Inkinga Yokushumeka I-Connes

Inkinga Yokushumeka Ama-Connes ingomunye wemibuzo ejule kakhulu kwizibalo zesimanje, ehlezi ezimpambanweni zama-algebra okusebenza, ithiyori yolwazi lwe-quantum, nobunkimbinkimbi bekhompyutha. Ihlongozwe isazi sezibalo esingumFulentshi u-Alain Connes ngo-1976 futhi saxazululwa ngokuqinisekile ngo-2020, impendulo yakhona yashintsha indlela izazi zezibalo nefiziksi eziqonda ngayo ukuhlobana kwe-quantum, izikhala ezinobukhulu obungapheli, kanye nayo kanye indwangu yokucabanga kwezibalo.

Iyini Inkinga Kahle Yokushumeka Izigaxa?

Emongweni wayo, Inkinga Yokushumeka I-Connes ibuze umbuzo olula ngokukhohlisayo: ingabe yonke i-algebra ye-von Neumann enomkhawulo enesimo sokulandelela ingashumeka kumandla amakhulu wesici se-hyperfinite II₁? Ngamagama alula, yaphenya ukuthi ingabe zonke izinhlelo ze-quantum "eziziphethe kahle" ezinobukhulu obungapheli zingalinganiselwa ngezinhlaka zezibalo ezinomkhawulo, ezinyakazekayo.

U-Alain Connes ekuqaleni waqagela ngo-1976 ukuthi impendulo ingu-yebo - ukuthi lokhu kushumeka kwakwenzeka njalo. Iminyaka engaphezu kwamashumi amane, le nkinga yahlala ivulekile, imelana nemizamo yezazi zezibalo ezihlakaniphe kakhulu emhlabeni. Ukulungiswa kwayo bekungeke kuqhamuke kokuthiyori ye-algebra yomsebenzisi omsulwa, kodwa kusukela ohlangothini olungalindelekile neze: inkimbinkimbi yekhompyutha yobufakazi obusebenzisanayo be-quantum.

"Ukuphikiswa kwenkinga yokushumeka kwe-Connes akulona nje ilukuluku lezibalo - kuveza igebe elibalulekile phakathi kwalokho okungenziwa izinhlelo ze-quantum kanye nokuthi ukulinganiselwa kwakudala okungathwebula, okunomthelela osuka ku-cryptography kuya kuzisekelo zefiziksi."

I-Quantum Computing Igcine Iyixazulule Kanjani Inkinga Yezibalo Yeminyaka Engama-44?

Ngo-2020, abacwaningi u-Ji, Natarajan, Vidick, Wright, kanye no-Yuen bashicilela iphepha eliyingqopha-mlando elithola ukuthi i-MIP* = RE, lapho i-MIP* isho isigaba sezinkinga ezixazululwa isiqinisekisi sakudala esisebenzisana nama-quantum prover amabili abambene, futhi i-RE iyisigaba sezilimi eziphindaphindwayo. Lo mphumela wawushaqisa: ubonise ukuthi ukuboshwa kwe-quantum kunikeza okungavamile - empeleni okungenamkhawulo - ukuthuthukiswa ezinhlelweni zobufakazi ezisebenzisanayo.

Ukuxhumeka ku-Connes? Ithimba lifakazele ukuthi Inkinga Yokushumeka Ama-Connes ilingana nesitatimende esithi MIP* = MIP (isigaba sobufakazi esisebenzayo se-multiprover). Njengoba i-MIP* ibonakale yaba yinkulu kakhulu kune-MIP - empeleni, ilingana ne-RE - ukuqagela kwe-Connes Embedding bekungamanga. Akuwona wonke ama-algebra e-von Neumann anomkhawulo ashumeka ku-ultrapower we-hyperfinite II₁ factor.

Iziphi Izimiso Eziyisisekelo Ezisemuva Kwenkinga?

Ukuqonda Inkinga Yokushumeka I-Connes kudinga ukujwayelana nezakhiwo ezimbalwa ezibalulekile zezibalo:

• I-Von Neumann Algebras: Ama-Algebra ama-opharetha abophezelekile esikhaleni sika-Hilbert avaliwe ngaphansi kwe-topology yomsebenzisi ebuthakathaka, okwenza ama-algebra e-matrix abe yizilinganiso ezingapheli.
• I-Hyperfinite II₁ Factor: I-algebra ye-von Neumann eyingqayizivele, e-canonical "engumkhawulo" wama-algebra e-matrix anomkhawulo — isistimu ye-quantum yemvelo engenamkhawulo.
• Amazwe E-Tracial: Imisebenzi eqondile kuma-algebra e-von Neumann eziphatha njengokulandelelwa okujwayelekile, ihlinzeka ngombono "wosayizi" noma "ubukhulu" bokuqagela.
• Amandla amakhulu: Ukwakhiwa kwemodeli-yethiyori ekhiqiza izakhiwo zezibalo ezintsha ngokuthatha imikhawulo yokulandelana kwama-algebra ngendlela ethile, engajwayelekile.
• I-Quantum Correlations: Isigaba sokuhlobana okungafezwa amaqembu amabili abelana ngezimo ze-quantum ezihilelekile, ingqikithi yethiyori yolwazi lwe-quantum kanye nokuxazululwa kwenkinga ekugcineni.

Iyini Ingqikithi Yomlando Nokuvela Kwale nkinga?

Imvelaphi yenkinga ilandela ephepheni lika-Connes lango-1976 elimayelana nezici zokujova, umsebenzi wokuguqula kuma-algebra omqhubi. Emashumini eminyaka alandelayo, izazi zezibalo zathola ukuthi i-CEP yayilingana nenqwaba yezinkinga ezazibonakala zingahlobene kuzo zonke zezibalo - kusukela ekuqaguleni kweQWEP yaseKirchberg kuthiyori ye-C*-algebra kuya enkingeni kaTsirelson kuthiyori yolwazi lwe-quantum, eyabuza ukuthi ukuhlobana kwe-quantum okukhiqizwe yilabo abasebenzisa umkhiqizo ofanayo> abasebenzisa umkhiqizo ofanayo>

Le webhu yokulingana yenze i-CEP yaba inkinga emaphakathi yokuhlela, "ihabhu" exhuma izinkambu ezihlukene. Lapho iwela ngo-2020, imiphumela ye-ripple yazwakala kuzo zonke izibalo, i-physics, nesayensi yekhompiyutha ngasikhathi sinye. Ubufakazi bokuthi inkinga ka-Tsirelson ibe nempendulo engeyinhle - eshiwo ngokuqondile yi-MIP* = RE - buqinisekise ukuthi i-quantum mechanics ibamba ubuqili obujule kakhulu kunalokho ososayensi befiziksi ababekucabanga.

Ayini Amathrendi Esikhathi esizayo kanye nemithelela esebenzayo yalesi sinqumo?

Ukulungiswa Kwenkinga Yokushumeka Ama-Connes kuvula imingcele yocwaningo emisha ngokuphelele. Ku-quantum cryptography, ilola ukuqonda kwethu ukuthi yiziphi izinhlobo zokuhlobana kwe-quantum ezibonakala zingokoqobo uma kuqhathaniswa nokungacatshangwa nje ngokwezibalo. Ngokwethiyori eyinkimbinkimbi, iphakamisa ukuthi amandla ama-quantum prover axakeke kakhulu kunendlela amodeliwe ngaphambilini. Ezisekelweni zezibalo, kuphakamisa imibuzo ejulile mayelana nobudlelwano phakathi kokusondelana okunomkhawulo kanye nezinto zezibalo ezingapheli.

Kochwepheshe bezibalo abasetshenziswayo kanye nonjiniyela be-quantum, umphumela ugcizelela ukubaluleka kokutadisha igebe phakathi kokuxhumana kwe-quantum "kwendawo" kanye "nohambo lokuya emsebenzini" - igebe elinemiphumela eqondile ye-cryptography ye-quantum ezimele kanye nedizayini yamanethiwekhi e-quantum.

Imibuzo Evame Ukubuzwa

Ingabe i-Connes Embedding Conjecture ifakazelwe ukuthi iyiqiniso noma ingamanga?

Umcabango wafakazelwa amanga ngo-2020 ngu-Ji, Natarajan, Vidick, Wright, kanye no-Yuen. Ubufakazi babo, obusungula i-MIP* = RE, bubonise ukuba khona kwama-algebra e-von Neumann angakwazi ukushumeka kumandla amakhulu wesici se-hyperfinite II₁, okuphikisa ngokuqondile ukucabanga kwangempela kuka-Connes.

Kungani Inkinga Yokushumeka I-Connes ibalulekile ngaphandle kwezibalo ezimsulwa?

Inkinga ixhumeka ngokuqondile ku-quantum physics ne-computer science. Ukulungiswa kwayo kuqinisekisile ukuthi ukuboshwa kwe-quantum kungaveza ukuhlobana okungajwayelekile futhi okujwayelekile ukulinganisa kwe-quantum-mechanical okungakwazi ukuphindaphinda. Lokhu kunemithelela ku-quantum cryptography, quantum computing architecture, kanye nezisekelo ze-quantum mechanics ngokwayo.

Iyini i-hyperfinite II₁ factor futhi kungani ibalulekile kule nkinga?

I-hyperfinite II₁ factor, evame ukuchazwa ngokuthi R, iyi-algebra ye-von Neumann ehlukile eyakhiwe njengomkhawulo wama-algebra e-matrix enobukhulu obulinganiselwe. Iwuhlelo lwe-quantum olulula futhi "olulinganisekayo" olungapheli. Umbuzo wokuthi ingabe ama-algebra ayinkimbinkimbi ashumekwe kumandla amakhulu e-R empeleni ubuza ukuthi ingabe wonke amasistimu e-quantum abelana ngale ndawo elinganiselwe enomkhawulo - futhi impendulo, njengoba imiphumela yango-2020 ibonisa, ithi cha.

Ukuthuthukiswa okufana nokuxazululwa kwenkinga yokushumeka kwe-Connes kubonisa ukuthi kwenzekani uma amasistimu ayinkimbinkimbi, axhumene eqondwa ezingeni lawo elijulile - okuveza ukuxhumana okungalindelekile futhi kuvule amathuba amasha ngokuphelele. Kwa-Mewayz, sikholelwa ukuthi isimiso esifanayo siyasebenza ekwakheni ibhizinisi lakho. Uhlelo lwethu lokusebenza lwebhizinisi lwamamojula angu-207 lunikeza abasebenzisi abangaphezu kuka-138,000 amathuluzi okuqonda, ukuxhuma, nokuthuthukisa zonke izici zemisebenzi yabo, kusukela kwezokukhangisa kanye ne-CRM kuya kuzibalo nangale kwalokho — konke kuqala ku-$19/ngenyanga.

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