Abachishanya:** Sergey Bravyi Andrew W. Cross Jay M. Gambetta Dmitri Maslov Patrick Rall Theodore J. Yoder Abstrak Kugundizana kwa zolakwika zakuthupi , , kumalepheretsa kuchitidwa kwa ma algorithm akuluakulu pamakompyuta quantum apano. Kukonza zolakwika za quantum kumalonjeza yankho polemba ma qubits achinsinsi kukhala chiwerengero chachikulu cha ma qubits akuthupi, kotero kuti zolakwika zakuthupi zimachepetsedwa mokwanira kuti zitheke kuchita ntchito yofunikira ndi kukhulupirika kololeka. Kukonza zolakwika za quantum kumakhala kotheka makamaka pamene chiwerengero cha zolakwika zakuthupi chili pansi pa mtengo wololeka womwe umadalira kusankha kwa code ya quantum, dera lozindikiritsa ndi algorithm yotsitsa . Tikuwonetsa njira yokonza zolakwika za quantum yochokera kumapeto mpaka kumapeto yomwe imagwiritsa ntchito kukumbukira kololeka molingana ndi banja la low-density parity-check codes . Njira yathu imapeza chololeka cha zolakwika cha 0.7% pamtengo wamba wamtengo wapakompyuta, wofanana ndi surface code , , , yomwe kwa zaka 20 inali code yoyamba potengera chololeka cha zolakwika. Ntchito yozindikiritsa chizindikiro cha ma code a kutalika- m'banja lathu imafuna ma qubits owonjezera ndi dera la kuya-8 ndi magulu a CNOT gates, kuyambitsa ma qubits ndi miyeso. Kufunikira kwa kulumikizana kwa qubit ndi graph ya digirii-6 yopangidwa ndi magawo awiri osalumikizana ndi magawo awiri. Makamaka, tikuwonetsa kuti ma qubits 12 achinsinsi amatha kusungidwa kwa pafupifupi maulendo a chizindikiro miliyoni imodzi pogwiritsa ntchito ma qubits 288 akuthupi, pamene surface code ingafune ma qubits pafupifupi 3,000 kuti athetse magwiridwe antchito awa. Zomwe tpeza zimabweretsa mawonetsero a kukumbukira kwa quantum kololeka ndi ndalama zochepa pafupi ndi makompyuta a quantum apafupi. 1 2 3 4 k n 5 6 7 8 9 10 n n Chikulu Kukonza kwa quantum kwakopa chidwi chifukwa cha kuthekera kwake kupereka mayankho ofulumira kwambiri ku gulu la mavuto a ziwerengero poyerekeza ndi ma algorithm apamwamba kwambiri achikale . Zikukhulupiriridwa kuti kompyuta ya quantum yayikulu yomwe ikugwira ntchito ingathandize kuthetsa mavuto a ziwerengero m'madera monga kupeza sayansi, kafukufuku wazinthu, chemistry ndi mapangidwe a mankhwala, kungotchula ochepa , , , . 5 11 12 13 14 Chopingacho chachikulu chofunikira pomanga kompyuta ya quantum ndi kusawoneka bwino kwa chidziwitso cha quantum, chifukwa cha zinthu zosiyanasiyana za phokoso zomwe zimakhudza izo. Popeza kusungitsa kompyuta ya quantum ku zotsatira zakunja ndi kuyitsatira kuti muwonetse ntchito yofunikira zikutsutsana wina ndi mnzake, phokoso likuwoneka kuti silingapeweke. Zotsatira za phokoso zimaphatikizapo zolakwika mu qubits, zinthu zogwiritsidwa ntchito, zida zoyendetsedwa, kukonzekera kwa chikhalidwe ndi zolakwika za muyeso, ndi zinthu zakunja zosiyanasiyana kuyambira pazinthu zapafupi zomwe zimapangidwa ndi munthu, monga mafunde amagetsi, mpaka zomwe chilengedwe chimakhala nazo, monga ma ray a cosmic. Onani ref. pafupipafupi. Pamene zinthu zina za phokoso zingathe kuchotsedwa ndi ulamuliro wabwino , zinthu ndi kuteteza , , , zinthu zina zingapo zikuoneka kuti ndizovuta ngati n'zothekadi kuchotsa. Mtundu womaliza ukhoza kuphatikizapo kutuluka kodzipangira komanso kutuluka molimbikitsidwa m'malo a ayoni , , ndi mgwirizano ndi bafa (Purcell effect) m'magawo amagetsi osamanga - kuphimba njira zonse ziwiri zazikulu za quantum. Motero, kukonza zolakwika kumakhala chofunikira chofunikira pomanga kompyuta ya quantum yayikulu. 15 16 17 18 19 20 1 2 3 Kuthekera kwa quantum fault tolerance kwakhazikitsidwa bwino . Kulowetsedwa kwa qubit yachinsinsi mobwerezabwereza m'ma qubits akuthupi ambiri kumalola kufufuza ndi kukonza zolakwika mwa kuyeza mobwerezabwereza ma syndromes a opareta onse ochepa. Komabe, kukonza zolakwika kumakhala kopindulitsa kokha ngati chiwerengero cha zolakwika za hardware chili pansi pa mtengo winawake womwe umadalira njira yeniyeni yotsitsira cholakwika. Zovomerezeka zoyambirira za kukonza zolakwika za quantum, monga concatenated codes , , , zimayang'ana pa kuwonetsa kuthekera kwaukadaulo kwa kuchepa kwa zolakwika. Pamene kumvetsetsa za kukonza zolakwika za quantum ndi mphamvu za matekinoloje a quantum kukulira, chidwi chinatembenukira ku kufunafuna njira zogwiritsidwa ntchito za kukonza zolakwika za quantum. Izi zidapangitsa kuti pakhale code ya surface code , , , yomwe imapereka chololeka chachikulu cha cholakwika chofika pafupifupi 1%, ma algorithm ofulumira otsitsa, ndi kugwirizana ndi ma processor a quantum omwe alipo kale pogwiritsa ntchito malo awiri (2D) a ma qubit. Zitsanzo zing'onozing'ono za surface code yokhala ndi qubit imodzi yachinsinsi zatsimikiziridwa kale ndi magulu angapo , , , , . Komabe, kukula kwa surface code mpaka ma qubits oposa 100 achinsinsi kungakhale kovuta kwambiri chifukwa cha kusinthasintha kwake kopanda mphamvu. Izi zidapangitsa chidwi cha ma code a quantum odziwika kwambiri otchedwa low-density parity-check (LDPC) codes . Kupita patsogolo kwaposachedwa mu kafukufuku wa ma code a LDPC kukuwonetsa kuti amatha kupeza quantum fault tolerance ndi mphamvu yayikulu yopangira . Pano, tikuyang'ana pa kafukufuku wa ma code a LDPC, popeza cholinga chathu ndi kupeza ma code okonza zolakwika za quantum ndi njira zomwe zimakhala zogwira mtima komanso zotheka kuwonetsa, poganizira zopinga za matekinoloje a quantum. 4 21 22 23 7 8 9 10 24 25 26 27 28 6 29 Code yokonza zolakwika ya quantum imakhala ya mtundu wa LDPC ngati opareta onse ochepa amafalikira pa ma qubits ochepa ndipo qubit iliyonse imakhudzidwa ndi ma opareshoni ochepa. Mitundu ingapo ya ma code a LDPC yatsopano yafotokozedwa posachedwapa kuphatikizapo hyperbolic surface codes , , , hypergraph product , balanced product codes , two-block codes based on finite groups , , , ndi quantum Tanner codes , . Yotsiritsirayi idawonetsedwa , kukhala 'abwino' mu njira yopereka mlingo wokhazikika wa coding ndi mtengo wolingana: chigawo choyesa chiwerengero cha zolakwika zomwe zingakonzedwe. Mosiyana ndi zimenezi, surface code ili ndi mlingo wokhazikika wa coding wopanda malire ndi mtengo wa square-root yekha. Kulumikiza surface code ndi code ya LDPC yokhala ndi mlingo wapamwamba, mtengo wapamwamba kungakhale ndi zotsatira zazikulu pakugwiritsa ntchito. Choyamba, ndalama zowonjezera za fault-tolerance (chiwerengero cha ma qubits akuthupi ndi achinsinsi) zingachepetsedwe kwambiri. Chachiwiri, ma code apamwamba kwambiri amasonyeza kuchepa kwakukulu kwa cholakwika cha achinsinsi: pamene kuthekera kwa cholakwika chakuthupi kukulowa pamtengo wololeka, kuchuluka kwa kuchepa kwa cholakwika komwe kumapezeka ndi code kumatha kuwonjezeka ndi ma order a magnitude ngakhale ndi kuchepa pang'ono kwa chiwerengero cha cholakwika chakuthupi. Chigawochi chimapangitsa ma code a LDPC apamwamba kukhala osangalatsa pama mawonetsero apafupi omwe angachite mu gawo la pafupi ndi chololeka. Komabe, kale zinkakhulupirira kuti kugonjetsa surface code pamafomulo enieni a phokoso kuphatikizapo kukumbukira, bata, ndi kukonzekera kwa chikhalidwe ndi zolakwika za muyeso kungafune ma code a LDPC akulu kwambiri okhala ndi ma qubits opitilira 10,000 . 30 31 32 33 34 35 36 37 38 39 40 39 40 31 Pano tikuwonetsa zitsanzo zingapo za ma code a LDPC okhala ndi ma qubits mazana angapo akuthupi okhala ndi dera lopanda kuya la muyeso wa chizindikiro, algorithm yotsitsa yothandiza, ndi njira yololeka kuti athane ndi ma qubits achinsinsi apadera. Ma code awa amasonyeza chololeka cha cholakwika chofika pafupifupi 0.7%, amasonyeza magwiridwe antchito abwino kwambiri m'dera la pafupi ndi chololeka, ndipo amapereka kuchepetsa kwa 10 koyambirira kwa ndalama zowonjezera poyerekeza ndi surface code. Zofunikira pa hardware kuti zitsatire njira zathu zotsitsira zolakwika ndizochepa, popeza qubit iliyonse yakuthupi imalumikizidwa ndi magulu awiri ndi ma qubits ena asanu ndi umodzi. Ngakhale graph yolumikizana ya qubit siyikhoza kuikidwa mwamtheradi mu grid ya 2D, ikhoza kugawidwa kukhala magawo awiri osalumikizana. Monga momwe tilongosolera pansipa, kulumikizana kotereku kumagwirizana ndi njira zochokera ku superconducting qubits. Ma code athu ndi mawonekedwe a bicycle codes omwe adayambitsa ndi MacKay et al. ndi kufufuzidwa mwatsatanetsatane m'mabuku. , , . Tidasankha ma code athu a bivariate bicycle (BB) chifukwa amayambira pa ma polynomials a bivariate, monga momwe zalongosoleredwa mu . Izi ndi stabilizer codes za mtundu wa Calderbank–Shor–Steane (CSS) , omwe angalongosoledwe ndi gulu la ma opareta oyendetsa (stabilizer) a ma qubit asanu ndi umodzi opangidwa ndi Pauli ndi . Pamlingo wapamwamba, code ya BB imafanana ndi 2D toric code . Makamaka, ma qubits akuthupi a code ya BB amatha kuikidwa pa malo awiri odutsana ndi zopinga zamalingaliro kotero kuti ma opareta onse ochezana amachokera ku awiri okha a ndi opareta polimbikitsa kuika kwa grid. Komabe, mosiyana ndi ma plaquette ndi vertex stabilizers omwe amafotokoza toric code, ma opareta ochezana a ma code a BB si m'dera lililonse. Kupatula apo, cheke chilichonse chimagwira ntchito pa ma qubits asanu ndi umodzi m'malo mwa anayi. Tidzafotokoza codeyo ndi Tanner graph kotero kuti vertex iliyonse ya imayimira qubit yachidziwitso kapena opareta ochezana. Ocheza cheke ndi ocheza zidziwitso amatumizidwa ndi m'mphepete ngati opareta ochezana a amachita non-trivially pa qubit yachidziwitso ya (poyendetsa Pauli kapena ). Onani Chithunzi. kwa zitsanzo za Tanner graphs za surface ndi BB codes, motsatira. Tanner graph ya code iliyonse ya BB ili ndi digirii ya vertex isanu ndi umodzi ndi graph thickness yofanana ndi ziwiri, zomwe zikutanthauza kuti ingagawidwe kukhala magawo awiri osalumikizana ndi magawo awiri. ). Kulumikizana kwa qubit ya digirii iwiri kumagwirizana ndi ma superconducting qubits opangidwa ndi ma resonators a microwave. Mwachitsanzo, magawo awiri osalala a ma couplers ndi mzere wawo woyendetsa angalumikizidwe kumtunda ndi pansi pa chip yomwe ili ndi qubits, ndi mbali ziwiri zimagwirizanitsidwa. 41 35 36 42 Njira 43 44 X Z 7 X Z G G i j i j X Z 1a,b 29 Njira , Tanner graph ya surface code, poyerekeza. , Tanner graph ya BB code yokhala ndi magawo [] yokhazikika mu torus. Aliyense m'mphepete mwa graph ya Tanner amalumikiza zidziwitso ndi cheke. Ma qubits achidziwitso okhudzana ndi ma register ( ) ndi ( ) amasonyezedwa ndi mabwalo abuluu ndi lalanje. Aliyense vertex ali ndi m'mphepete isanu ndi umodzi kuphatikizapo ma m'mphepete anayi achidule (kulozera kumpoto, kumwera, kummawa ndi kumadzulo) ndi ma m'mphepete awiri a nthawi yayitali. Tikuwonetsa ma m'mphepete ochepa ochepa chabe kuti tipewe kusokoneza. M'mphepete zomwe zatsala ndi zomwe zili ndi mzere zimasonyeza magawo awiri osalumikizana omwe amayendetsa graph ya Tanner, onani . , Zojambula za kukulitsa kwa Tanner graph poyesa ndi pambuyo pa ref. , kulumikizana ndi surface code. Ancilla yomwe ikugwirizana ndi muyeso wa itha kulumikizidwa ndi surface code, kulola ntchito za load-store za ma qubits onse achinsinsi pogwiritsa ntchito quantum teleportation ndi ma unitary achinsinsi ena. Chojambula cha Tanner chowonjezeredwa ichi chili ndi ntchito mu digirii iwiri kupyolera mu ndi m'mphepete ( ). a b q L q R Njira c 50 A B Njira Code ya BB yokhala ndi magawo [[ , , ]] imaphatikiza ma qubits achinsinsi kukhala ma data qubits kupereka code distance , kutanthauza kuti cholakwika chilichonse chachinsinsi chimakhudza ma data qubits osachepera . Timagawira ma data qubits kukhala ma register ( ) ndi ( ) aliwonse okhala ndi ma qubits /2 aliyense. Cheke chilichonse chimagwira ntchito pa ma qubits atatu ochokera ku ( ) ndi atatu ochokera ku ( ). Codeyo imadalira ma check qubits owonjezera kuyeza chizindikiro cha cholakwika. Timagawira ma check qubits kukhala ma register ( ) ndi ( ) aliwonse okhala ndi ma qubits /2 omwe amasonkhanitsa ma syndromes a mtundu wa ndi , motsatira. Pophatikizana, kulowetsedwa kumadalira ma qubits 2 akuthupi. Choncho, mlingo woyambira wa coding ndi = /(2 ). Mwachitsanzo, standard surface code architecture imaphatikiza qubit imodzi yachinsinsi = 1 kukhala ma data qubits = 2 pamtengo wa code ndipo imagwiritsa ntchito ma check qubits -1 kuyesa chizindikiro. Mlingo woyambira wa coding ndi ≈ 1/(2 2), zomwe zimakhala zosatheka mwachangu popeza munthu amakakamizidwa kusankha mtengo waukulu wa code, chifukwa, mwachitsanzo, zolakwika zakuthupi zili pafupi ndi mtengo wololeka. Mosiyana ndi zimenezi, ma code a BB ali ndi mlingo wa coding ≫ 1/ 2, onani Table kwa zitsanzo za code. Momwe timadziwira, ma code onse osonetsedwa mu Table ndi atsopano. Code ya mtengo-12 [] ingakhale yothandiza kwambiri pama mawonetsero apafupi, popeza imagwirizanitsa mtengo waukulu ndi mlingo wapamwamba wa coding = 1/24. Poyerekeza, surface code ya mtengo-11 ili ndi mlingo woyambira wa coding = 1/241. Pansipa, tikuwonetsa kuti BB code ya mtengo-12 imagwira ntchito bwino kuposa surface code ya mtengo-11 pamtengo wofunikira wa zolakwika. 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 Kuti muletse kuwonjezereka kwa zolakwika munthu ayenera kukhala ndi mphamvu yoyesa chizindikiro cha cholakwika mokwanira. Izi zimachitika ndi dera lozindikiritsa chizindikiro lomwe limalumikiza ma data qubits m'malo a opareta aliyense ochezana ndi qubit yowonjezera ndi opareta ochezanawo pogwiritsa ntchito mndandanda wa magulu a CNOT. Ma qubits ochezanawo amayezedwa akuwonetsa mtengo wa chizindikiro cha cholakwika. Nthawi yomwe imatenga kuti mugwiritse ntchito dera lozindikiritsa chizindikiro ndi yofanana ndi kuya kwake: chiwerengero cha magawo a chipata omwe amapangidwa ndi CNOTs osalumikizana. Popeza zolakwika zatsopano zimapitilira kuchitika pamene dera lozindikiritsa chizindikiro likugwiritsidwa ntchito, kuya kwake kuyenera kuchepetsedwa. Ntchito yonse yozindikiritsa chizindikiro cha code ya BB imalongosoledwa mu Chithunzi. . Ntchito ya chizindikiro im 2
