Ababhali: Sergey Bravyi Andrew W. Cross Jay M. Gambetta Dmitri Maslov Patrick Rall Theodore J. Yoder Isishwethiso esifutshane Ukuqokelelana kweempazamo zomzimba , , kuthintela ukwenziwa kwe-algorithms ezinkulu kwii-computer zamanje ze-quantum. Ukuphuculwa kweempazamo ze-quantum kuthembisa isisombululo ngokubeka iilokhi zeqibha kwi-n yeembumba zomzimba, ukuze iimpazamo zomzimba zicofwe ngokwaneleyo ukuze kukwazi ukusebenza ubalo olufunwayo ngobunyaniso obuvumelekileyo. Ukuphuculwa kweempazamo ze-quantum kuyenzeka xa izinga lempazamo yomzimba lingaphantsi komgangatho othile oxhomekeke kukhetho lwe-quantum code, isekethe yokulinganisa i-syndrome kunye ne-algorithm yokuchaza . Siyazisa inkqubo yokubuyisela impazamo ye-quantum ukusuka ekuqaleni ukuya ekugqibeleni enika inkumbulo ekhusela impazamo esekelwe kusapho lwee-low-density parity-check codes . Indlela yethu ifumana umda we-0.7% wokubuyisela impazamo , , , enoba yeyona code ibalulekileyo kwiminyaka engama-20 yokubuyisela impazamo. Umjikelo wokulinganisa i-syndrome we-code enobude obungu-n kwintsapho yethu ufuna i-ancillary qubits ezingama-n kunye nesekethe enobude obuyi-8 enee-CNOT gates, ukubekwa kwee-qubits kunye nemilinganiselo. Ukuqhagamshelana kwe-qubit okufunekayo yigraphu eyi-degree-6 eyenziwe ngamaphepha amabini angenaso isiphelo esiqhelekileyo. Ngokukodwa, sibonisa ukuba i-12 logical qubits zingagcinwa kangange-1 yezigidi zemijikelo ye-syndrome kusetyenziswa ii-qubits ezingama-288 zomzimba, ngokuchasene ne-surface code iya kufuna ii-qubits ezingama-3,000 zomzimba ukufezekisa le ntsebenzo. Izinto esizifumanileyo zizisa imiboniso yenkumbulo ye-quantum engenazintlawulo iphantsi ye-fault-tolerant kwii-processors zamanje ze-quantum. 1 2 3 4 k 5 6 7 8 9 10 Iimfundo eziphambili I-Quantum computing itsale umdla ngenxa yayo iyakwazi ukunika izisombululo ezikhawulezayo kwiingxaki ezithile zokubala xa kuthelekiswa ne-algorithms yakutshanje ye-classical . Kukholelwa ukuba i-quantum computer esebenza kwaye iyasebenza inokunceda ukusombulula iingxaki zokubala kwiindawo ezinje ngokufunyaniswa kwenzululwazi, uphando lwezinto, amayeza kunye noyilo lweziyobisi, ukubalula nje ezimbalwa , , , . 5 11 12 13 14 Isithintelo esikhulu ekwakheni i-quantum computer kukuthotywa kolwazi lwe-quantum, ngenxa yezizathu ezahlukeneyo zengxolo ezichaphazela yona. Njengoko ukwahlula i-quantum computer kwiziphumo zangaphandle kunye nokuyilawula ukuze kunikezelwe ubale obufunekayo kuyaphikisana, ingxolo ibonakala ingenakuphetshwa. Iimfuyo zengxolo zibandakanya ukungapheleli kwiimbumba, izinto ezisetyenzisiweyo, izixhobo zokulawula, ukulungiswa kwemeko kunye neziphumo zemilinganiselo kunye neendlela ezahlukenyo zangaphandle ezisusela kwizinto ezenziwe ngabantu ezifana nemisinga yombane, ukuya kwezo zingenakuphikiswa kwindalo iphela, ezinjengezikrelekrele zobukhulu. Jonga kwi-ref. ngokufingqa. Ngelixa ezinye iimfuyo zengxolo zinokupheliswa ngolawulo olungcono , izinto kunye nokukhuselwa , , , ezinye izizathu ezininzi zibonakala zinzima, ukuba kunokwenzeka, ukususa. Uhlobo lokugqibela lunokubandakanya ukukhutshwa okuzenzekelayo nokuncedisiweyo kwi-ions ezibanjisiweyo , , kunye nokusebenzisana kunye ne-bath ( Purcell effect) kwiiseti zesekethe ze-superconducting—ezibandakanya zombini iiteknoloji ze-quantum eziphambili. Ngoko ke, ukubuyisela impazamo kufuneka kube yimfuneko ebalulekileyo ekwakheni i-quantum computer esebenza kwaye iyasebenza. 15 16 17 18 19 20 1 2 3 Ubume bokubuyisela impazamo ye-quantum buqatshelwe kakuhle . Ukubeka i-logical qubit ngokungafunekiyo kwiimbumba ezininzi zomzimba kwenza kube nokwenzeka ukuxilonga kunye nokulungisa iimpazamo ngokuphinda imilinganiselo ye-syndrome ye-parity-check operators. Nangona kunjalo, ukubuyisela impazamo kunokuba luncedo kuphela ukuba izinga lempazamo yehardware lingaphantsi komda othile oxhomekeke kwinkqubo ethile yokubuyisela impazamo. Iziphakamiso zokuqala zokubuyisela impazamo ye-quantum, ezinjenge-concatenated codes , , , zigxile ekubonakaliseni ubume bokubuyisela impazamo. Njengoko ukuqonda ukubuyisela impazamo ye-quantum kunye namandla eeteknoloji ze-quantum kwandile, ingqwalaselo yafudukela ekufumaneni iinkqubo zokubuyisela impazamo ze-quantum. Oku kukhokelele kuphuhliso lwe-surface code , , , inikezela ngomda omkhulu wokubuyisela impazamo osondele ku-1%, ii-algorithms zokuchaza ezikhawulezayo kunye nokuhambelana nee-processors zamanje ze-quantum ezixhomekeke ku-two-dimensional (2D) square lattice qubit connectivity. Iimzekelo ezincinci ze-surface code enye i-logical qubit sele ibonakaliswe ngokwezinto ezithile ngamaqela ahlukeneyo , , , , . Nangona kunjalo, ukwandisa i-surface code ukuya kwi-100 okanye nangaphezulu ii-logical qubits kuya kuba yintlawulo enkulu ngenxa yokungafanelei kwayo kwe-encoding. Oku kuye kwakhuthaza umdla kwi-quantum codes ezaziwa ngokubanzi ezifana nee-low-density parity-check (LDPC) codes . Ukuqhubela phambili kwamuva nje kufundo lwee-LDPC codes kubonisa ukuba zinokufumana i-fault tolerance ye-quantum kunye nokufanelela okungaphezulu kokubekwa . Apha, sigxile kufundo lwee-LDPC codes, njengoko injongo yethu kukufumana i-quantum error correction codes kunye neenkqubo ezifanelekileyo kwaye zinokuboniswa ngokwezinto, ngokunikezelweyo kwimilinganiselo yeetheminali ze-quantum computing technologies. 4 21 22 23 7 8 9 10 24 25 26 27 28 6 29 I-quantum error correcting code ingeyawo uhlobo lwe-LDPC ukuba bonke aba-operators bokukhangela be-code benza kuphela kwiimbumba ezimbalwa kwaye yonke i-qubit iyabandakanyeka kwizikhangeli ezimbalwa. Iindidi ezininzi zee-LDPC codes ziye zaphaqama kutshanje kubandakanya i-hyperbolic surface codes , , , i-hypergraph product , i-balanced product codes , i-two-block codes esekelwe kwi-finite groups , , , kunye nee-quantum Tanner codes , . Ezi zokugqibela zibonisiwe , ukuba ziya kuba ‘zilungile’ kwimida ye-encoding rate kunye nomlinganiselo omkhulu: iparameter ebalawula inani leempazamo ezinokulungiswa. Ngokungafaniyo, i-surface code inomlinganiselo wokubeka ongagqibekanga kunye nomlinganiselo wesikwere. Ukubuyisela i-surface code nge-high-rate, high-distance LDPC code kungaba neziphumo ezinkulu kwezinto. Okokuqala, i-fault-tolerance overhead (umlinganiselo phakathi kwenani lee-physical kunye nee-logical qubits) ungancitshiswa kakhulu. Okwesibini, i-high-distance codes ibonisa ukuhla okubukhali kwinqanaba lempazamo ye-logical: njengoko ubungqongqo bempazamo yomzimba bugqitha kumda, ubungakanani bokucudiswa kwempazamo obufumaneka yi-code bunganda ngemiyalelo eyongezelelekileyo nangona ngokusasazwa okuncinci kobungqongqo bomzimba. Esi sici senza i-high-distance LDPC codes zitsalele kwiimboniso zexesha elizayo ezinokusebenza kwindawo ekufutshane nomda. 30 31 32 33 34 35 36 37 38 39 40 39 40 Apha sibonisa imizekelo ethile ye-high-rate LDPC codes enee-hundreds ezimbalwa ze-physical qubits ezixhotyiswe ngesekethe yokulinganisa i-syndrome enobude obufutshane, i-algorithm yokuchaza efanelekileyo kunye nenkqubo ye-fault-tolerant yokujongana nee-logical qubits ezizodwa. Ezi codes zibonisa umda wokubuyisela impazamo osondele ku-0.7%, zibonisa intsebenzo egqwesileyo kwindawo ekufutshane nomda kwaye zinikezela ngoku-10x ukuncitshiswa kwe-encoding overhead xa kuthelekiswa ne-surface code. Iimfuno zehardware zokubonisa iinkqubo zethu zokubuyisela impazamo azinzima, njengoko i-qubit nganye yomzimba idityaniswa nge-two-qubit gates kunye nezinye iimbumba ezintandathu. Nangona i-qubit connectivity graph ayikho kwi-2D grid, ingahlulwa ibe ngamaphepha amabini angenaso isiphelo esiqhelekileyo. Njengoko sibonisa ngezantsi, olu qhagamshelwano lwee-qubits lufanelekile kwii-architectures ezisekelwe kwi-superconducting qubits. Iikhowudi zethu ziyingqokelela yee-bicycle codes ezaphanza uMacKay et al. kwaye zafunyaniswa ngokubanzi kwi-refs. , , . Sibizile iikhowudi zethu ze-bivariate bicycle (BB) kuba zisekelwe kwi-bivariate polynomials, njengoko kuchaziwe kwi-Methods. Ezi zi-stabilizer codes kuhlobo lwe-Calderbank–Shor–Steane (CSS) , ezinokuchazwa yi-collection ye-six-qubit check (stabilizer) operators eziquka i-Pauli kunye ne . Kwinqanaba eliphezulu, i-BB code ifana ne-two-dimensional toric code . Ngokukodwa, iimbumba zomzimba ze-BB code zinokubekwa kwisithintelo sobubini esine-periodic boundary conditions ukuze zonke ii-check operators zifunyanwe kwisibini esinye se- kunye ne- checks ngokusasaza kunye ne-vertical shifts yesithintelo. Nangona kunjalo, ngokungafaniyo ne-plaquette kunye ne-vertex stabilizers ezichaza i-toric code, ii-check operators ze-BB codes azikho kwi-geometrically local. Ngaphezu koko, zonke i-check zisebenza kwiimbumba ezithandathu endaweni ezine. Siza kuchaza i-code nge-Tanner graph ukuze yonke i-vertex ye- imele i-data qubit okanye i-check operator. I-check vertex kunye ne-data vertex zidityaniswe negama ukuba i- th check operator yenza ngokungafaniyo kwi- th data qubit (ngokusasaza i-Pauli okanye i- ). Jonga uMfanekiso. ngeemizekelo ye-Tanner graphs ye-surface kunye nee-BB codes, ngokulandelelana. I-Tanner graph yayo nayiphi na i-BB code inobubanzi obuyi-degree six kunye ne-graph thickness elingana no-two, oko kuthetha ukuba ingahlulwa ibe ngamaphepha amabini angenaso isiphelo esiqhelekileyo ( ). Ububanzi obuyi-Thickness-2 qubit connectivity bufanelekile kwi-superconducting qubits ezidibene ne-microwave resonators. Ngokomzekelo, amaphepha amabini angenaso isiphelo abagqabantshi kunye neentambo zabo zolawulo zingabotshelelwa phezulu nasemva kwesithende kwisiphaluka-bhodi esingama-qubits, kwaye iziphaluka zombini zidityaniswe. 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 ye-BB code enee-parameters [] efakwe kwisithintelo. Nayiphi na igama ye-Tanner graph idibanisa i-data kunye ne-check vertex. Iimbumba zedatha ezihambelana nezigaba ( ) kunye ne ( ) ziboniswa zii-circles eziluhlaza okwesibhakabhaka kunye nezomvundululo. Yonke i-vertex inee-edges ezintandathu ezihambelanayo kubandakanya i-edges ezine ezifutshane (ezikhombisa umntla, umzantsi, umntla nasentshona) kunye nee-edges ezimbini ezide. Sibonisa kuphela ii-edges ezimbalwa ezide ukuze kuxakeke. Ii-edges ezifilishelweyo nezolayini zibonisa amaphepha amabini angenaso isiphelo adibanisa i-Tanner graph, jonga kwi-Methods. , Iskrach ye-Tanner graph extension yokulinganisa kunye ne ngokulandela i-ref. , ehlanganiswa kwi-surface code. I-ancilla ehambelana ne-measurement ingadityaniswa kwi-surface code, ivumela ukusebenza kokuthwala-gcina kuzo zonke ii-logical qubits ngendlela ye-quantum teleportation kunye nezinye ii-unitaries ezilawulwayo. Le Tanner graph eyandisiweyo nayo iyasebenza kwisithintelo esiyi-thickness-2 ngokusebenzisa ii-edges ze-A kunye ne-B (jonga kwi-Methods). a b q L q R c 50 I-BB code enee-parameters [[ , , ]] ibeka i-k logical qubits kwi-n data qubits inikezela nge-code distance , oko kuthetha ukuba nayiphi na impazamo ye-logical ihlanganisa ubuncinci ii-d data qubits. Sahlula ii-n data qubits kwii-registers ( ) kunye ne ( ) yobukhulu obuyi-n/2 nganye. Lonke i-check lisebenza kwiimbumba ezintathu ukusuka kwi-q(L) kunye nezintathu ukusuka kwi-q(R). I-code ixhomekeke kwii-ancillary check qubits ezingama-n ukulinganisa i-syndrome yempazamo. Sahlula ii-check qubits ezingama-n kwii-registers ( ) kunye ne ( ) yobukhulu obuyi-n/2 ezihlanganisa ii-syndromes zeentlobo ze-X kunye ne-Z, ngokulandelelana. Ngokubanzi, i-encoding ixhomekeke kuma-2n e-physical qubits. I-net encoding rate ke ngoko yi-r = k/(2n). Ngokomzekelo, i-standard surface code architecture ibeka i-k = 1 logical qubit kwi-n = d2 data qubits kwi-code distance-d kwaye isebenzisa ii-check qubits ezingama-n − 1 kuzo zonke imilinganiselo ye-syndrome. I-net encoding rate yi-r ≈ 1/(2d2), nto leyo ngokukhawuleza iba yinto engenakwenzeka njengoko umntu unyanzelekile ukuba akhethe i-distance enkulu ye-code, ngenxa, ngokomzekelo, iimpazamo zomzimba ezikufutshane nomda. Ngokungafaniyo, i-BB codes inomlinganiselo wokubeka i-r ≫ 1/d2, jonga Ithebula ngeemizekelo ze-code. Kangangoko sisazi, zonke iikhowudi eziboniswe kwiTabelle zintsha. I-distance-12 code [] ingaba yeyona inomdla kakhulu kwiimboniso zexesha elizayo, njengoko idibanisa i-distance enkulu kunye ne-net encoding rate ephezulu r = 1/24. Ukuthelekisa, i-distance-11 surface code inenqanaba lokubeka i-r = 1/241. Ngaphantsi, sibonisa ukuba i-distance-12 BB code igqitha i-distance-11 surface code kwindawo efanelekileyo yobungqongqo bempazamo. n k d d q L q R q X q Z 1 1 Ukuthintela ukuqokelelana kweempazamo kufuneka kukwazi ukulinganisa i-syndrome yempazamo ngokwaneleyo rhoqo. Oku kufezekiswa yiseti ye-syndrome yokulinganisa ejongana ne-data qubits kwinkxaso yalo naliphi na i-check operator kunye ne-ancillary qubit ehambelanayo ngoluhlu lwee-CNOT gates. Emva koko iimbumba zokukhangela zilinganiswa zibonise ixabiso le-syndrome yempazamo. Ixesha elithatha ukwenza isekethe ye-syndrome yokulinganisa lilingana nobubanzi bayo: inani lamalaka e-gate enziwe ngama-CNOTs angadibanisi. Njengoko iimpazamo ezintsha ziqhubeka zenzeka ngelixa isekethe ye-syndrome yokulinganisa isenziwa, ububanzi bayo kufuneka buncitshiswe. Umjikelo opheleleyo wokulinganisa i-syndrome we-BB code uchaziwe kuMfanekiso. . Umjikelo we-syndrome ufuna kuphela iilayini ezisixhenxe ze-CNOTs kungakhathaliseki ubude be-code. Iimbumba zokukhangela ziqalwa kwaye zilinganiswe ekuqaleni nasemva komjikelo we-syndrome ngokulandelelana (jonga kwi-Methods ngenani elingakumbi). Isiketi sijonga isasazeko sokujikeleza okujikelezayo se-code esekelwe kuyo. 2 Umjikelo opheleleyo wemilinganiselo ye-syndrome esebenzisa iilayini ezisixhenxe ze-CNOTs. Sinikezela ngombono ongagqibelelwanga wesekethe obandakanya kuphela i-qubit enye yedatha ukusuka kulo naliphi na igaba ( ) kunye ne q L q
