1. Gabatarwa

Tafiya Bazuwar Quantum (QRW) tana wakiltar bambanci na asali daga tafiya bazuwar gargajiya, tana amfani da haɗakar quantum da tsangwama don cimma tafiya cikin sauri mai sau biyu a tsarin zane. Wannan iyawa ita ce tushen wasu algorithms na quantum, gami da Binciken Tafiya Bazuwar Quantum (QRWS). Wannan aikin yana bincika bambancin QRWS wanda ke amfani da tsarin quantum mai matakai da yawa (qudit) da ma'aikacin kwalin tafiya da aka gina ta hanyar tunani na gabaɗaya na Householder, da nufin haɓaka ƙarfin algorithm ɗin akan gazawar sigogi—kalubale mai mahimmanci a cikin na'urorin quantum na ɗan gajeren lokaci.

2. Tsarin Ka'idar

2.1 Tafiya Bazuwar Quantum & Bincike

QRWs sun faɗaɗa ra'ayin tafiya bazuwar zuwa tsarin quantum. Halin mai tafiya quantum yana haɓakawa a cikin sararin Hilbert wanda shine samfurin tensor na sararin matsayi da sararin kwalin (halin ciki). Algorithm na QRWS yana amfani da wannan motsi don nemo alamar node a cikin zane, yana ba da yuwuwar sauri fiye da binciken gargajiya.

2.2 Qudits vs. Qubits

Yayin da yawancin algorithms na quantum ke amfani da qubits (tsarin matakai 2), qudits (tsarin matakai d, d>2) suna ba da fa'idodi masu mahimmanci: haɓakar yawan bayanai a kowace mai ɗaukar kaya, ƙarfin juriya ga wasu ƙofofi, da yuwuwar haɓaka aikin algorithm, kamar yadda aka gani a cikin daidaitawar algorithms na Grover da Shor.

2.3 Kwalin Tunani na Householder

Ma'aikacin kwalin, wanda ke ba da umarnin alkiblar mai tafiya, an gina shi ta amfani da tunani na gabaɗaya na Householder da aka haɗa tare da mai ninka lokaci. Tunani na Householder, wanda aka ayyana don vector naúrar $|u\rangle$ kamar $H = I - 2|u\rangle\langle u|$, an faɗaɗa shi don qudits. Wannan hanyar tana ba da hanya mai inganci da ma'auni don gina ayyukan unitary na sabani don tsarin manyan girma idan aka kwatanta da jerin jujjuyawar Givens.

3. Hanyoyi & Haɗin Koyon Injin

3.1 Gina Algorithm

Algorithm na QRWS da aka yi nazari yana amfani da qudit guda ɗaya a matsayin rajistar kwalin. Matakin tafiya haɗaɗɗe ne na ma'aikacin kwalin na tushen Householder $C(h, \vec{\theta})$—wanda aka ƙayyade ta hanyar lokaci $h$ da vector na kusurwoyi $\vec{\theta}$—da ma'aikacin motsi wanda ke motsa mai tafiya tsakanin nodes na zane bisa ga halin kwalin.

3.2 Ingantaccen Ƙarfi ta hanyar ML

Don yaƙar hankali ga gazawa a cikin sigogin kwalin (misali, daga sarrafa laser mara daidaituwa a cikin tarkon ion), marubutan suna amfani da tsarin haɗin gwiwa. Simulashin Monte Carlo yana samar da bayanai kan aikin algorithm (misali, yuwuwar nasara) a ƙarƙashin karkatar da sigogi. Wannan bayanan yana horar da cibiyar sadarwar jijiya mai zurfi (DNN) don koyon alaƙa tsakanin sigogin kwalin (girma $d$, $h$, $\vec{\theta}$) da ƙarfin algorithm. DNN ɗin da aka horar daga nan yana hasashen mafi kyawun saiti na sigogi masu ƙarfi don girma na qudit na sabani.

Ma'aunin Ingantawa na Asali

Yuwuwar Nasarar Algorithm a ƙarƙashin hayaniyar sigogi $\delta$: $P_{success}(\vec{\theta}_0 + \delta)$

Shigarwar Model na ML

Girman Qudit $d$, sigogi na yau da kullun $\vec{\theta}_0$, samfurin hayaniya.

Fitarwar Model na ML

Hasashen mafi kyawun sigogi $\vec{\theta}_{opt}$ don matsakaicin $\mathbb{E}[P_{success}]$.

4. Sakamako & Nazari

4.1 Binciken Simulashin Monte Carlo

Simulashin ya nuna cewa aikin QRWS na yau da kullun yana raguwa sosai tare da ƙananan karkata a cikin sigogin kwalin na Householder. Duk da haka, an gano takamaiman yankuna a cikin babban sararin sigogi inda yuwuwar nasarar algorithm ɗin ta kasance mai girma ko da tare da hayaniyar da aka gabatar, yana nuna ƙarfin asali don wasu daidaitawar kwalin.

4.2 Hasashen Cibiyar Sadarwar Jijiya

DNN ɗin da aka horar ya yi nasarar zana ƙasar sigogi mai sarƙaƙiya. Zai iya hasashen sigogin kwalin masu ƙarfi don girma na qudit waɗanda ba a gan su a fili yayin horo ba. "Kwaloli masu ƙarfi mafi kyau" da aka hasashen sun nuna ƙasa madaidaiciya, mafi faɗin kololuwa a cikin yuwuwar nasara a kusa da sigogi na yau da kullun idan aka kwatanta da kwalolin da ba a inganta su ba, yana tabbatar da haɓakar juriya ga kurakurai.

Fassarar Taswira (Ra'ayi): Zanen 3D zai nuna Yuwuwar Nasarar Algorithm (Z-axis) akan manyan sigogin kwalin guda biyu (X & Y axes). Don kwalin na yau da kullun, saman yana nuna kololuwa mai kaifi, kunkuntar. Ga kwalin mai ƙarfi na ML da aka inganta, kololuwar tana da ƙasa a tsayin matsakaici amma mafi faɗi da madaidaiciya, yana nuna ci gaba da aiki a kan yanki mafi girma na sigogi.

5. Zurfin Fasaha

An ayyana ma'aikacin kwalin na asali kamar haka: $$C(h, \vec{\theta}) = \Phi(h) \cdot H(\vec{\theta})$$ inda $\Phi(h) = \text{diag}(e^{i\phi_0}, e^{i\phi_1}, ..., e^{i\phi_{d-1}})$ shine mai ninka lokaci kuma $H(\vec{\theta})$ shine tunani na gabaɗaya na Householder. Don vector naúrar $|u(\vec{\theta})\rangle$ a cikin sararin qudit, $H = I - 2|u\rangle\langle u|$. Sigogin $\vec{\theta}$ suna ayyana abubuwan $|u\rangle$. Ana auna aikin algorithm ɗin bincike ta yuwuwar gano alamar node bayan matakai $T$: $P_{success} = |\langle \text{alamar} | \psi(T) \rangle|^2$, inda $|\psi(T)\rangle = (S \cdot (I \otimes C))^T |\psi(0)\rangle$.

6. Tsarin Nazari & Nazarin Lamari

Tsarin Don Tantance Ƙarfi:

  1. Ayyana Samfurin Hayaniya: Kayyade tushen kurakurai na gaske (misali, hayaniyar Gaussian akan $\vec{\theta}$, son zuciya na tsari akan $h$).
  2. Samar da Ƙungiyar da aka Damu: Ƙirƙiri saitin sigogi $N$ $\{\vec{\theta}_i\}$ ta hanyar samfuri daga samfurin hayaniya.
  3. Simulashi & Aunawa: Gudanar da QRWS don kowane $\vec{\theta}_i$ kuma a rubuta $P_{success}(i)$.
  4. Lissafin Ma'aunin Ƙarfi: Lissafin matsakaicin yuwuwar nasara $\bar{P}$ da daidaitaccen karkacewarsa $\sigma_P$ akan ƙungiyar. Babban $\bar{P}$ da ƙananan $\sigma_P$ suna nuna ƙarfi.
  5. Inganta ta hanyar ML: Yi amfani da $\bar{P}$ a matsayin manufa don horar da DNN mai lissafi. DNN yana koyon aikin $f: (d, \vec{\theta}_{nominal}) \rightarrow \bar{P}$.
  6. Tabbatarwa: Gwada hasashen sigogi na DNN akan sabon saitin lamuran hayaniya da girma na qudit da aka ajiye.
Nazarin Lamari (Babu Lamba): Yi la'akari da qudit tare da $d=4$. Kwalin na yau da kullun daga wallafe-wallafen da suka gabata yana ba da $\bar{P}=0.95$ a ƙarƙashin ƙananan hayaniya amma ya faɗi zuwa $\bar{P}=0.65$ a ƙarƙashin karkatar da sigogi na 5%. Aiwatar da tsarin ML, an sami sabon saitin sigogi. Yayin da kololuwar $P_{success}$ a hayaniyar sifili ya kasance $0.92$, a ƙarƙashin karkatar da 5% iri ɗaya, $\bar{P}$ ya kasance a $0.88$, yana nuna mafi kyawun amfani a zahiri a cikin yanayi mai hayaniya.

7. Aikace-aikace na Gaba & Jagorori

  • Na'urorin Quantum na ɗan Gajeren Lokaci: Aikace-aikace kai tsaye a cikin tsarin tarkon ion ko na hoto ta amfani da qudits, inda kurakuran sarrafawa suka yawaita. Wannan hanyar na iya sa algorithms na QRWS su yi aiki a kan kayan aikin da ba su da kyau na yanzu.
  • Rage Kuskuren Sanin Algorithm: Matsawa bayan gyaran kuskure na gabaɗaya don haɗa kai algorithms tare da ƙarfin asali, falsafar da ta dace da mayar da hankali na Ƙaddamarwar Quantum ta Amurka akan "Algorithms masu Juriya ga Hayaniya."
  • Faɗaɗawa zuwa Sauran Tafiyar Quantum: Aiwatar da tsarin ML-don-ƙarfi ga tafiya quantum na ci gaba da lokaci ko tafiya akan zane-zane masu sarƙaƙiya (misali, hanyoyin sadarwa masu matsayi).
  • Haɗin kai tare da Sauran Dabarun ML: Yin amfani da koyon ƙarfafawa don daidaita sigogi a hankali yayin aiwatar da algorithm bisa ga amsawar aikin na ainihin lokaci.
  • Ƙirar Algorithm na Quantum mai Faɗi: Hanyar tana kafa misali don amfani da ML na gargajiya don gano ƙayyadaddun sigogi na sauran algorithms na quantum da aka ƙayyade (PQAs), kamar Masu Magance Eigensolvers na Bambance-bambancen Quantum (VQEs) ko Cibiyoyin Sadarwar Jijiya na Quantum.

8. Nassoshi

  1. Ambainis, A. (2003). Tafiya quantum da aikace-aikacen su na algorithm. International Journal of Quantum Information.
  2. Childs, A. M., et al. (2003). Saurin algorithm na exponential ta hanyar tafiya quantum. STOC '03.
  3. Kempe, J. (2003). Tafiya bazuwar quantum - bayani na gabatarwa. Contemporary Physics.
  4. Cibiyar Ƙididdiga da Fasaha ta Ƙasa (NIST). (2023). Gidan Algorithm na Quantum. [Kan layi]
  5. Preskill, J. (2018). Kwakwalwan kwamfuta na Quantum a zamanin NISQ da bayansa. Quantum.
  6. Biamonte, J., et al. (2017). Koyon injin quantum. Nature.
  7. Wang, Y., et al. (2020). Canjin Gidan Quantum. Physical Review A.
  8. Tonchev, H., & Danev, P. (2023). [Aikin da ya gabata da aka ambata a cikin PDF].

9. Nazarin Kwararru & Zargi

Zurfin Fahimta: Wannan takarda ba kawai game da kwalin tafiya quantum mafi kyau ba ne; yana da juyi na dabarun ƙira a cikin ƙirar algorithm na quantum don zamanin Quantum Matsakaici mai Hayaniya (NISQ). Marubutan sun gano daidai cewa gyaran kuskuren quantum mai ƙarfi ba zai yiwu ba don na'urorin ɗan gajeren lokaci kuma a maimakon haka suna ba da shawarar dabarun haɗin gwiwa: saka ƙarfi kai tsaye cikin sigogin algorithm ɗin ta amfani da Koyon Injin na gargajiya a matsayin kayan gano. Wannan yayi daidai da falsafar da ke bayan dabarun kamar CycleGAN ta amfani da asarar daidaiton zagaye don fassarar hoto mara biyu—a maimakon tilasta cikakkiyar taswira ta mataki ɗaya, kuna tsara matsalar koyo don nemo mafita masu tsayayye. Amfani da tunanin Householder don ƙofofin qudit yana da hikima, saboda sun fi asali da inganci don tsarin manyan girma fiye da rarrabuwa zuwa ƙofofin qubit, yana rage zurfin da'ira na asali da yuwuwar tarin kuskure.

Kwararar Ma'ana: Ma'ana tana da ban sha'awa: 1) Qudits suna ba da iyawa da fa'idodin hayaniya amma suna buƙatar sarrafawa daidai. 2) Kwalolin Householder suna da ƙarfi amma suna da hankali ga sigogi. 3) Saboda haka, bari mu yi amfani da ML don bincika babban sararin sigogi don yankunan da suke da ƙarfi a asali maimakon kawai kololuwa (mafi kyau a cikin yanayi masu kyau). Haɗin tsakanin simulashin Monte Carlo (samar da "ƙasar hayaniya") da koyo mai kulawa (koyon yanayinsa) yana da hujja da amfani.

Ƙarfi & Aibobi: Ƙarfi: Hanyar haɗin quantum-gargajiya ita ce babban kadarta, tana amfani da ƙididdiga na gargajiya don magance matsalar da ba za a iya warwarewa ga nazarin quantum mai tsafta ba. Yana da amfani sosai ga aikace-aikacen NISQ. Mayar da hankali kan ƙarfin algorithm, maimakon kawai kololuwar aiki, ya dace da ƙuntatawa na zahiri da masu bincike kamar John Preskill suka haskaka.
Aibobi: Takarda mai yiwuwa ta yi watsi da "farashin ƙarfi." Kololuwar aiki madaidaiciya, mafi faɗi sau da yawa yana nufin ƙananan yuwuwar nasara. Menene ciniki? Shin faɗuwar 10% a cikin aikin da ya dace ya cancanci haɓakar juriya na 300%? Wannan yana buƙatar ƙididdiga a fili. Bugu da ƙari, sarƙaƙiyar samfurin ML da buƙatun bayanan horo sun zama sabon kaya. Shin DNN zai buƙaci sake horo don kowane sabon yanayin zane ko samfurin hayaniya? Hanyar tana da haɗarin zama ta musamman ga matsala.

Hanyoyin Aiki: Ga masu haɓaka algorithm na quantum, abin da za a ɗauka a bayyane yake: fara gina ƙarfi a matsayin ɗan ƙasa na farko a cikin ma'aunin ƙirarku, ba abin da za a yi tunani bayan haka ba. Yi amfani da kayan aikin simulashi da ML da wuri a cikin zagayen ƙira don nemo bambance-bambancen algorithm masu tsayayye a asali. Ga ƙungiyoyin kayan aiki, wannan aikin yana jaddada buƙatar samar da daidaitaccen sarrafawa, mai kyau a kan sigogin qudit—ML ɗin zai iya inganta abin da kayan aikin zasu iya daidaitawa da aminci. Mataki na gaba na ma'ana shine buɗe tsarin simulashi da horo, yana ba da damar al'umma su gwada wannan hanyar akan tarin algorithms, daga VQE zuwa QAOA, ƙirƙirar ɗakin karatu na "ƙarfafa" aikin quantum. Wannan zai iya hanzarta hanyar zuwa fa'idar quantum mai amfani fiye da neman ƙididdiga na qubit mafi girma kaɗai.