Abalebebe: Neereja Sundaresan Theodore J. Yoder Youngseok Kim Muyuan Li Edward H. Chen Grace Harper Ted Thorbeck Andrew W. Cross Antonio D. Córcoles Maika Takita Mkonzi Kukonza kwa zolakwika za quantum kumapereka njira yoyenera yochitira masamu apamwamba a quantum. Ngakhale kuti ntchito zodziletsa za cholakwika zodziletsa sizikwaniritsidwa, kukula kwaposachedwa kwa zida zowongolera ndi hardware ya quantum kumathandiza kuwonetseredwa kwaukadaulo kwazofunikira pakukonza cholakwika. Pano, timachita kukonza cholakwika cha quantum pa ma qubits operekera ma super ovunguliridwa mu lattice ya hexagon yolemetsa. Timakonza ma logical qubits okhala ndi mtunda wa atatu ndipo timachita magawo angapo oyezetsa a syndrome osadziletsa omwe amalola kukonza chilichonse cholakwika chimodzi mu zigawozo. Pogwiritsa ntchito kuwongolera kwenikweni, timabwezeretsanso ma qubits a syndrome ndi mbendera motsatira gawo lililonse la extraction ya syndrome. Tikuwonetsa cholakwika cha logical chodalira decoder, ndi cholakwika chapakatikati cha logical pa muyeso wa syndrome mu Z (X) -basis wa ~0.040 (~0.088) ndi ~0.037 (~0.087) kwa ofanana ndi decoders omwe ali ndi chiwerengero chachikulu, motsatira, pa deta yosankhidwa ndi kutuluka. Chiyambi Zotsatira za masamu a quantum zimatha kukhala zolakwika, pakuyankha, chifukwa cha phokoso mu hardware. Kuti muchotse zolakwika zomwe zimachitika, ma code okonza cholakwika cha quantum (QEC) angagwiritsidwe ntchito kukonza zidziwitso za quantum mu malo otetezedwa, otetezedwa, kenako ndikukonza zolakwikazo mwachangu kuposa momwe zimakhalira zimathandizira masamu osadziletsa (FT). Kukwaniritsidwa kwathunthu kwa QEC kudzafuna: kukonzekera kwa mayiko amaganizo; kukwaniritsidwa kwa gulu la zigoro logwirizana, lomwe lingafune kukonzekera kwa mayiko aumishoni; kuyesedwa mobwerezabwereza kwa ma syndrome; ndi kumasulira kwa ma syndrome kuti mukonze zolakwika. Ngati zikuyenda bwino, mitengo yotsalira yolakwika iyenera kukhala yotsika kuposa mitengo yotsalira yochulukirapo, ndipo ichepe ndi kuwonjezeka kwa mtunda wa code mpaka kufika pamtengo wochepa. Kusankha code ya QEC kumafuna kuganizira za hardware yapansi ndi zake phokoso. Kwa lattice ya hexagon yolemetsa , ya ma qubits, ma code a subsystem QEC ndi osangalatsa chifukwa amagwirizana bwino ndi ma qubits okhala ndi kulumikizana kochepa. Ma code ena awonetsa chiyembekezo chifukwa cha gawo lawo lapamwamba la FT kapena chiwerengero chachikulu cha ma gates amaganizo. Ngakhale kuti malo awo ndi nthawi yovuta ikhoza kukhala chopinga chachikulu pakukula, pali njira zolimbikitsira zochepetsera zinthu zokwera mtengo kwambiri popindulitsa mtundu wina wa kuchepetsa cholakwika . 1 2 3 4 6 Mu njira yomasulira, kukonza kopambana kumadalira osati pa ntchito ya hardware ya quantum, komanso pakuyika kwa zida zowongolera zomwe zimagwiritsidwa ntchito posonkhanitsa ndi kukonza zidziwitso zachidule zomwe zimapezeka kuchokera kumiyeso ya syndrome. Pamenepa, kuyambitsa ma qubits a syndrome ndi mbendera kudzera mu kuwongolera kwenikweni pakati pa magawo oyezetsa kumatha kuthandiza kuchepetsa zolakwika. Pamlingo wosulira, pamene pali njira zina zochitira QEC mwachisawawa mkati mwa FT formalism , , mlingo umene ma syndrome olakwika amalandilidwa uyenera kufanana ndi nthawi yawo yokonza zidziwitso kuti asapewe kuchuluka kwa deta ya syndrome. Komanso, njira zina, ngati kugwiritsa ntchito umishoni wa T-gate , zimafuna kugwiritsa ntchito feed-forward yeniyeni. 7 8 9 Chifukwa chake, masomphenya a nthawi yayitali a QEC samapita pamtima pa cholinga chimodzi chomaliza koma ayenera kuwonedwa ngati njira yophatikizana ya ntchito zosiyanasiyana. Njira yoyeserera pakukula kwa ukadaulo uwu imaphatikizapo kuwonetseredwa kwa ntchitozi motsatira njira yoyamba kenako kuphatikiza kwawo pang'onopang'ono pambuyo pake, nthawi zonse pokhazikika kuwonjezereka kwa metrics awo. Zina mwazinthu izi zikuwonetsedwa m'mabuku ambiri aposachedwa pa machitidwe a quantum pa nsanja zosiyanasiyana, zomwe zawonetsa kapena kuyandikira zinthu zingapo za zomwe zikufunika kwa FT quantum computing. Makamaka, kukonzekera kwa mayiko a FT kwawonetsedwa pa ma ions , ma spin a nyukiliya mu diamondi ndi ma qubits operekera ma super . Magawo obwerezabwereza a syndrome extraction awonetsedwa mu ma qubits a super mu ma code ochepa owonetsera zolakwika , , kuphatikiza kukonza cholakwika pang'ono komanso gulu logwirizana (ngakhale kuti si FT) la ma gates amodzi a qubit . Chiwonetsero cha FT cha gulu logwirizana pa ma qubits awiri a logical chidalimbikitsidwa posachedwapa m'ma ions . M'dera lokonza cholakwika, pakhala pali zochitika zaposachedwa za code ya mtunda-3 pamagulu operekera ma super okhala ndi kumasulira ndi post-selection , komanso kukhazikitsidwa kwa FT kwa kukumbukira quantum kodzitchinjiriza pogwiritsa ntchito code ya mtundu ndi FT state preparation, ntchito, ndi muyeso, kuphatikiza zolemba zake, za logical state mu Bacon-Shor code m'ma ions , . 10 11 12 13 14 15 16 17 18 19 20 20 21 Pano timaphatikiza luso lowongolera kwenikweni pa dongosolo la qubit la super ndi njira yomasulira yowonjezereka yomwe sinayesedwepo poyesera kuti tiwonjezere kuchuluka kwa mayiko. Tikuwonetsa zida izi ngati gawo la ntchito ya FT ya code ya subsystem , code ya hexagon yolemetsa , pa purosesa ya quantum ya super. Chofunika pakuwonjezera kukhazikitsidwa kwa code iyi kukhala kotetezedwa ndi cholakwika ndi ma qubits a mbendera omwe, akaipeza kuti siili, amawonetsa zolakwika za zigawo kwa decoder. Potsatira kubwezeretsanso ma qubits a mbendera ndi syndrome pambuyo pa gawo lililonse loyezetsa syndrome, timateteza dongosolo lathu motsutsana ndi zolakwika zomwe zimachokera ku kusagwirizana kwa phokoso lomwe limapezeka mu mpweya. Tikuwonjezeranso njira zodziwika za kumasulira ndikukulitsa malingaliro a kumasulira kuti mulowetse malingaliro owonjezereka , , . 22 1 15 4 23 24 Zotsatira Code ya Hexagon Yolemetsa ndi Zigawo Zazigawo Zambiri Code ya hexagon yolemetsa yomwe tikuiganizira ndi code ya ma qubits 9 ikukonza ma logical qubits 1 okhala ndi mtunda wa 3 . Magulu a Z ndi X gauge (onani Fig. 1a) ndi stabilizer amapangidwa ndi 1 Magulu a stabilizer ndi malo a magulu a gauge motsatira . Zikutanthauza kuti ma stabilizers, ngati zinthu za ma operators a gauge, amatha kuwerengedwa kuchokera kumiyeso ya ma operators a gauge okha. Ma operators achinyengo amatha kusankhidwa kukhala XL = X1X2X3 ndi ZL = Z1Z3Z7. Z (buluu) ndi X (wobiriwira) gauge operators (zigawo. (1) ndi (2)) zalembedwa pa ma qubits 23 ofunika okhala ndi code ya hexagon yolemetsa ya mtunda wa 3. Code qubits (Q1 - Q9) akuwonetsedwa mu yellow, syndrome qubits (Q17, Q19, Q20, Q22) ogwiritsidwa ntchito kwa Z stabilizers mu buluu, ndi mbendera qubits ndi syndromes zimagwiritsidwa ntchito kwa X stabilizers mu white. Dongosolo ndi njira imene CX gates amagwiritsidwa ntchito mkati mwa gawo lililonse (0 mpaka 4) zikuwonetsedwa ndi mivi yowerengeredwa. Popeza nthawi ya chipata chilichonse cha ma qubits awiri imasiyana, kukonza kwa chipata chomaliza kumatsimikiziridwa ndi njira yokonza chipata yodziwika bwino (as-late-as-possible); pambuyo pake, dynamical decoupling imawonjezeredwa ku data qubits kumene nthawi imalola. Miyeso ndi kubwezeretsanso ma operations amachotsedwa ku ma operations ena a chipata ndi mipata kuti mulole kuwonjezera kophatikizana kwa dynamical decoupling kwa ma data qubits osagwira. Masitepe otanthauzira kwa magawo atatu a ( ) Z ndi ( ) X miyeso ya stabilizer yokhala ndi phokoso la zigawo imalola kukonza Z ndi X zolakwika, motsatira. Ma nodes a buluu ndi ofiira m'maganizo amafanana ndi ma syndrome osiyanasiyana, pamene ma nodes akuda ndi malire. Mipata imatsegulira njira zosiyanasiyana zomwe zolakwika zimachitika mu zigawozo monga momwe zalembedwera m'nkhaniyi. Ma nodes alembedwa ndi mtundu wa muyeso wa stabilizer (Z kapena X), pamodzi ndi chizindikiro chokhazikika cha stabilizer, ndi zolembera zapamwamba kusonyeza gawo. Mipata yakuda, yochokera ku Pauli Y zolakwika pa code qubits (ndipo motero ndi 2 okha), imalumikiza maganizo awiri mu ndi , koma sizigwiritsidwa ntchito mu matching decoder. Ma hyperedges a kukula kwa 4, omwe sagwiritsidwa ntchito ndi matching, koma amagwiritsidwa ntchito mu maximum likelihood decoder. Mitundu ndi yongonena za kufotokoza. Kusintha chilichonse mu nthawi ndi gawo limodzi kumaperekanso hyperedge yogwirizana (ndi kusintha pang'ono pamalire a nthawi). Komanso sizikuwonetsedwa ndi ma hyperedges a kukula kwa 3. a c d e c d f Pano timayang'ana kwambiri pa zigawo za FT zenizeni, zambiri mwa njira zathu zitha kugwiritsidwa ntchito ndi ma code ndi zigawo zosiyanasiyana. Magawo awiri apansi, akuwonetsedwa mu Fig. 1b, amapangidwa kuti ayese ma Z-gauge operators. -gauge. Z-gauge measurement circuit imapezanso zidziwitso zofunika mwa kuyeza ma flag qubits. X Timakonzekera mayiko a code mu logical () state mwa kukonzekera ma qubits asanu ndi anayi mu () state ndikuyeza Z-gauge (X-gauge). Kenako timachita magawo r a syndrome measurement, kumene gawo limaphatikizapo Z-gauge measurement kenako X-gauge measurement (motsatira, X-gauge kenako Z-gauge). Potsiriza, timawerenga ma qubits asanu ndi anayi onse mu Z (X) basis. Timachita mayesero omwewo kwa mayiko oyambirira achinyengo ndi komanso, mwa kungoyambitsa ma qubits asanu ndi anayi mu ndi motsatira. Ma Algorithms Otanthauzira Mu malo a FT quantum computing, decoder ndi algorithm yomwe imalandira kuyeza kwa syndrome kuchokera ku code yokonza cholakwika ndikupereka kukonza kwa ma qubits kapena deta yoyezetsa. M'chigawo chino tikuwonetsa ma algorithms awiri otanthauzira: perfect matching decoding ndi maximum likelihood decoding. The decoding hypergraph ndi chidule cha zidziwitso zomwe zimasonkhanitsidwa ndi FT circuit ndikuperekedwa kwa algorithm yomasulira. Imakhala ndi gulu la vertices, kapena zochitika zosavomerezeka ndi zolakwika, V , ndi gulu la hyperedges E , zomwe zimalimbikitsa kulumikizana pakati pazochitika zomwe zimayambitsidwa ndi zolakwika mu dera. Fig. 1c-f ikuwonetsa magawo a decoding hypergraph kwa mayesero athu. 15 Kupanga decoding hypergraph kwa stabilizer circuits ndi Pauli noise kumatha kuchitidwa pogwiritsa ntchito standard Gottesman-Knill simulations kapena njira zina za Pauli tracing . Choyamba, chochitika chosavomerezeka ndi cholakwika chimapangidwa kwa muyeso uliwonse umene uli wotsimikizika mu dera lopanda cholakwa. Muyeso wotsimikizika M ndi muyeso uliwonse amene chotsatira chake m {0,1} chingatsimikiziridwe powonjezera motsatira ma awiri zotsatira za mlingo wa mlingo wa magawo am'mbuyomu S . Ndiye kuti, kwa dera lopanda cholakwa, , kumene gulu la S chingapezeke ndi simulation ya dera. Khazikitsani mtengo wa chochitika chosavomerezeka ndi cholakwika mpaka m - FM(mod2), chimene chili chopanda (chotchedwanso chopanda tanthauzo) popanda zolakwika. Chifukwa chake, kuwona chochitika chosavomerezeka chopanda mtengo (chotchedwanso chopanda tanthauzo) kumasonyeza kuti dera lidalandira zolakwika zosachepera imodzi. Mu zigawo zathu, zochitika zosavomerezeka ndi cholakwika ndi kuyeza kwa mbendera qubit kapena kusiyana kwa miyeso yotsatizana ya stabilizer yomweyo (yomwe imatchedwanso ma syndrome osiyanasiyana). 25 26 Kenako, hyperedges amawonjezeredwa poganizira zolakwika za dera. Mtundu wathu uli ndi mwayi wa cholakwika pC pa gawo lililonse la zigawo zingapo Pano timasiyanitsa ntchito ya identity id pa ma qubits panthawi imene ma qubits ena akudutsa ma gates a unitary, ndi ntchito ya identity idm pa ma qubits pamene ena akudutsa muyeso ndi kubwezeretsanso. Timabwezeretsa ma qubits pambuyo powatenga, pamene timayambitsa ma qubits omwe sanagwiritsidwe ntchito mu mayesero kale. Pomaliza cx ndi controlled-not gate, h ndi Hadamard gate, ndi x, y, z ndi Pauli gates. (Onani Njira "IBM_Peekskill ndi zambiri zachiyesero" kuti mumve zambiri). Mitengo ya ziwerengero ya pC ili pamndandanda mu Njira "IBM_Peekskill ndi zambiri zachiyesero". Mtundu wathu wa cholakwika ndi circuit depolarizing noise. Kwa zolakwika zoyambira ndi kubwezeretsanso, Pauli X imagwiritsidwa ntchito ndi mwayi woyenerera pinich ndi presetch pambuyo pokonzekera koyambirira. Pamene cholakwika chimodzi chichitika mu dera, chimayambitsa gawo la zochitika zosavomerezeka ndi cholakwika kuti zikhale zosavomerezeka. Gulu ili la zochitika zosavomerezeka ndi cholakwika limakhala hyperedge. Gulu la hyperedges onse ndi E . Zolakwika ziwiri zosiyanasiyana zikhoza kupangitsa hyperedge yomweyo, kotero hyperedge iliyonse ikhoza kuonedwa ngati ikuyimira gulu la zolakwika, limene chilichonse chimayambitsa zochitika mu hyperedge kukhala zosavomerezeka. Zogwirizana ndi hyperedge iliyonse ndi mwayi, umene, poyamba, ndi chiwerengero cha mwayi wa zolakwika mu gulu. Cholakwika chimathanso kuyambitsa cholakwika, chomwe, chikafika kumapeto kwa dera, chimatsutsana ndi chimodzi kapena zingapo mwa ma operators achinyengo a code, kufuna kukonza kwachinyengo. Tikupeza kuti chololeka kuti code ili ndi ma logical qubits k ndi maziko a 2k logical operators, koma dziwani kuti k = 1 kwa code ya hexagon yolemetsa yogwiritsidwa ntchito poyesera. Titha kusunga zomwe logical operators zimagwirizana ndi cholakwika pogwiritsa ntchito vector kuchokera ku . Motero, hyperedge iliyonse h alinso zilembedwa ndi imodzi mwamavvelu awa , yotchedwa logical label. Dziwani kuti ngati code ili ndi mtunda wosachepera atatu, hyperedge iliyonse ili ndi logical label yapadera. Pomaliza, timadziwa kuti decoder algorithm ikhoza kusankha kuphatikiza decoding hypergraph m'njira zosiyanasiyana. Njira imodzi imene nthawi zonse timagwiritsa ntchito pano ndi njira ya deflagging. Miyezo ya mbendera kuchokera ku qubits 16, 18, 21, 23 imangosiyidwa popanda kukonza kulikonse kugwiritsidwa ntchito. Ngati mbendera 11 siili yodziwikiratu ndipo 12 ili yodziwikiratu, gwiritsani ntchito Z kwa 2. Ngati 12 ndi yodziwikiratu ndipo 11 ili yodziwikiratu, gwiritsani ntchito Z kwa qubit 6. Ngati mbendera 13 ndi yodziwikiratu ndipo 14 ili yodziwikiratu, gwiritsani ntchito Z kwa qubit 4. Ngati 14 ili yodziwikiratu ndipo 13 ili yodziwikiratu, gwiritsani ntchito Z kwa qubit 8. Onani ref. 15 kuti mumve zambiri za chifukwa chake izi ndizokwanira pakutetezedwa ndi cholakwika. Izi zikutanthauza kuti m'malo mofotokozera zochitika zosavomerezeka kuchokera kumiyeso ya mbendera molunjika, timakonza data pogwiritsa ntchito zidziwitso za mbendera kuti tigwire ntchito ma corrections a virtual Pauli Z ndikusintha zochitika zotsatira zosavomerezeka motsatira. Hyperedges za deflagged hypergraph zitha kupezeka kudzera mu stabilizer simulation kuphatikiza Z corrections. Lolani r kuyimira chiwerengero cha magawo. Pambuyo pa deflagging, kukula kwa gulu V kwa Z (resp. X basis) experiments ndi |V| = 6r + 2 (resp. 6r + 4), chifukwa cha kuyeza ma stabilizers asanu ndi limodzi pa gawo komanso kukhala ndi awiri (resp. anayi) oyambirira zochitika zosavomerezeka ndi cholakwika pambuyo pa kukonzekera kwa state. Kukula kwa E ndi chimodzimodzi |E| = 60r - 13 (resp. 60r - 1) kwa r > 0. Pogwiritsa ntchito zolakwika za X ndi Z mosiyana, vuto la kupeza kukonza kwa cholakwika chochepa kwambiri cha surface code litha kuchepetsedwa mpaka kupeza machulukidwe apamwamba kwambiri pamalingaliro. Matching decoders amapitabe kufufuza chifukwa cha pragmatism yawo ndi kufalikira kwawo , . M'chigawo chino, tikuwonetsa matching decoder ya code ya hexagon yolemetsa ya mtunda wa 3. 27 28 29 Maganizo otanthauzira, amodzi kwa X-errors (Fig. 1c) ndi amodzi kwa Z-errors (Fig. 1d), pakukhathamiritsa machulukidwe apamwamba kwambiri kwenikweni ndi magawo apansi a decoding hypergraph mu chigawo chapitachi. Tiyang'ana apa pa lingaliro lojambulira zolakwika za X, popeza lingaliro la Z-error limafanana. Pamenepa, kuchokera ku decoding hypergraph timasunga ma nodes VZ omwe amayenderana ndi (kusiyana kwa motsatizana) Z-stabilizer measurements ndi mipata (ndiye kuti, hyperedges okhala ndi awiri) pakati pawo. Kuphatikiza apo, malire vertex b amapangidwa, ndipo hyperedges za kukula kwa chimodzi mwa mawonekedwe {v} ndi v ∈ VZ, zimayimiridwa powonjezera mipata {v, b}. Ma mipata onse mu X-error graph amalandira mwayi ndi mayina achinyengo kuchokera ku hyperedges zawo motsatira (onani Table 1 kuti mumve zambiri za X ndi Z-error edge kwa 2-round experiment). Algorithm ya machulukidwe apamwamba kwambiri imatenga lingaliro lokhala ndi mipata yolinganizidwa ndi gulu la ma nodes lolongosoka lokha, ndipo imapereka gulu la mipata mu lingaliro limene limalumikiza ma nodes olongosoka onse awiriawiri ndipo ali ndi kulemera kwakung'ono kwambiri pakati pa magulu onse oterowo a mipata. Pamenepa, ma nodes olongosoka ndi zochitika zosavomerezeka ndi cholakwika (ngati pali chiwerengero chachilendo, malire node alinso olongosoka), ndipo kulemera kwa mipata kumakhala koyenera kuti zonse zikhale umodzi (njira yofananira) kapena kuyikidwa ngati , kumene pe ndi mwayi wa mpata (njira yofotokozera). Chisankho chomaliza chikhoza kutanthauza kuti kulemera konse kwa gulu la mipata ndi chidziwitso chawo chawo chawo, ndipo machulukidwe apamwamba kwambiri amayesa kuwonjezera chidziwitsochi pa mipata mu lingaliro. Popeza tapatsidwa machulukidwe apamwamba kwambiri, tingagwiritse ntchito mayina achinyengo a mipata mu machulukidwewo kuti titsimikizire kukonza ku dongosolo lachinyengo. M'malo mwake, X-error (Z-error) graph ya matching decoder imakonzedwa kuti mpata uliwonse ukhoza kugwirizanitsidwa ndi qubit ya code (kapena muyeso wolakwika), kotero kuti kuphatikiza mpata mu machulukidwe kumatanthauza X (Z) correction iyenera kugwiritsidwa ntchito pa qubit yolingana. Maximum likelihood decoding (MLD) ndi njira yabwino, ngakhale yosakwanira, yomasulira ma code okonza zolakwika za quantum. M'lingaliro lake loyambirira, MLD idagwiritsidwa ntchito pamitundu ya phokoso yofotokozera pomwe zolakwika zimachitika nthawi isanayezetsere ma syndrome , . Izi, ndithudi, zimanyalanyaza nkhani yochuluka kwambiri imene zolakwika zingafalikire kudutsa zigawo za muyeso wa syndrome. Posachedwapa, MLD yakulitsidwa kuti iphatikize phokoso la dera 24 30
