1. Gabatarwa & Bayyani

Wannan takarda ta gabatar da wata hanya mai ban mamaki ga binciken na'urar lura ta quantum (QDT) ta hanyar amfani da kwamfuta mai ƙarfi (HPC). Babban ƙalubalen da aka magance shi ne tantance manyan tsarin quantum, kamar na'urorin lura na haske da ake amfani da su a cikin tsarin ƙididdiga na quantum kamar samfurin Boson. Yayin da waɗannan tsarin suke ƙaruwa, tabbatarwa ta al'ada ta zama mai wahala a lissafa. Marubutan sun nuna cewa, duk da cewa cikakken simintin quantum na iya zama ba zai yiwu ba, ana iya sake amfani da HPC don "mai sauƙi" amma har yanzu babban aikin sake gina tomographic, yana ba da bayanin quantum-mechanical mai daidai na na'urar lura.

Aikin ya cimma sake gina na'urar lura ta haske ta quantum mai girma wacce ta rufe sararin Hilbert na $10^6$, wanda ya haɗa da tantance abubuwa $10^8$ na Ma'aunin Ƙimar Ma'aikacin Mai Kyau (POVM) na na'urar lura. An cimma wannan a cikin mintuna kaɗan na lokacin lissafi ta hanyar amfani da tsarin matsala ta musamman da kuma cimma ingantacciyar daidaitawa ta layi daya.

2. Tsarin Aiki na Asali & Tsarin Fasaha

Hanyar tana haɗa ka'idar bayanai ta quantum da kimiyyar lissafi.

2.1 Tushen Binciken Na'urar Lura ta Quantum

QDT tana nufin sake gina jerin POVMs ${ \pi_n }$ waɗanda ke bayyana cikakken na'urar aunawa ta quantum. Ana yin haka ta hanyar bincika na'urar lura tare da cikakken jerin jihohin shigarwa na tomographic waɗanda suka rufe sararin sakamakonsa. Girman matsalar sake ginawa yana ƙaruwa kamar $M^2 \cdot N$, inda $M$ shine girman sararin Hilbert na shigarwa kuma $N$ shine adadin sakamakon aunawa. Ga $M$ mai girma, wannan yana haifar da sararin sigogi mai yawa sosai.

2.2 Haɗa Kwamfuta Mai Ƙarfi

Babban ƙirƙira shine haɓaka algorithms na buɗe tushe na al'ada waɗanda aka tsara don tsarin HPC. Takardar ta jaddada cewa dabarun daidaitawa na gaba ɗaya sau da yawa suna kasawa don tomography na quantum saboda takamaiman tsari da ƙuntatawa na matsalar ingantawa (misali, kiyaye tabbataccen da cikakken POVM). Algorithms na marubutan an keɓance su don amfani da wannan tsari, yana ba da damar rarraba nauyin lissafi cikin inganci a cikin dubunnan ƙwayoyin CPU.

2.3 Tsarin Lissafi & Tsarin Matsala

Ana tsara sake ginawa a matsayin matsalar ingantawa mai ƙuntatawa: rage nisan tsakanin yuwuwar gwaji da tsinkayar samfurin, bisa ga ƙuntatawa cewa $\pi_n \geq 0$ (tabbatacce) da $\sum_n \pi_n = I$ (cikakke). Takardar ta nuna alamar amfani da yalwa ko daidaito a cikin POVM don wani nau'in na'urar lura na musamman (misali, na'urar lura mai ƙididdigar adadin photon) don rage girman matsala mai tasiri da kuma ba da damar daidaitawa mai inganci.

3. Sakamakon Gwaji & Aiki

Sararin Hilbert da Aka Sake Gina

$10^6$

Abubuwan POVM da Aka Ƙaddara

$10^8$

Lokacin Lissafi

Mintuna

Girman da Ake Hasashen

$10^{12}$ abubuwa

3.1 Sake Gina Na'urar Lura Mai Girma

Babban sakamako shine nasarar tomography na na'urar lura tare da girman sararin Hilbert na miliyan daya ($M=10^6$). Wannan yayi daidai da sake gina POVM tare da sigogi masu zaman kansu miliyan ɗari ($10^8$). Takardar tana nuna cewa an yi wannan akan samfurin na'urar lura da aka yi siminti ko ma'auni, kamar yadda ake buƙatar sake gina na'urar lura ta zahiri ta wannan girma da cikakken jerin jihohin bincike masu girma da ba za su yiwu ba.

3.2 Ingantacciyar Ƙididdiga & Girma

Mafi ban sha'awa sakamako shine kusan cikakkiyar daidaitawa ta layi daya da aka cimma. Algorithms sun nuna ƙaramin nauyin sadarwa tsakanin nodes na lissafi, yana ba da damar rarraba matsala kusan bisa son rai. Wannan dokar girma ita ce tushen hasashen takardar: hanyar, bisa ka'ida, na iya sake gina abubuwan quantum har zuwa $10^{12}$ abubuwan POVM. "Mintuna na lokacin lissafi" don matsalar abubuwa $10^8$ yana nuna amfani da babban tarin HPC.

Bayanin Jadawali (An fayyace): Wata jadawali mai yiwuwa tana nuna ƙarfi mai ƙarfi (rage lokacin magance matsala tare da ƙara adadin ƙwayoyin) da rauni mai rauni (iyawar magance manyan matsaloli ta hanyar ƙara ƙarin ƙwayoyin) don algorithm na tomography. Lankwasa za ta kasance kusa da ingantacciyar daidaitawa ta layi daya, yana nuna ingantacciyar daidaitawa ta layi daya.

4. Muhimman Bayanai & Ra'ayi na Manazarta

Bayanin Asali

Wannan takarda ba kawai game da saurin tomography ba ce; juyawa ce mai dabara a cikin mu'amalar quantum-classical. Marubutan sun gano daidai cewa, duk da cewa simintin manyan tsarin quantum yana da wahala a al'ada, tantance su ta hanyar tomography ana iya jefa su a matsayin matsala ta "kawai" babban girman ingantaccen lamba—wani yanki inda HPC na al'ada ya yi fice. Wannan yana sake tsara HPC daga mai fafatawa zuwa mai ba da dama mai mahimmanci don tabbatar da fa'idar quantum, wani batu da misalin samfurin Boson ya jaddada inda haske na al'ada ke ba da damar tantance na'ura. Yana da wayo a kusa da cikakkiyar matsalar siminti.

Kwararar Hankali

Hujjar tana da inganci amma ta dogara ne akan wani muhimmin zato, wanda sau da yawa ake wucewa: kasancewar cikakken jerin jihohin bincike na tomographic a matakin girma. Samarwa da sarrafa jihohin quantum daban-daban $10^6$ a cikin gwaji babban aiki ne da kansa, wanda za a iya cewa yana da wahala kamar lissafin da suke son tabbatarwa. Takardar ta warware matsalar ƙididdiga cikin hazaka amma a hankali ta sauke rikitarwar gwaji. Wannan yayi daidai da ƙalubale a cikin koyon inji na al'ada inda, kamar yadda aka lura a cikin albarkatun kamar Google's AI Blog, samun bayanai da tsarawa sau da yawa suka zama abin da ke takura bayan nasarorin algorithm.

Ƙarfi & Kurakurai

Ƙarfi: Girman da aka nuna na musamman ne kuma yana ba da taswirar hanya bayyananne. Al'amarin buɗe tushe yana da yabo don sake yin samfuri. Mayar da hankali kan sake ginawa na POVM ya fi kawai daidaita sakamako mahimmanci, yana ba da samfurin quantum-mechanical mai zurfi.

Kurakurai: "Girma" nunin ya bayyana a matsayin ma'auni na lissafi akan samfurin na'urar lura, ba na zahiri ba. Tsalle zuwa aikace-aikace na zahiri don tabbatarwa, a ce, samfurin Boson na photon 50 yana da girma. Hanyar kuma tana ɗauka cewa tsarin na'urar lura yana ba da damar amfani da daidaiton da aka yi amfani da su; na'urar lura gaba ɗaya ta son rai, mara tsari bazata ga irin wannan ribar inganci ba.

Bayanai Masu Aiki

Ga kamfanonin kayan aikin quantum: Ku saka hannun jari a cikin haɗin gwiwa tsakanin ƙungiyoyin ku na kimiyyar lissafi da HPC. Keɓance algorithms na tantancewa zuwa takamaiman tsarin kayan aikin ku, kamar yadda aka yi a nan, fa'ida ce ta gasa ta zahiri. Ga hukumomin ba da kuɗi: Wannan aikin yana tabbatar da kuɗi a mahadar bayanin quantum da babban kwamfuta na al'ada. Shirye-shirye kamar waɗanda ke ofishin NSF's Office of Advanced Cyberinfrastructure ko EU's EuroHPC, waɗanda ke haɗa waɗannan fagagen, suna da mahimmanci. Mataki na gaba shine haɗa wannan tsarin lissafi tare da masu samar da jihar quantum ta atomatik, mai shirye-shirye don magance ƙalubalen jihar bincike kai tsaye.

5. Cikakkun Bayanai na Fasaha & Tsarin Lissafi

Ana iya tsara babbar matsalar lissafi ta QDT kamar haka:

Idan aka ba da jerin jihohin bincike $\rho_i$ da kuma yuwuwar gwaji mai dacewa $p_{n|i}$ na samun sakamako $n$ don jihar $i$, nemo abubuwan POVM $\pi_n$ waɗanda ke rage aikin yuwuwar, sau da yawa mara kyau log-yuwuwar:

$$ \mathcal{L}(\{\pi_n\}) = -\sum_{i,n} f_{n|i} \log\left(\text{Tr}(\rho_i \pi_n)\right) $$ bisa ga ƙuntatawa: $$ \pi_n \geq 0 \quad \forall n, \quad \text{da} \quad \sum_n \pi_n = I $$ inda $f_{n|i}$ suke mitocin da aka lura. Gudunmawar HPC ta takardar ta ta'allaka ne a magance wannan babban matsalar ingantawa mai ƙuntatawa ta hanyar rarraba ta cikin tsarin $\pi_n$ ko ma'anar $i$, yana ba da damar sabuntawa ta layi daya yayin kiyaye ƙuntatawa.

6. Tsarin Nazari: Nazarin Lamari na Ra'ayi

Yanayi: Tantance cibiyar sadarwar haske ta layi 100 (ɗan takarar samfurin Boson) ta amfani da banki na na'urorin lura masu ƙididdigar adadin photon.

Aiwatar da Tsarin:

  1. Girman Matsala: Kowane yanayi na iya riƙe har zuwa, a ce, photon 2. Sararin Hilbert kowane yanayi shine girma 3 (0,1,2 photon). Ga yanayi 100, jimillar girman sararin Hilbert shine $3^{100} \approx 10^{48}$—ba za a iya magance shi ba. Duk da haka, na'urar lura na iya warwarewa har zuwa jimillar $K$ photon a cikin dukkan yanayi. Idan $K=20$, girman sararin Hilbert mai dacewa ana bayar da shi ta hanyar yadda ake rarraba photon 20 a cikin yanayi 100, wanda shine $\binom{100+20-1}{20} \approx 10^{23}$—har yanzu babba amma an tsara shi.
  2. Amfani da Tsari: POVM don irin wannan na'urar lura yana da daidaito a ƙarƙashin musanya yanayi (idan na'urorin lura iri ɗaya ne). Wannan daidaito yana rage adadin sigogi masu zaman kansu sosai. Maimakon sigogi $\sim (10^{23})^2$, mutum yana buƙatar sake gina POVM don tsarin adadin photon har zuwa musanya, ƙaramin saiti ne.
  3. Rarraba HPC: Ana iya daidaita ingantawa ta hanyar sanya nau'ikan sararin samaniya daban-daban na tsarin adadin photon ko tubalan daban-daban na ma'anar jihar bincike $i$ zuwa ƙwayoyin CPU daban-daban. Ƙuntatawar daidaito tana aiki azaman wurin daidaitawa na duniya.
  4. Tabbatarwa: Yi amfani da POVM da aka sake gina don hasashen sakamako don sanannun jihohin al'ada (masu haɗin kai) da kwatanta tare da sabbin bayanan gwaji, tabbatar da daidaiton samfurin.

7. Ayyukan Gaba & Hanyoyin Bincike

  • Tabbatar da Fa'idar Quantum: Babban aikace-aikacen shine samar da ingantattun hanyoyi masu girma don tantance na'urorin lura a cikin na'urorin samfurin quantum, mataki mai mahimmanci a cikin jayayya don fa'idar ƙididdiga ta quantum a kan yaudarar al'ada.
  • Haɗawa tare da Rage Kuskure: Ingantattun samfuran na'urar lura suna da mahimmanci ga dabarun rage kuskure na ci gaba a cikin ƙididdiga ta quantum. Wannan tomography na tushen HPC zai iya samar da ingantattun samfuran da ake buƙata.
  • Bayan Haske: Aiwatar da irin waɗannan hanyoyin HPC masu tsari zuwa tomography na jerin qubit superconducting ko sarkar ion da aka kama.
  • Haɗin gwiwar Koyon Injin: Haɗawa tare da wakilcin hanyoyin sadarwa na jijiyoyi na jihohin quantum (kamar yadda aka bincika a cikin ayyuka kamar "Quantum Model Learning Agent") don sarrafa tsarin masu canzawa ci gaba ko bayanai masu hayaniya.
  • Tantancewa na Ainihi-Lokaci: Matsawa zuwa daidaitawa a kan tashi na na'urorin lura a cikin manyan gwaje-gwajen quantum, ta amfani da albarkatun HPC na keɓaɓɓu.
  • Daidaituwa: Wannan aikin zai iya haifar da daidaitattun ka'idojin tomography masu girma waɗanda masana'antar quantum ta karɓa, kamar yadda ake amfani da ma'aunin Linpack a cikin HPC na al'ada.

8. Nassoshi

  1. Schapeler, T., Schade, R., Lass, M., Plessl, C., & Bartley, T. J. Scalable quantum detector tomography by high-performance computing. arXiv:2404.02844 (2024).
  2. Aaronson, S., & Arkhipov, A. The computational complexity of linear optics. Proceedings of the 43rd annual ACM symposium on Theory of computing, 333–342 (2011).
  3. Lund, A. P., et al. Boson sampling from a Gaussian state. Physical Review Letters, 113, 100502 (2014).
  4. Lvovsky, A. I., & Raymer, M. G. Continuous-variable optical quantum-state tomography. Reviews of Modern Physics, 81, 299 (2009).
  5. Altepeter, J. B., et al. Ancilla-assisted quantum process tomography. Physical Review Letters, 90, 193601 (2003).
  6. Google AI Blog. "The Unreasonable Effectiveness of Data." (An shiga don kwatanta kan ƙalubalen bayanai da algorithm).
  7. National Science Foundation. Office of Advanced Cyberinfrastructure. (Don mahallin shirye-shiryen ba da kuɗi na HPC).
  8. Isola, P., et al. Image-to-Image Translation with Conditional Adversarial Networks (CycleGAN). CVPR (2017). (An ambata a matsayin misalin ci gaban algorithm na musamman na yanki).