathu ezininzi zibonakala zinzima ukuba zingasuswa. Uhlobo lokugqibela lungabandakanya ukukhutshwa okuzimeleyo kunye nokukhutshwa okubangelwa kukukhutshwa kwi-ions ezibanjisiweyo , , kunye nokunxibelelana nedama (i-Purcell effect) kwiisiphaluka ezingapheliyo—ezingqongileyo zombini ubuchwepheshe obuphambili bequantum. Ngoko ke, ukulungiswa kweempazamo kufuneka kube yimfuneko yokuqala ekwakheni ikhompyutha yequantum esebenzayo. 15 16 17 18 19 20 1 2 3 Ubume be-quantum fault tolerance buzinzile . Ukugqithisa i-qubit enye ngenombolo enkulu yee-qubits zomzimba kuyenza kube lula ukuxilonga kunye nokulungisa iimpazamo ngokulinganisa rhoqo i-syndromes zoqeqesho lwe-parity. Nangona kunjalo, ukulungiswa kweempazamo kunokuba luncedo kuphela ukuba izinga lempazamo yehardware lingaphantsi kwexabiso lemida elithile elixhomekeke kwinkqubo ethile yokulungisa impazamo. Iziphakamiso zokuqala zokulungiswa kweempazamo zequantum, ezinje ngeekhowudi ezigqithisiweyo , , , zigxile ekubonisaneni ubukho bokuncitshiswa kweempazamo. Njengoko ukuqonda kwe-quantum error correction kunye namandla ezobuchwepheshe bequantum zikhula, ingqalelo yaguqukela ekufumaneni iinkqubo ezingokoqobo zokulungisa impazamo zequantum. Oku kukhokelele kuphuhliso lwekhowudi ye-surface , , , enikezela ngomda omkhulu weempazamo osondeleyo kwi-1%, ii-algorithms zokudeka ezikhawulezayo kunye nokuhambelana kunye nee-processors ze-quantum ezisekelwe kwi-two-dimensional (2D) square lattice qubit connectivity. Imizekelo emincinci yekhowudi ye-surface kunye ne-qubit enye yomimiselo sele ibonisiwe ngokwezobuchwepheshe ngamaqela amaninzi , , , , . Nangona kunjalo, ukwandisa ikhowudi ye-surface ukuya kwi-100 okanye ngaphezulu ii-qubits ezingokwemimiselo kungabiza kakhulu ngenxa yokusebenza kwayo okubi kokugqithisa. Oku kukhuthaze umdla kwiikhowudi ezininzi ze-quantum ezaziwa njengeekhowudi ze-low-density parity-check (LDPC) . Uphuhliso lwamva nje kwi-study yeekhowudi ze-LDPC lubonisa ukuba zingafikelela kwi-quantum fault tolerance ngendlela yokugqithisa enamandla ngakumbi . Apha, sigxile kwi-study yee-LDPC codes, njengoko injongo yethu kukufumana iikhowudi zokulungisa impazamo ze-quantum kunye neenqubo ezisebenzayo kunye nezifanelekileyo zokubonisa ngokwezobuchwepheshe, ngenxa yemiqobo yezobuchwepheshe be-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 kwimisebenzi embalwa yokujonga. Iindidi ezininzi zekhowudi ze-LDPC ziphakamisiweyo kutshanje kubandakanya iikhowudi ze-hyperbolic surface , , , i-hypergraph product , iikhowudi ezilinganisiweyo , iikhowudi ezimbini ezisekelwe kumaqela ngamaqela , , , kunye nee-quantum Tanner codes , . Ezi zokugqibela zibonisiwe , ukuba zifikelela kwi-‘good’ ngokwengqiqo yokubonelela nge-rate yokugqithisa efanelekileyo kunye nomgama olungelelanayo: iparameter ebalayo inani leempazamo ezingalungiswa. Ngokungafaniyo, ikhowudi ye-surface inomgama othe ngqo okhawulezayo kunye nomgama we-square-root. Ukubuyisela ikhowudi ye-surface ngekhowudi ye-LDPC enomgama omkhulu kunye ne-rate ephezulu kungaba neziphumo ezibalulekileyo ngokwezobuchwepheshe. Okokuqala, i-overhead ye-fault-tolerance (umlinganiselo phakathi kwenani lee-qubits zomzimba kunye neye-logical) ingancitshiswa kakhulu. Okwesibini, iikhowudi ezinomgama omkhulu zibonisa ukuhla okucacileyo kwinqanaba lempazamo ye-logical: njengoko ubungakanani bempazamo yomzimba bugqitha kwixabiso lemida, ubungakanani bokuncitshiswa kwempazamo obufumaneka yikhawudi bunganda ngama-orders emandla nakubuncinci bokuncipha kobungakanani bempazamo yomzimba. Esi sici senza iikhowudi ze-LDPC ezinomgama omkhulu zifunwe kakhulu kwimiboniso ye-near-term elingelayo ukusebenza kwindawo eyimida. Nangona kunjalo, kwakukholelwa ngaphambili ukuba ukugqitha kwi-surface code kwii-models ezingaqhelekanga zengxaki ezibandakanya imemori, i-gate kunye nokulungiswa kwesigaba kunye neempazamo zokulinganisa kungafuna iikhowudi ezinkulu ze-LDPC ezinee-qubits ezingaphezu kwe-10,000 zomzimba . 30 31 32 33 34 35 36 37 38 39 40 39 40 31 Apha sibonisa imizekelo emininzi ecacileyo yee-LDPC codes eziphezulu-rate ezinee-hundreds ezimbalwa zama-qubits omzimba anesekethe yoku-syndrome ephantsi, i-algorithm yokudeka esebenzayo kunye nenkqubo yokulungisa impazamo yokujongana nee-qubits ezizimeleyo. Ezi khowudi zibonisa umda weempazamo osondeleyo kuma-0.7%, zibonisa ukusebenza okugqwesileyo kwindawo eyimida kwaye zinikezela ngokuphindaphindeka kwe-10 kwi-overhead yokugqithisa xa kuthelekiswa ne-surface code. Iimfuno zehardware zokufezekisa iinkqubo zethu zokulungisa impazamo zithobekile, njengoko i-qubit nganye yomzimba idityaniswe ngee-gates ezimbini-qubit kunye nee-qubits ezintandathu kuphela. Nangona i-qubit connectivity graph ayifakwanga kwigridi ye-2D, ingahlulwa ibe ngama-subgraphs amabini ayi-planar. Njengoko sibonisa ngezantsi, i-connectivity enjalo yeqhubu iyayidinga ngakumbi iindlela ezisekelwe kwi-superconducting qubits. Iikhowudi zethu ziyingqokelela yee-bicycle codes ezaphuhliswa nguMacKay et al. kwaye zafundwa ngokunzulu kwi-refs. , , . Siye sabiza iikhowudi zethu ze-bivariate bicycle (BB) kuba zisekelwe kwi-bivariate polynomials, njengoko kuchaziwe kwi- . Ezi yimizekelo yeenkqubo ze-stabilizer zeCalderbank–Shor–Steane (CSS) , ezingachazwa liqela lemisebenzi yeenqaba ezisithoba (stabilizer operators) equka ii-Pauli kunye . Kumgangatho ophezulu, i-BB code ifana ne-toric code ye-two-dimensional . Ngokukodwa, ii-qubits zomzimba zekhowudi ye-BB zingabekwa kwi-gridi ye-two-dimensional kunye nemida ye-periodic apho zonke imisebenzi yeenqaba ifumaneka kusuka kubumbeko olunye lwee-checks ze ne ngokusebenzisa izinyuko ezitibileyo kunye nezithe tye zegridi. Nangona kunjalo, ngokungafaniyo ne-plaquette kunye ne-vertex stabilizers ezichaza i-toric code, imisebenzi yeenqaba yeekhowudi ze-BB ayifani ngokwemizobo. Ngaphezu koko, i-check nganye isebenza kwi-qubits ezithandathu endaweni yezine. Siza kuchaza ikhowudi yigraphu ye-Tanner njengokuba i-vertex nganye ye-G imele i-qubit yedatha okanye umsebenzi woku-check. I-vertex yeenqaba kunye ne-vertex yedatha zidityaniswe ngomda ukuba umsebenzi wama-check we-i-th usebenza ngokungafaniyo kwi-qubit yedatha ye-j-th (ngokusebenzisa i-Pauli okanye ). Bona i-Fig. ngemizekelo yeegrafu ze-Tanner zekhowudi ye-surface kunye neye-BB ngokulandelanayo. I-graph ye-Tanner ye-BB code nayiphi na inobubunzulu be-vertex ezintandathu kunye nobubanzi begeyimu bulingana ezimbini, oku kuthetha ukuba ingahlulwa ibe ngama-subgraphs amabini ayi-planar awayahlulwa kwi-edge ( ). Ububanzi obuyi-2 be-qubit connectivity buyayifaneleela i-superconducting qubits edityaniswe ngee-microwave resonators. Ngokomzekelo, iigaba ezimbini ze-couplers kunye nemigca yazo yolawulo zingafakelwa kwicala eliphezulu nelisezantsi le-chip enee-qubits, kwaye iipateni ezimbini ziyafana. 41 35 36 42 Methods 43 44 X Z 7 X Z G i j X Z 1a,b 29 Methods , I-graph ye-Tanner yekhowudi ye-surface, ukuthelekisa. , I-graph ye-Tanner ye-BB code ene-parameters [[144, 12, 12]] efakwe kwi-torus. Nawuphi na umda we-graph ye-Tanner udibanisa idatha kunye ne-vertex yeenqaba. Ii-qubits zedatha ezihambelana neengxowa ( ) kunye ( ) ziboniswa nge-blue kunye ne-orange circles. I-vertex nganye inemida eyisithandathu kuquka imida emine emfutshane (ejonge kumantla, umzantsi, empumalanga naseNtshona) kunye nemida emibini emide. Sibonisa kuphela imida emide ukuze singadibanisi. Imida eyahlukileyo kunye nemida eqinileyo ibonisa ama-subgraphs amabini ayi-planar achaza i-graph ye-Tanner, bona i- . , Isiqwengana se-graph ye-Tanner yokwandiswa kokulinganisa kunye landela i-ref. , ifakwe kwi-surface code. I-ancilla ehambelana nokulinganisa kwe- ingadityaniswa kwikhawudi ye-surface, ivumela ukusebenza kokulayisha-gcina kwi-qubits zonke ezingokwemimiselo ngokuphathelele kwi-quantum teleportation kunye ne-unitaries ethile. Le graph ye-Tanner eyandisiweyo ikwanayo nokuphunyezwa kwisakhono sobubanzi obuyi-2 nge-edges kunye >( ). a b q L q R Methods c 50 A B Methods I-BB code ene-parameters [[ , , ]] igqithisa i- yee-qubits ezingokwemimiselo kwii- data qubits enikezela ngomgama wekhowudi , oko kuthetha ukuba nayiphi na impazamo ye-logical idlula ubuncinci ii-data qubits ezingama- . Sahlula i-data qubits eyi- kwiingxowa ( ) kunye ( ) eziyimilinganiselo ye- /2 nganye. Nawuphi na umsebenzi woku-check usebenza kwi-qubits ezintathu ukusuka kwi- ( ) kunye nezintathu ukusuka kwi- ( ). Ikhowudi ixhomekeke kwi- ama-qubits ancedisayo ukuqokelela ii-syndromes zempazamo. Sahlula ii-check qubits eyi- kwiingxowa ( ) kunye ( ) eziyimilinganiselo ye- /2 eququ igama le-syndromes ze- >kunye >ngokulandelelana. Ngokubambisana, i-encoding ixhomekeke kwi-2 ii-qubits zomzimba. I-rate yokugqithisa enet net yiyo ngoko = /(2 ). Ngokomzekelo, indlela ye-surface code eqhelekileyo igqithisa i- = 1 logical qubit kwi- = 2 data qubits yekhowudi yomgama- >kwaye isebenzisa ii-check qubits eyi- − 1 ngokulinganisa i-syndrome. I-rate yokugqithisa enet net yi- ≈ 1/(2 2), ekhawuleza ukuba ibe yinto engenakwenzeka njengoko kukufuneka ukhethe umgama omkhulu wekhowudi, ngenxa, umzekelo, iimpazamo zomzimba ezisondeleyo kwixabiso lemida. Ngokungafaniyo, iikhowudi ze-BB zine-rate yokugqithisa ≫ 1/ 2, bona iThebhile 1 yemizekelo yeekhowudi. Ngokwazi kwethu, zonke iikhowudi ezibonisiweyo kwiThebhile 1 >zintsha. Ikhowudi yomgama-12 [[144, 12, 12]] ingaba yeyona iyimfuneko kakhulu kwimiboniso ye-near-term, njengoko idibanisa umgama omkhulu kunye ne-rate ephezulu yokugqithisa enet = 1/24. Ukuthelekisa, i-surface code yomgama-11 ine-rate yokugqithisa enet = 1/241. Ngezantsi, sibonisa ukuba i-BB code yomgama-12 igqitha i-surface code yomgama-11 kwindawo efanelekileyo yeempazamo. 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 r r Ukuthintela ukuhlanganiswa
