Daidaitawar ma'aikatan Pauli aikin yau da kullun ne na asali a yawancin algorithms na quantum, musamman don kimanta ƙimar tsammanin abubuwan lura kamar Hamiltonians a cikin Mai-Sauya Quantum Eigensolver (VQE). A kan na'urorin quantum na zamani masu iyakancewar haɗin kai da yawan kuskure, gina kewayoyin lantarki masu inganci don daidaitawa yana da mahimmanci. Wannan aikin ya gabatar da tsarin Na'ura-Mai-Daidaitawa (HT) wanda ke tsara kewayoyin lantarki masu ƙarancin ƙofofi don daidaita rukunoni na ma'aikatan Pauli masu tafiya tare, yana cike gibin tsakanin cikakkun kewayoyin lantarki masu haɗin kai da hanyoyin Tushen Samfurin Tensor (TPB) masu tsauri.
An gina tsarin ne akan ƙalubalen auna abubuwan lura $O = \sum_{i=1}^{M} c_i P_i$, inda $P_i$ su ne ma'aikatan Pauli. Aunawa mai inganci yana buƙatar rarraba Paulis masu tafiya tare zuwa rukunoni waɗanda za a iya daidaita su lokaci guda.
Kewayoyin lantarki na gama gari don rukunonin Tafiya Gabaɗaya (GC) suna buƙatar ƙofofin qubit biyu $O(n^2)$ kuma suna haifar da nauyin Ƙofar Musanya mai yawa akan kayan aiki masu iyakancewar haɗin qubit (misali, tsarin layi ko grid). Madadin, ta amfani da ƙofofin qubit ɗaya kawai, yana iyakance daidaitawa zuwa Tushen Samfurin Tensor (TPB), yana iyakance girman rukunonin da za a iya aunawa kuma yana ƙara yawan kewayoyin lantarki na aunawa (harbe-harbe) da ake buƙata.
Daidaitawar HT ta samo matsakaici. Tana ba da izinin adadin ƙofofin qubit biyu da aka sarrafa (kamar CNOTs), an sanya su bisa dabarun bisa ga zanen haɗin kai na na'urar, don daidaita rukunin Paulis mafi girma fiye da TPB, yayin da ake guje wa cikakken nauyin kewayoyin lantarki na GC na gama gari. Manufar ita ce haɓaka adadin Paulis a kowane zagaye na aunawa ƙarƙashin ƙuntatawa na kayan aiki.
Rukunin ma'aikatan Pauli masu tafiya tare $\mathcal{P} = \{P_1, ..., P_k\}$ ana iya daidaita shi ta HT akan na'ura mai zanen haɗin kai $G$ idan akwai kewayar lantarki $C$, wanda ya ƙunshi ƙofofin qubit ɗaya da ƙofofin qubit biyu kawai tare da gefuna na $G$, kamar yadda $C P_i C^\dagger$ ya zama diagonal (samfurin $Z$ da $I$ ma'aikata) ga duk $i$. Kewayar lantarki $C$ tana juyar da tushen eigen na rukuni na $\mathcal{P}$ zuwa tushen lissafi.
Marubutan sun gabatar da algorithm don rarraba sharuɗɗan Pauli na Hamiltonian zuwa rukunonin da za a iya daidaita su tare ta HT. Wannan matsala ce ta haɗaɗɗiyar ingantacciyar matsala wacce ke la'akari da dangantakar tafiya tare tsakanin Paulis da haɗin kai na kayan aiki. Algorithm ɗin yana nufin rage yawan rukunoni gabaɗaya, don haka rage yawan gudanar da kewayoyin lantarki na quantum daban-daban da ake buƙata.
Ga wani rukuni na Paulis masu tafiya tare da zanen kayan aiki, tsarin yana ba da tsari na tsari don gina kewayar lantarki ta daidaitawa $C$. Wannan ya haɗa da nemo jerin aikace-aikacen Clifford (ƙofofin qubit ɗaya da CNOTs tare da gefunan kayan aiki) waɗanda ke tsara kowane Pauli a cikin rukuni zuwa siffar diagonal. Tsarin yana da sassauci sosai kuma ana iya daidaita shi don rage zurfin ko ƙididdigar ƙofofi na musamman.
Shigarwa: Hamiltonian $H$, Zanen Haɗin Kayan Aiki $G$.
Wannan tsarin aiki yana rage nauyin aunawa mafi mahimmanci kai tsaye a cikin algorithms kamar VQE.
Ga nau'ikan Hamiltonian na kwayoyin halitta da yawa (misali, $H_2$, $LiH$, $H_2O$), an kwatanta hanyar rarrabawar HT da rarrabawar TPB ta al'ada. Ma'aunin maɓalli shine adadin rukunonin aunawa (kewayoyin lantarki) da ake buƙata. Sakamakon ya nuna akai-akai cewa rarrabawar HT tana buƙatar ƙananan rukunoni fiye da TPB. Misali, akan topology na sarkar layi na qubit 6 da ke kwatanta kwayoyin $H_2$, rarrabawar HT ta rage adadin rukuni da kusan kashi 20-30% idan aka kwatanta da TPB, wanda kai tsaye ke fassara zuwa raguwar daidai da adadin harbin quantum da ake buƙata don ƙayyadaddun kimantawa.
Ma'auni: Hamiltonian $H_2$ (qubits 4-6)
Rukunonin TPB: ~8-10
Rukunonin HT (Kayan Aiki na Layi): ~6-8
Ragewa: ~25% ƙananan kewayoyin lantarki na aunawa.
A matsayin hujja, marubutan sun aiwatar da kewayoyin HT akan masu sarrafa quantum na IBM na tushen girgije. Sun auna ƙimar tsammanin ƙananan lamuran Hamiltonian. Gwaje-gwajen sun tabbatar da cewa kewayoyin HT da aka gina ana iya aiwatar da su akan ainihin kayan aiki masu iyakancewar haɗin kai (misali, masu sarrafa Falcon na IBM) kuma sun samar da ƙimar tsammanin daidai cikin nasara a cikin iyakokin kuskure, suna tabbatar da yuwuwar aikin a aikace.
Bayanin Ginshiƙi (Ra'ayi): Taswirar sanduna za ta nuna "Adadin Kewayoyin Lantarki na Aunawa" akan axis-y, tare da hanyoyin rarrabawa daban-daban (TPB, GC-Ideal, HT) akan axis-x ga ƙananan kwayoyin halitta daban-daban. Sandunan HT za su kasance gajere sosai fiye da sandunan TPB amma sun fi tsayi fiye da sandar GC mai kyau (wacce ke ɗaukar haɗin kai duka-zuwa-duka), suna nuna ribar ingancin matsakaici na HT a zahiri.
Fahimtar jigon takardar tana da ma'ana sosai: madaidaicin kewayar lantarki na ka'idar ba shi da ma'ana idan bai yi daidai da kayan aiki na zahiri ba. Tsarin ma'ana ba shi da aibi: 1) Gano toshewar cikin algorithms na zamani (nauyin aunawa). 2) Gano tushen dalili (rashin daidaituwa tsakanin kewayoyin lantarki na GC na zahiri da zane-zanen kayan aiki marasa yawa). 3) Ba da mafita ta ƙuntatawa mai inganci (kewayoyin HT) wacce ta haɗa zanen kayan aiki a matsayin ɗan ƙasa na farko a cikin tsarin ƙira. Wannan ba ɗan gyara kaɗan ba ne; canji ne na asali daga ƙira don kwamfuta ta quantum zuwa ƙira don wannan takamaiman kwamfutar quantum. Yana maimaita falsafar haɗa kai ta sanin kayan aiki da aka gani a cikin lissafin gargajiya da masu haɗawa na quantum masu ci gaba kamar mai fassara Qiskit ko TKET, amma yana amfani da shi kai tsaye ga ainihin algorithm na daidaitawa.
Ƙarfafawa: Tsarin yana da tsari da sassauci, babbar fa'ida ce akan dabaru na ad-hoc. Haɗin kai kai tsaye tare da ƙuntatawa na kayan aiki yana sa shi zama mai aiwatarwa nan da nan. Ragewar da aka nuna a cikin rukunonin aunawa fa'ida ce ta zahiri, marar alaƙa da kayan aiki. Yana da kyau a tsaka da tsaki tsakanin TPB da GC, yana ba da maɓalli mai daidaitawa don rikitaccen kewayar lantarki.
Kurakurai Masu Muhimmanci & Tambayoyin Budadden: Giwa a cikin ɗaki shine zurfin kewayar lantarki da amincin. Duk da yake HT yana rage adadin kewayoyin lantarki, kowane kewayar lantarki na iya zama mai zurfi (mafi yawan CNOTs) fiye da kewayar lantarki ta TPB. A kan na'urori masu hayaniya na yau, kewayar lantarki mai zurfi na iya samun ƙarancin aminci, mai yuwuwa ya soke fa'idar rage harbi. Takardar tana buƙatar ƙarin cikakken bincike na farashin albarkatu gabaɗaya: (Adadin Rukunoni) * (Harbi kowane Rukuni * Bambanci kowane Harbi). Bambancin kowane harbi ya dogara da amincin kewayar lantarki. Bugu da ƙari, girman algorithm ɗin rarrabawa zuwa manyan kwayoyin halitta masu rikitarwa (misali, masu haɓakawa tare da qubits 50+) da rikitaccen lissafinsa a gefen gargajiya sun kasance don cikakken bincike. Yana haɗarin zama matakin pre-processing mai nauyi na lissafi.
Ga masu haɓaka algorithm na quantum da kamfanoni kamar IBM, Pasqal, ko Quantinuum, wannan aikin yana ba da zane mai aiki. Na farko, ya kamata a haɗa shi cikin kayan haɓaka software na quantum (SDKs) a matsayin zaɓi na rarrabawa na al'ada tare da TPB da GC. Na biyu, masu ƙira na kayan aiki ya kamata su lura: wannan bincike yana ƙididdige ƙimar haɗin kai. Tsarin gine-gine mafi haɗin kai (misali, mai nauyi-hex vs. layi) zai ba da damar kewayoyin HT su kusanci aikin GC mai kyau, yana ba da ma'auni na musamman don ciniki na gine-gine. Na uku, ga masu aikin VQE a yau, abin da za a ɗauka nan da nan shine gwada HT da TPB akan matsalar da kayan aikinku. Kada ku ɗauka TPB ita ce mafi kyau. Matsayi mafi kyau akan bakan TPB-HT-GC ya dogara da matsala da kayan aiki. Wannan tsarin yana ba da kayan aiki don gano wannan mafi kyau, yana motsawa fiye da dabarun daidaitawa guda ɗaya.