Ababhungqulu: Neereja Sundaresan Theodore J. Yoder Youngseok Kim Muyuan Li Edward H. Chen Grace Harper Ted Thorbeck Andrew W. Cross Antonio D. Córcoles Maika Takita Isishwankathelo I-Quantum error correction ibonelela ngendlela ethembisayo yokwenza izibalo eziphakamileyo zekhompyutha. Nangona ukusetyenziswa ngokupheleleyo kwezixhobo ezinganyelwayo ekungenziwa ngayo izixhobo, ukuphucuka kwamva nje kulawulo lwe-elektroniki kunye ne-quantum hardware kuvumela imiboniso ephucukileyo yezinto eziyimfuneko kulungiso lwempazamo. Apha, senza i-quantum error correction kwi-superconducting qubits ekhutshwe kwilattice enzima ye-hexagon. Sigqiba i-logical qubit kunye nomgama omthathu kwaye senza imijikelezo emininzi yezilinganiso zempazamo ezinganyelwayo eziphakamileyo eziphakamileyo eziphakamileyo eziphakamileyo eziphakamileyo eziphakamileyo ezivumela ukulungiswa kuyo nayiphi na impazamo enye kwisilasi. Ukusebenzisa impendulo yexesha langempela, sibuyisela isilinganiso kunye ne-qubits yefulegi ngokujoliswe emva komjikelo ngamnye wokukhutshwa kwesilinganiso. Sibika impazamo yengqiqo ekhethwe ngumthengisi, kunye nempazamo ephakathi yengqiqo ngelilitha yomlinganiso we-syndrome kumaleko e-Z(X) ka-0.040 (0.088) kunye no-0.037 (0.087) kwimatchi kunye ne-maximum likelihood decoders, ngokulandelanayo, kwidatha ekhethiweyo yokuvuza. Intshayelelo Izibalo zekhompyutha zeQuantum zingaba neempazamo, ngokwenza, ngenxa yengxolo kwi-hardware. Ukucima iimpazamo ezivelayo, iikhowudi zokulungisa impazamo zeQuantum (QEC) zingasetyenziselwa ukubeka ulwazi lweQuantum kumanyathelo achitshiweyo, achitshiweyo, kwaye emva koko ngokulungisa iimpazamo ngaphezu kokuba ziqokelela ukwenza izibalo ezinganyelwayo (FT). Ukusetyenziswa ngokupheleleyo kwe-QEC kuya kufuna: ukulungiswa kwe-logical states; ukufezekiswa kwekiti epheleleyo ye-logical gates, enokufuna ukulungiswa kwamagundane em magic; imilinganiso ephindaphindayo yamagundane; kunye nokukhutshwa kwamagundane ukuze kulungiswe iimpazamo. Ukuba iyaphumelela, iikhowudi zempazamo ezithunyelweyo ziya kufana neekhowudi zempazamo ezisebenzayo, kwaye ziya kuncipha ngokunyuka kwemigama yekhowudi ukuya kumaxabiso angabonakaliyo. Ukukhetha ikhowudi ye-QEC kufuna ukuqwalaselwa kwe-hardware esezantsi kunye neempawu zayo zengxolo. Kwilattice enzima ye-hexagon, iikhowudi ze-QEC ezijikelezayo ziyatsala ngoba zifanelekile kwi-qubits kunye noxhumo oluncitshisiweyo. Ezinye iikhowudi ziye zabonisa isithembiso ngenxa yomda wazo ophakamileyo wokuba yi-FT okanye inani elikhulu le-transversal logical gates. Nangona imodeli yabo yesikhala kunye nexesha ingabangela umqobo omkhulu wokusala, kukho iindlela ezikhuthazayo zokunciphisa izixhobo ezibiza kakhulu ngokusebenzisa uhlobo oluthile lokuphuculwa kwempazamo. Kwinkqubo yokukhutshwa, ukulungiswa okuphumelelayo kuxhomekeke kungekuphela kwintsebenzo ye-quantum hardware, kodwa kunye nokusetyenziswa kwe-electronics yolawulo esetyenziselwa ukuqokelela kunye nokucubungula ulwazi lweClassical olufunyenweyo kwimilinganiso ye-syndrome. Kwimeko yethu, ukuqalisa i-syndrome kunye ne-flag qubits ngempendulo yexesha langempela phakathi kwemijikelezo yomlinganiso kunganceda ekunciphiseni iimpazamo. Kumgangatho wokukhutshwa, nangona iinkqubo ezithile zikhona ukwenza i-QEC asynchronously ngaphakathi komkhetho we-FT, isantya apho ama-syndrome empazamo afunyenweyo kufanele afane ixesha lawo lokucubungula i-classical ukuze kuthintelwe ukuqokelela okwandayo kwidatha ye-syndrome. Kwakhona, ezinye iinkqubo, njengokusebenzisa igundane lem magic elingu-logical T-gate, zifuna ukusetyenziswa kwempendulo yexesha langempela. Ke ngoko, umbono weminyaka yokuphila we-QEC awuhambeli kumgangatho omnye omkhulu kodwa kufuneka ubhinywe njengento eqhubekayo yemisebenzi ehambelanayo. Indlela ye-experimental yophuhliso lwale teknoloji iya kubandakanya umboniso wale misebenzi ngokwahlukileyo kuqala kunye nokudibanisa kwabo okukhulayo kamva, ngelixa uphucula rhoqo iimmetric zabo ezihambelanayo. Ezinye zale ntsilelo zibonakaliswa kwimicimbi emininzi yakutshanje kwiinkqubo zeQuantum kwiinkonzo ezahlukeneyo zePhysical, ezibonise okanye zavaleleka izinto ezithile ze-FT quantum computing. Ngokukodwa, i-FT logical state preparation ibonisiwe kwiions, i-nuclear spins kwidiyamond kunye ne-superconducting qubits. Imijikelezo ephindaphindayo yokukhutshwa kwe-syndrome ibonisiwe kwi-superconducting qubits kwiikhowudi zokufumanisa impazamo ezincinci, kuquka ukulungiswa kwempazamo okuyinxalenye kunye nekiti epheleleyo (nangona ingekho i-FT) yamagundane e-single-qubit. Umboniso we-FT wekiti epheleleyo yamagundane kubini ama-logical qubits uye wabhengezwa kutshanje kwiions. Kummandla wokulungiswa kwempazamo, kube nemicimbi yakutshanje yekhowudi ye-surface distance-3 kwi-superconducting qubits kunye nokukhutshwa kunye nokukhethwa kwangaphambili, kunye nokusetyenziswa kwe-FT kwimemori ye-quantum evikelweyo ngokusebenzisa ikhowudi yombala kunye nokulungiswa kwe-FT, ukusebenza, kunye nomlinganiso, kuquka ii-stabilizers zayo, ye-logical state kwikhowudi ye-Bacon-Shor kwiions. Apha sidibanisa ubuchule bempendulo yexesha langempela kwi-superconducting qubit system kunye nenkqubo yokukhutshwa kwe-maximum likelihood engazange iphicwe ngaphambili ukuze kuphuculwe ukusinda kwe-logical states. Sibonisa le zixhobo njengecandelo lokusebenza kwe-FT yekhowudi yesubsystem, ikhowudi ye-heavy-hexagon, kwi-superconducting quantum processor. Kubalulekile ukwenza ukusetyenziswa kwale khowudi kube yimpazamo kukuquka ama-qubits emifanekiso angalungisiyo anikela ingqalelo kumthengisi malunga neempazamo zesilasi. Ngokujoliswe ekubuyiseleni i-flag kunye ne-syndrome qubits emva komjikelo ngamnye wokulinganisa we-syndrome, sivikela inkqubo yethu kwiimpazamo ezivelayo kwingxolo ye-asymmetry eyenziwe yokuphazamiseka kwe-energy. Siphinde sisebenzise izicwangciso zokukhutshwa ezichazwe kutshanje kwaye sandisa izimvo zokukhutshwa ukubandakanya imiqondo ye-maximum likelihood. Iziphumo Ikhowudi ye-heavy-hexagon kunye nezilasi zemijikelezo emininzi Ikhowudi ye-heavy-hexagon esiyiqwalelayo yi-n = 9 qubit code encoding k = 1 logical qubit kunye nomgama d = 3. I-Z kunye ne-X gauge (bona iFig. 1a) kunye namaqela e-stabilizer banikwa ngayo AmaQela e-stabilizer S_i yiyona maphakathi yamaqela e-gauge ahlukeneyo. Oku kuthetha ukuba ii-stabilizers, njengeemveliso zemisebenzi ye-gauge, zingachazwa kwimilinganiso yomsebenzi we-gauge kuphela. Imisebenzi ye-logical ingakhethwa ukuba ibe yi-XL = X1X2X3 kunye ne-ZL = Z1Z3Z7. Imisebenzi ye-Z (blue) kunye ne-X (red) gauge (eqs. (1) kunye (2)) zibekwe kwi-qubits 23 efunekayo kunye nekhowudi ye-distance-3 heavy-hexagon. I-Code qubits (Q1-Q9) ziboniswa ngomthubi, ii-syndrome qubits (Q17, Q19, Q20, Q22) ezisetyenziselwa ii-stabilizers ze-Z ngombala oluhlaza okwesibhakabhaka, kunye ne-flag qubits kunye nee-syndromes ezisetyenziselwa ii-stabilizers ze-X ngomhlophe. Umyalelo kunye nenkqubo apho i-CX gates zisetyenziswa kwiindidi nganye (0 ukuya kwezi-4) ziboniswa ziintolo ezibotshiweyo. Umboniso wesilasi wenye indawo yomlinganiso we-syndrome, kuquka ii-stabilizers ze-X kunye ne-Z. Umboniso wesilasi ubonisa ukuhambelana okungalinganiyo kwe-gate operations: ezo zingaphakathi kwemida ebhalwe ziibharari zokucwangcisa (imigca eqengqayo emi-vertical). Njengoko unxibelelwano ngalunye lwe-two-qubit lwahlukile, ukucwangcisa kokugqibela kwe-gate kucetyiswa kunye nomgangatho wokucwangcisa wokuphuculwa kwesilasi; emva koko i-dynamical decoupling yongezwa kwi-qubits yedatha apho ixesha livumela. Imilinganiso kunye nokuseta ngokutsha kuwahlulwa kwezinye izinto zeqeqo ngeebharari ukuvumela i-dynamical decoupling eyiyo yongezwe kwi-qubits yedatha evulekileyo. Imizobo yokukhutshwa yemijikelezo emitatu ye-Z (c) kunye ne-X (d) imilinganiso ye-stabilizer kunye ne-circuit-level noise ivumela ukulungiswa kwe-X kunye ne-Z errors, ngokulandelanayo. Amanqaku aluhlaza kunye obomvu kwimizobo axela umahluko we-syndromes, ngelixa amanqaku amnyama ayimida. Iintolo zibhalwe ngohlobo lomlinganiso we-stabilizer (Z okanye X), kunye ne-subscript ebonisa i-stabilizer, kunye ne-superscript ebonisa umjikelo. Iintolo ezimnyama, ezivelayo kwiimpazamo ze-Pauli Y kwi-code qubits (kwaye ngoko ziyi-size-2 kuphela), zidityanisa imizobo emibini kwi-c kunye ne-d, kodwa azisetyenziswa kumthengisi wokulinganisa. I-hyperedges ezwi-4, ezingasetyenziswa ngabathathi-nxaxheba, kodwa zisetyenziswa kumthengisi we-maximum likelihood. Imibala yeyokucaca. Ukuguqulela nganye kwixesha elinye lijikeleza kunika i-hyperedge esebenzayo (kunye notshintsho oluthile kwimida yexesha). Kwakhona akubonakaliswa zizo naziphi na ii-hyperedges ezwi-3. a b e f Apha sigxila kwisithuthi esithile esinganyelwayo, iindlela zethu ezininzi zingasetyenziswa ngokubanzi kunye neekhowudi ezahlukeneyo kunye nezilasi. Iindidi ezimbini zesilasi, eziboniswa kwiFig. 1b, zenziwe ukulinganisa imisebenzi ye-X kunye ne-Z gauge. Isilasi somlinganiso we-Z gauge ikwazuza ulwazi oluluncedo ngokulinganisa ii-flag qubits. Silungiselela i-code states kwilothelo ye-logical |i> (i=0, 1) ngokulungisa kuqala ii-qubits ezilithoba kwi-|i> state kwaye silinganise i-X-gauge (Z-gauge). Emva koko sisebenzisa imijikelezo ye-syndrome measurement 'r', apho umjikelo ubandakanya umlinganiselo we-Z-gauge okulandelwa ngumlinganiselo we-X-gauge (ngokulandelanayo, umlinganiselo we-X-gauge okulandelwa ngumlinganiselo we-Z-gauge). Okokugqibela, sifunda zonke ii-qubits ezilithoba kwisiseko se-Z (X). Sisebenzisa iziqhushumbisi ezifanayo kwiilothelo ze-logical |i> kunye ne-|i+> ngokulungisa nje ii-qubits ezilithoba kwi-|i> kunye ne-|i+> ngokulandelanayo. Iinkqubo zokukhutshwa Kwicandelo le-FT quantum computing, umthengisi yinkqubo ethatha njengokufakwayo imilinganiso ye-syndrome ukusuka kwikhodi yokulungisa impazamo kunye nemveliso isilungiso kwi-qubits okanye idatha yomlinganiso. Kulecandelo sichaza iinkqubo ezimbini zokukhutshwa: ukukhutshwa okulinganayo kunye nokukhutshwa kwe-maximum likelihood. I-decoding hypergraph yinkcazo ecocekileyo yolwazi oluqokelelwe yi-FT circuit kwaye lufumaneke kwi-decoding algorithm. Ine qela lezibonelelo, okanye iziganeko ezibuthathaka kwiimpazamo, V, kunye neqela le-hyperedges E, ezibeka phantsi ubudlelwane phakathi kweziganeko ezibangelwa ziimpazamo kwisithuthi. Umfanekiso 1c-f ubonisa iinxalenye ze-decoding hypergraph yovavanyo lwethu. Ukwakha i-decoding hypergraph ye-stabilizer circuits kunye nePauli noise kungaqhutywa kusetyenziswa i-Gottesman-Knill simulations okanye iindlela ezifanayo zePauli tracing. Okokuqala, isiganeko esibuthathaka kwiimpazamo senziwa kulo naliphi na umlinganiselo ongqinelanayo kwisithuthi esingenampazamo. Umlinganiselo ongqinelanayo M ngumlinganiso wakhetho lowo imveliso yawo m ∈ {0, 1} ingabikezelwa ngokongeza i-modulo 2 imiphumo yomlinganiso ukusuka kwiseti V yeemilinganiso zangaphambili. Oko kukuthi, kwisithuthi esingenampazamo, FM(M) = m, apho iseti V ingafunyanwa ngokumodeliswa kwesithuthi. Beka ixabiso lesiganeko esibuthathaka kwiimpazamo ku m - FM(mod2), elinguziro (ekwabizwa ngokuba yinto engafaniyo) xa kungekho mpazamo. Ke ngoko, ukubona isiganeko esingafaniyo (ekwabizwa ngokuba yinto engazenzisiyo) sibonisa ukuba isithuthi siye sabandezeleka ubuncinane impazamo enye. Kwizilasi zethu, iziganeko ezibuthathaka kwiimpazamo zezilinganiso ze-flag qubit okanye umahluko weemilinganiso ezilandelanayo zefani yesi-stabilizer (ekwabizwa ngokuba zi-difference syndromes). Okulandelayo, i-hyperedges ziyongezwa ngokujonga iimpazamo zesithuthi. Imimodeli yethu iquka imodeli yempazamo ye-pC kwiinqanaba ngalinye lezithako zesithuthi Apha sahlula umsebenzi wokuchongwa id kwii-qubits ngexesha apho ezinye ii-qubits zisenziwa iigates ze-unitary, kumsebenzi wokuchongwa idm kwii-qubits xa ezinye zisenziwa umlinganiselo kunye nokuseta ngokutsha. Sibuyisela ii-qubits emva kokuba zilinganisiwe, ngelixa silungisa ii-qubits ezingekasetyenziswa kuvavanyo. Okokugqibela cx yingeyo-controlled-not gate, h yingeyo-Hadamard gate, kunye ne-x, y, z ziip Pauli gates. (bona iindlela "IBM_Peekskill kunye neenkcukacha zovavanyo" ngolwazi oluthe kratya). Amaxabiso emvume ka-pC adweliswe kwiindlela "IBM_Peekskill kunye neenkcukacha zovavanyo". Imodeli yempazamo yethu yi-circuit depolarizing noise. Ngempazamo yokuqalisa kunye nokuseta ngokutsha, i-Pauli X ifakwa ngemodeli ye-pinit kunye ne-preset nganye emva kokulungiswa kwemodeli engekhoyo. Ngempazamo yokulinganisa, i-Pauli X ifakwa ngemodeli ye-p measurement ngaphambi kokulinganisa okungekhoyo. I-one-qubit unitary gate (two-qubit gate) C ibandezeleka ngemodeli ye-pC enye yezi-Pauli errors ezintathu (ezilishumi elinamibini) ezingezizo ezokuchongwa emva kwesango elingeza. Kukho ithuba elilinganayo lokuba naziphi na ii-Pauli errors ezintathu (ezilishumi elinamibini) zenzeke. Xa impazamo enye yenzeka kwisithuthi, ibangela ukuba uluhlu oluthile lweziganeko ezibuthathaka kwiimpazamo zibe ngaphezu komlinganiselo. Esi sethi yeziganeko ezibuthathaka kwiimpazamo iba yi-hyperedge. Isiseti sazo zonke ii-hyperedges yi-E. Iimpazamo ezimbini ezahlukeneyo zingabisa i-hyperedge efanayo, ngoko ke i-hyperedge nganye ingabonwa njengento emele iseti yeempazamo, nganye kuzo ibangele ngokuzimeleyo iziganeko kwi-hyperedge ukuba zingaphezu komlinganiselo. Inxaxheba kwi-hyperedge nganye, ngowona mda, yisuma yeemodeli zeempazamo kuseto. Impazamo ingabangela kwakhona impazamo, edluliselwe ekugqibeleni kwisithuthi, i-anti-commutes kunye nenye okanye ngaphezulu kwemisebenzi ye-logical yekhowudi, ifuna isilungiso se-logical. Sicinga ngobuninzi bokuba ikhowudi inee-logical qubits 'k' kunye nekiti ye-2k imisebenzi ye-logical, kodwa qaphela k=1 kwi-heavy-hexagon code esetyenzisiweyo kuvavanyo. Singagcina umkhondo wokuba imisebenzi ye-logical iphi i-anti-commutes kunye nempazamo kusetyenziswa i-vector ukusuka ngo. Ke ngoko, i-hyperedge nganye 'h' iphinde ibhalwe ngomnye wale vectors L, ebizwa ngokuba yi-logical label. Qaphela ukuba ukuba ikhowudi inomgama ubuncinane obuthathu, i-hyperedge nganye inombhalo we-logical oyingqayi. Okokugqibela, siqaphela ukuba inkqubo yokukhutshwa ingakhetha ukucocwa kwe-decoding hypergraph ngeendlela ezahlukeneyo. Indlela enye esihlala siyisebenzisa apha yinkqubo yokuchaza. Imilinganiso yeFlag ukusuka kwii-qubits 16, 18, 21, 23 ayifunwanga ngaphandle kokulungiswa. Ukuba iflegi 11 ayifani kwaye 12 ifani, faka i-Z kwi-2. Ukuba 12 ayifani kwaye 11 ifani, faka i-Z kwi-qubit 6. Ukuba iflegi 13 ayifani kwaye 14 ifani, faka i-Z kwi-qubit 4. Ukuba 14 ayifani kwaye 13 ifani, faka i-Z kwi-qubit 8. Bona iref. ngeenkcukacha malunga nokuba kutheni oku kwanela kulwazi olunempazamo. Oku kuthetha ukuba endaweni yokubandakanya iziganeko ezibuthathaka kwiimpazamo ukusuka kwimilinganiso ye-flag qubit ngokuthe ngqo, sixoxa kwangaphambili idatha ngokusebenzisa ulwazi lweflegi ukufaka izilungiso ze-Pauli Z ezibonakalayo kunye nokulungelelanisa iziganeko ezibuthathaka kwiimpazamo ezilandelanayo ngokufanelekileyo. Ii-hyperedges ze-deflagged hypergraph zingafumaneka ngokulungiswa kwe-stabilizer ngokubandakanya ii-Z corrections. Vumela 'r' ukubonisa inani lemijikelezo. Emva kokuchaza, ubungakanani beseti V ye-Z (resp. X basis) experiments ziyi |V| = 6r + 2 (resp. 6r + 4), ngenxa yomlinganiso we-six stabilizers ngomjikelo kunye nokuba no-two (resp. four) initial error-sensitive stabilizers emva kokulungiswa kwemodeli. Ubungakanani be-E bubonisa ngokufanayo |E| = 60r - 13 (resp. 60r - 1) ye-r > 0. Ukujonga iimpazamo ze-X kunye ne-Z ngokwahlukeneyo, ingxaki yokufumana isilungiso esincinci sempahla kwisurface code ingancitshiswa ekufumaneni ukulinganisa okuyimfuneko okuyimfuneko kumbonelelo. Izixhobo zokulinganisa ziyaqhubeka zifundwa ngenxa yokusebenza kwazo kunye nokusetyenziswa okubanzi. Kule candelo, sichaza isixhobo sokulinganisa sekhowudi yethu ye-distance-3 heavy-hexagon. ImiZobo yokukhutshwa, enye yeempazamo ze-X (Fig. 1c) nenye yeempazamo ze-Z (Fig. 1d), kwingqiqo yempazamo yomda omncinci ziyinxalenye ye-decoding hypergraph kwicandelo langaphambili. Masigxile apha kumbonelelo wokulungisa iimpazamo ze-X, njengoko umbonelelo weempazamo ze-Z ufana nawo. Kule meko, ukusuka kwi-decoding hypergraph sigcina amanqaku VZ ahambelana nemilinganiso ye-Z-stabilizer (yomahluko wezilandelanayo) kunye neentolo (oko kukuthi, ii-hyperedges ezizi-size-two) phakathi kwazo. Ukongeza, kwenziwa inqaku ledanga b, kwaye ii-hyperedges ezizi-size-one ze-form {v} kunye ne-v ∈ VZ, ziboniswa ngokubandakanya intolo {v, b}. Zonke iintolo kumdwebo weempazamo ze-X zifumana amathuba kunye neelogi zolwabiwo ezivela kwii-hyperedges ezihambelanayo (bona Itheyibhile 1 nge data yeempazamo ze-X kunye ne-Z kuvavanyo lwe-2-round). Inkqubo yomlinganiso ongalinganiyo ethatha umbonelelo onama-edges anobunzima kunye neseti yamanqaku achaziweyo, kwaye ibuyisela isethi yeentolo kumbonelelo ezidibanisa onke amanqaku achaziweyo ngababini kwaye inobunzima obuncinci obuncinci phakathi kweesethi ezinjalo zezintolo. Kwimeko yethu, amanqaku achazweyo ngamacandelo angabonakaliyo empazamo (ukuba kunomdla ongeyomda, idanga ledanga layo libaluleke kakhulu), kunye nobunzima be-edge bunokukhethwa ukuba bonke babe njengo-1 (indlela efanayo) okanye babekwe njengo-, apho pe yimodeli yentolo (indlela ye-analytic). Olu khetho lokugqibela luthetha ukuba ubunzima bonke beseti yentolo buyafana nelog-likelihood yeso seti, kwaye ukulinganisa okuncinci okuyimfuneko kuzama ukunyusa le likelihood phezu kweentolo kumbonelelo. Unikwe ukulinganisa okuyimfuneko okuyimfuneko, unokusebenzisa ii-labels eziyimfuneko zezintolo kumlinganiso ukugqiba isilungiso kwilothelo ye-logical. Kungenjalo, umdwebo weempazamo ze-X (we-Z) womthengisi kukuba intolo nganye ingalungiswa kwi-qubit yekhowudi (okanye impazamo yokulinganisa), apho ukufaka intolo kumlinganiso kuthetha ukuba i-X (i-Z) isilungiso kufuneka sifakwe kwi-qubit ehambelanayo. Ukhutsho lwe-Maximum Likelihood (MLD) luyindlela efanelekileyo, nangona ingekho scalable, yokukhutshwa kwekhowudi yokulungisa impazamo yeQuantum. Kwi-concept yayo yoqobo, i-MLD yasebenza kwiimodeli zengxolo ye-phenomenological apho iimpazamo zenzeka nje ngaphambi kokuba i-syndromes ilinganiswe. Oku kunjalo kuthintela imeko enyanisekileyo apho iimpazamo zingadluliselwa kwisithuthi sokulinganisa i-syndrome. Kutshanje, i-MLD iye yanda ukubandakanya ingxolo yesithuthi. Apha, sichaza indlela i-MLD elungisa ngayo ingxolo yesithuthi kusetyenziswa i-decoding hypergraph. I-MLD ifumana isilungiso esona sicace ngakumbi ngokusekelwe kwinkcazelo yeziganeko ezibuthathaka kwiimpazamo. Oku kwenziwa ngokubala uhambulo lwethuba Pr[β, γ], apho β yenziwa ngeziganeko ezibuthathaka kwiimpazamo kunye ne-γ yimfuneko yesilungiso se-logical. Singabala i-Pr[β, γ] ngokubandakanya yonke i-hyperedge ukusuka kwi-decoding hypergraph, Fig. 1c-f, siqala ngokuhambulo olungenampazamo, oko kukuthi, Pr[0|V|, 0^2k] = 1. Ukuba i-hyperedge h inemodeli ph yayo, ngokuzimeleyo kwezinye ii-hyperedges, siyifaka ngokwenza uhlaziyo apho βh ngumdlalo we-binary vector wemele i-hyperedge. Olu hlaziyo kufuneka lwenziwe kanye kulo naliphi na i-hyperedge kwi-E. Nje ukuba i-Pr[β, γ] ibalelwe, singayisebenzisa ukuchaza isilungiso esilungcono se-logical. Ukuba β* ibonwa kumjikelo wovavanyo, ibonisa indlela apho imilinganiso ye-logical operators ifanele ilungiswe ngayo. Ngolwazi oluthe kratya malunga nokusetyenziswa okukhethekileyo kwe-MLD, khangela iindlela "Izicwangciso zeMaximum Likelihood". Ukufezekiswa kwe-experimental Kulolu ngcaciso sisebenzisa i-ibm_peekskill v2.0.0, iprosesa ye-IBM Quantum Falcon ye-27 qubit enoxhumano olunika amandla ikhowudi ye-distance-3 heavy-hexagon, bona iFig. 1. Ixesha elipheleleyo lokulinganisa i-qubit kunye nokuseta ngokukhawuleza kokulandelayo, kuyo yonke imijikelezo, kuthatha i-768ns kwaye kufana nazo zonke ii-qubits. Zonke imilinganiselo ye-syndrome kunye nokuseta ngokutsha kwenzeka ngaxeshanye ukuze kuphuculwe intsebenzo. I-simple Xπ-Xπ dynamical decoupling sequence yongezwa kwiikhowudi qubits ngexesha lezikhathi zabo zokungasebenzi. Ukuvuza kwe
