Quantum computers thiab quantum xam - tshiab , uas tau ntxiv rau peb cov ntaub ntawv chaw nrog rau , thiab lwm cov ntsiab lus high-tech. Nyob rau tib lub sijhawm, kuv yeej tsis tuaj yeem nrhiav cov ntaub ntawv hauv Is Taws Nem uas yuav muab tso ua ke rau hauv kuv lub taub hau hu ua "Yuav ua li cas quantum computers ua haujlwm". Yog lawm, muaj ntau yam haujlwm zoo heev, suav nrog ntawm Habr (saib. ), cov lus uas, raws li feem ntau cov ntaub ntawv, yog ntau tshaj qhia thiab muaj txiaj ntsig, tab sis daim duab hauv kuv lub taub hau, raws li lawv hais, tsis ntxiv.
Thiab tsis ntev los no kuv cov npoj yaig tuaj rau kuv thiab nug tias, "Koj puas nkag siab tias quantum computer ua haujlwm li cas? Koj puas tuaj yeem qhia peb? Thiab tom qab ntawd kuv pom tau hais tias kuv tsis yog tib tus uas muaj teeb meem nrog kev sib koom ua ke ib daim duab sib txuas hauv kuv lub taub hau.
Yog li ntawd, ib qho kev sim tau ua los sau cov ntaub ntawv hais txog quantum computers rau hauv ib qho kev sib txuas lus sib xws uas theem pib, tsis muaj qhov tob tob hauv kev ua lej thiab cov qauv ntawm lub ntiaj teb quantum, nws tau piav qhia tias lub khoos phis tawj quantum yog dab tsi, lub hauv paus ntsiab lus nws ua haujlwm li cas, thiab cov teeb meem dab tsi uas cov kws tshawb fawb ntsib thaum tsim thiab ua haujlwm.
Cov txheej txheem
Tsis lees paub
Tus sau tsis yog tus kws tshaj lij hauv quantum xam, thiab Cov neeg tuaj saib lub hom phiaj ntawm tsab xov xwm yog tib cov neeg IT, tsis yog cov kws tshaj lij quantum, leej twg kuj xav muab ib daim duab tso rau hauv lawv lub taub hau hu ua "Quantum computers ua haujlwm li cas." Vim li no, ntau lub ntsiab lus hauv tsab xov xwm yog txhob txwm ua kom yooj yim kom nkag siab zoo dua quantum technologies ntawm qib "basic", tab sis tsis muaj. .
Cov ntawv hauv qee qhov chaw siv cov ntaub ntawv los ntawm lwm qhov chaw, . Txhua qhov uas ua tau, cov kev sib txuas ncaj qha thiab cov lus qhia rau cov ntawv qub, lub rooj lossis daim duab raug tso. Yog hais tias kuv tsis nco qab ib yam dab tsi (los yog ib tug neeg) qhov twg, sau ntawv thiab kuv mam li kho nws.
Taw qhia
Nyob rau hauv tshooj no, peb yuav luv luv saib yuav ua li cas lub quantum era pib, dab tsi yog qhov kev txhawb siab rau lub tswv yim ntawm quantum computer, leej twg (lub teb chaws twg thiab cov tuam txhab) tam sim no yog cov thawj coj hauv daim teb no, thiab kuj tham luv luv. hais txog cov lus qhia tseem ceeb ntawm txoj kev loj hlob ntawm quantum xam.
Nws pib li cas
Lub sijhawm pib ntawm quantum era yog suav tias yog xyoo 1900, thaum M. Planck thawj zaug tso rau pem hauv ntej. hais tias lub zog yog emitted thiab absorbed tsis tu ncua, tab sis nyob rau hauv cais quanta (ib feem). Lub tswv yim tau khaws thiab tsim los ntawm ntau tus kws tshawb fawb zoo ntawm lub sijhawm ntawd - Bohr, Einstein, Heisenberg, SchrΓΆdinger, uas thaum kawg coj mus rau kev tsim thiab kev loj hlob ntawm xws li kev tshawb fawb. . Muaj ntau cov ntaub ntawv zoo hauv Is Taws Nem hais txog kev tsim quantum physics raws li kev tshawb fawb; hauv tsab xov xwm no peb yuav tsis nyob ntawm qhov no kom meej, tab sis nws yuav tsum tau qhia txog hnub thaum peb nkag mus rau quantum era tshiab.
Quantum physics tau coj ntau yam kev tsim kho thiab thev naus laus zis rau hauv peb lub neej niaj hnub, tsis muaj qhov tam sim no nyuaj rau xav txog lub ntiaj teb nyob ib puag ncig peb. Piv txwv li, ib lub laser, uas tam sim no siv nyob txhua qhov chaw, los ntawm cov khoom siv hauv tsev (laser qib, thiab lwm yam) mus rau high-tech systems (lasers rau kho qhov muag, nyob zoo. ). Nws yuav yog qhov xav tau los xav tias tsis ntev los sis tom qab ib tug neeg yuav los nrog lub tswv yim tias vim li cas ho tsis siv quantum systems rau xam. Thiab ces nyob rau hauv 1980 nws tshwm sim.
Wikipedia qhia tias thawj lub tswv yim ntawm quantum xam tau nthuav tawm hauv xyoo 1980 los ntawm peb tus kws tshawb fawb Yuri Manin. Tab sis lawv yeej pib tham txog nws tsuas yog nyob rau hauv 1981, thaum tus paub zoo R. Feynman , sau tseg tias nws yog tsis yooj yim sua kom simulate evolution ntawm ib tug quantum system ntawm ib tug classical computer nyob rau hauv ib tug npaum txoj kev. Nws tau npaj ib qho qauv tsim , uas yuav muaj peev xwm ua tau xws li qauv.
Muaj ib , nyob ntawd yog suav hais tias ntau dua kev kawm thiab nthuav dav, tab sis peb yuav dhau mus luv luv:
Cov ntsiab lus tseem ceeb hauv keeb kwm ntawm kev tsim quantum computers:
- [1994]. P. Nkoj. Tsim los ntawm
- [1998]. Tsim
- [2001]. IBM tau qhia txog kev ua tiav rau expansion ntawm tus lej 15
- [2007-2016]. tsim thiab tsim lub computer nrog 128-2000 qubits
- [2012]. Ua tiav hauv University of California
- [2016]. Google ntawm 9-qubit computer
- [2017]. (peb atoms)
- [2019]. . 20-qubit computer hauv huab
- [2019]. . 53 qub computer. ?
Raws li koj tuaj yeem pom, 17 xyoo dhau los (los ntawm 1981 txog 1998) los ntawm lub sijhawm ntawm lub tswv yim mus rau nws thawj qhov kev siv hauv computer nrog 2 qubits, thiab 21 xyoo (los ntawm 1998 txog 2019) mus txog rau thaum cov qubits tau nce mus rau 53. Nws siv sijhawm 11 xyoo (los ntawm 2001 txog 2012) los txhim kho cov txiaj ntsig ntawm Shor's algorithm (peb mam li saib nws kom ntxaws me ntsis tom qab) los ntawm tus lej 15 mus rau 21. Tsis tas li ntawd, tsuas yog peb xyoos dhau los peb tuaj txog ntawm qhov chaw. ua raws li qhov Feynman tham txog, thiab kawm ua qauv ntawm lub cev yooj yim tshaj plaws.
Kev loj hlob ntawm quantum xam yog qeeb. Cov kws tshawb fawb thiab cov kws tshaj lij tau ntsib nrog cov haujlwm nyuaj heev, lub xeev quantum muaj lub neej luv luv thiab tsis yooj yim, thiab txhawm rau khaws cia lawv ntev txaus los ua kev suav, lawv yuav tsum tsim sarcophagi rau kaum lab nyiaj daus las, nyob rau hauv qhov kub thiab txias. tsuas yog saum toj kawg nkaus xoom, thiab uas muaj kev tiv thaiv ntau tshaj plaws los ntawm kev cuam tshuam sab nraud. Tom ntej no peb yuav tham txog cov haujlwm thiab cov teeb meem no kom ntxaws ntxiv.
Leading Players
Cov slides rau seem no yog muab los ntawm kab lus , los ntawm tus kws tshawb fawb Alexey Fedorov. Cia kuv muab cov lus qhia ncaj qha rau koj:
Txhua lub teb chaws muaj kev vam meej technology tam sim no nquag tsim quantum technologies. Muaj nyiaj ntau tau nqis peev rau hauv qhov kev tshawb fawb no, thiab cov kev pabcuam tshwj xeeb los txhawb quantum technologies raug tsim.
Tsis tsuas yog xeev, tab sis kuj tseem cov tuam txhab ntiag tug tau koom nrog kev sib tw quantum. Nyob rau hauv tag nrho, Google, IBM, Intel thiab Microsoft tsis ntev los no tau nqis peev txog $ 0,5 nphom hauv kev txhim kho quantum computers thiab tsim cov chaw soj ntsuam loj thiab chaw tshawb fawb.
Muaj ntau cov ntawv hauv Habre thiab hauv Is Taws Nem, piv txwv li, , ΠΈ , nyob rau hauv uas tam sim no lub xeev ntawm affairs nrog rau txoj kev loj hlob ntawm quantum technologies nyob rau hauv txawv teb chaws yog soj ntsuam nyob rau hauv ntau yam. Qhov tseem ceeb tshaj plaws rau peb tam sim no yog tias txhua tus thawj coj thev naus laus zis tsim lub teb chaws thiab cov neeg ua si tau nqis peev ntau ntawm cov nyiaj hauv kev tshawb fawb hauv qhov kev taw qhia no, uas ua rau muaj kev cia siab rau txoj hauv kev tawm ntawm txoj kev tsis txaus ntseeg tam sim no.
Cov lus qhia kev txhim kho
Lub sijhawm no (Kuv tuaj yeem ua yuam kev, thov kho kuv), kev siv zog tseem ceeb (thiab ntau dua lossis tsawg dua cov txiaj ntsig tseem ceeb) ntawm txhua tus thawj coj tau tsom mus rau ob qhov chaw:
- Tshwj xeeb quantum computers, uas yog tsom rau kev daws ib qho teeb meem tshwj xeeb, piv txwv li, ib qho teeb meem optimization. Ib qho piv txwv ntawm cov khoom yog D-Wave quantum computers.
- Universal quantum computers - uas muaj peev xwm ntawm kev siv quantum algorithms arbitrary (Shor, Grover, thiab lwm yam). Kev nqis tes ua los ntawm IBM, Google.
Lwm cov vectors ntawm kev loj hlob uas quantum physics muab rau peb, xws li:
- ua lub hauv paus rau
- thiab ntau ntxiv
Tau kawg, nws kuj yog nyob rau hauv cov npe ntawm thaj chaw rau kev tshawb fawb, tab sis tam sim no zoo li tsis muaj ntau lossis tsawg dua qhov tseem ceeb.
Tsis tas li ntawd koj tuaj yeem nyeem tau zoo, google"", Piv txwv li, , ΠΈ .
Cov hauv paus. Quantum object thiab quantum systems
Qhov tseem ceeb tshaj plaws kom nkag siab los ntawm ntu no yog qhov ntawd
Quantum computer (tsis zoo li niaj zaus) siv raws li cov ntaub ntawv nqa quantum khoom, thiab kom ua tiav kev suav, quantum khoom yuav tsum tau txuas nrog quantum system.
Dab tsi yog quantum object?
Quantum khoom - ib yam khoom ntawm microworld (quantum world) uas nthuav tawm cov khoom quantum:
- Nws muaj ib lub xeev txhais nrog ob tug ciam teb theem
- Nws yog nyob rau hauv ib tug superposition ntawm nws lub xeev mus txog rau thaum lub sij hawm ntawm kev ntsuas
- Entangles nws tus kheej nrog lwm yam khoom los tsim quantum systems
- Txaus siab rau qhov tsis muaj-cloning theorem (ib yam khoom lub xeev tsis tuaj yeem luam tawm)
Cia peb saib ntawm txhua yam khoom kom ntxaws ntxiv:
Muaj ib lub xeev txhais nrog ob theem ciam teb (lub xeev kawg)
Ib qho piv txwv ntawm lub ntiaj teb tiag tiag yog npib. Nws muaj lub xeev "sab", uas yuav siv sij hawm ntawm ob theem ciam teb - "taub hau" thiab "tails".
Nws yog nyob rau hauv ib tug superposition ntawm nws lub xeev mus txog rau thaum lub sij hawm ntawm kev ntsuas
Lawv pov ib npib, nws ya thiab tig. Thaum nws tig, nws tsis tuaj yeem hais tias nyob rau theem twg ntawm tus ciam teb nws lub xeev "sab" nyob. Tab sis sai li sai tau thaum peb slam nws thiab saib qhov tshwm sim, lub superposition ntawm xeev tam sim ntawd tsoo mus rau hauv ib qho ntawm ob lub xeev ciam teb - "lub taub hau" thiab "tails". Slapping ib npib hauv peb rooj plaub yog qhov ntsuas.
Entangles nws tus kheej nrog lwm yam khoom los tsim quantum systems
Nws nyuaj nrog npib, tab sis cia peb sim. Xav txog tias peb pov peb lub npib kom lawv tig mus rau ib leeg, qhov no yog juggling nrog npib. Nyob rau txhua lub sijhawm, tsis yog txhua tus ntawm lawv nyob rau hauv lub xeev superposition, tab sis cov xeev no cuam tshuam ib leeg (cov nyiaj npib sib tsoo).
Txaus siab rau qhov tsis muaj-cloning theorem (ib yam khoom lub xeev tsis tuaj yeem luam tawm)
Thaum cov npib ya thiab tig, tsis muaj txoj hauv kev uas peb tuaj yeem tsim ib daim qauv ntawm lub xeev spinning ntawm ib qho ntawm cov nyiaj npib, cais tawm ntawm lub system. Lub kaw lus nyob hauv nws tus kheej thiab khib heev ntawm kev tso tawm cov ntaub ntawv rau lub ntiaj teb sab nraud.
Ob peb lo lus ntxiv txog lub tswvyim nws tus kheej βsuperpositionsβ, nyob rau hauv yuav luag tag nrho cov kab lus superposition yog piav raws li "nyob hauv txhua lub xeev tib lub sijhawm", uas yog, ntawm chav kawm, muaj tseeb, tab sis nyob rau lub sij hawm tsis tsim nyog tsis meej pem. Lub superposition ntawm lub xeev kuj tseem xav txog qhov tseeb tias txhua lub sijhawm ntawm lub sijhawm muaj quantum khoom muaj qee qhov tshwm sim ntawm kev sib tsoo rau hauv txhua theem ntawm nws cov ciam teb, thiab hauv cov ntsiab lus no qhov tshwm sim yog sib npaug li 1. Tom qab ntawd, thaum xav txog qubit, peb yuav nyob ntawm qhov no hauv kev nthuav dav ntxiv.
Rau cov npib, qhov no tuaj yeem pom - nyob ntawm qhov pib ceev, lub kaum sab xis ntawm pov, lub xeev ntawm ib puag ncig uas lub npib ya ya, txhua lub sijhawm nyob rau lub sijhawm qhov tshwm sim tau txais "taub hau" lossis "tails" txawv. Thiab, raws li tau hais ua ntej, lub xeev ntawm cov nyiaj npib ya tuaj yeem xav tias "nyob hauv txhua lub xeev ciam teb tib lub sijhawm, tab sis muaj qhov sib txawv ntawm lawv qhov kev siv."
Txhua yam khoom uas cov khoom saum toj no tau ntsib thiab uas peb tuaj yeem tsim thiab tswj tau tuaj yeem siv los ua cov ntaub ntawv nqa khoom hauv quantum computer.
Ib me ntsis ntxiv peb yuav tham txog cov xwm txheej tam sim no nrog rau kev siv lub cev ntawm qubits li quantum khoom, thiab cov kws tshawb fawb tam sim no siv li cas hauv lub peev xwm no.
Yog li cov cuab yeej thib peb hais tias cov khoom quantum tuaj yeem ua entangled los tsim quantum systems. Dab tsi yog quantum system?
Quantum system - ib qho system ntawm entangled quantum khoom nrog cov khoom hauv qab no:
- Lub quantum system yog nyob rau hauv ib tug superposition ntawm tag nrho cov ua tau lub xeev ntawm cov khoom uas nws muaj
- Nws yog tsis yooj yim sua kom paub lub xeev ntawm lub system mus txog rau thaum lub sij hawm ntawm kev ntsuas
- Thaum lub sijhawm ntsuas, lub kaw lus siv ib qho ntawm cov kev hloov pauv tau ntawm nws cov ciam teb
(thiab, saib tom ntej me ntsis)
Corollary rau quantum programs:
- Ib qho kev pab cuam quantum muaj ib lub xeev ntawm lub system ntawm cov tswv yim, ib tug superposition sab hauv, ib tug superposition ntawm cov zis
- Ntawm qhov tso zis ntawm qhov kev pab cuam tom qab ntsuas peb muaj qhov ua tau zoo ntawm ib qho ntawm qhov ua tau kawg ntawm lub kaw lus (ntxiv rau qhov ua yuam kev)
- Txhua qhov kev pab cuam quantum muaj lub chimney architecture (input -> output. Tsis muaj loops, koj tsis tuaj yeem pom lub xeev ntawm lub kaw lus nyob rau hauv nruab nrab ntawm cov txheej txheem.)
Kev sib piv ntawm quantum computer thiab ib qho pa
Tam sim no cia peb piv ib lub tshuab computer thiab ib qho quantum.
| lub computer tsis tu ncua | Quantum computer | |
|
Logic
|
0 / 1 | `a|0> + b|1>, a^2+b^2=1` |
|
Kuaj Mob
|
Semiconductor transistor | Quantum khoom |
|
Media cab kuj
|
Voltage theem | Polarization, tig, ... |
|
Haujlwm
|
TSIS TAU, THIAB, LOSSIS, XOR hla cov khoom | Valves: CNOT, Hadamard,β¦ |
|
Kev sib raug zoo
|
Semiconductor nti | Tsis meej pem nrog ib leeg |
|
Algorithms
|
Standard (saib Whip) | Tshwj xeeb (Shore, Grover) |
|
Ntsiab Cai
|
Digital, kev txiav txim siab | Analog, probabilistic |
Qib logic
Nyob rau hauv lub computer tsis tu ncua qhov no yog me ntsis. Paub zoo rau peb los ntawm thiab dhau los kev txiav txim me ntsis. Muaj peev xwm coj qhov tseem ceeb ntawm 0 lossis 1. Nws copes zoo kawg nkaus nrog lub luag haujlwm logical unit rau lub khoos phis tawj tsis tu ncua, tab sis tsis tsim nyog rau kev piav qhia lub xeev quantum khoom, uas, raws li peb twb tau hais lawm, nyob rau hauv qus yog nyob rau hauvsuperpositions ntawm lawv ciam teb xeev.
Nov yog qhov lawv tuaj txog . Hauv nws lub xeev ciam teb nws paub cov xeev zoo ib yam li 0 thiab 1 , thiab nyob rau hauv superposition sawv cev probability faib hla nws ciam teb xeev |0> ΠΈ |1>:
a|0> + b|1>, ΡΠ°ΠΊΠΎΠ΅, ΡΡΠΎ a^2+b^2=1a thiab b sawv cev , thiab cov squares ntawm lawv cov modules yog qhov tseeb tshwm sim ntawm kev tau txais raws nraim li qhov tseem ceeb ntawm cov ciam teb xeev |0> ΠΈ |1>, yog tias koj tsoo lub qubit nrog kev ntsuas tam sim no.
Lub cev txheej
Nyob rau theem kev tsim kho thev naus laus zis tam sim no, kev siv lub cev ntawm me ntsis rau lub tshuab computer yog semiconductor transistorrau quantum, raws li peb tau hais lawm, tej yam khoom quantum. Hauv seem tom ntej peb yuav tham txog dab tsi tam sim no siv los ua lub cev tawm rau qubits.
Cia khoom nruab nrab
Rau lub computer niaj hnub no yog hluav taws xob - voltage theem, muaj lossis tsis muaj tam sim no, thiab lwm yam, rau quantum - tib yam lub xeev ntawm ib qho khoom quantum (kev taw qhia ntawm polarization, kiv, thiab lwm yam), uas tej zaum yuav nyob rau hauv lub xeev ntawm superposition.
Haujlwm
Txhawm rau siv cov logic circuits ntawm lub computer tsis tu ncua, peb siv cov paub zoo , rau kev khiav hauj lwm ntawm qubits nws yog tsim nyog los mus nrog ib tug txawv kiag li system ntawm kev khiav hauj lwm, hu ua . Cov rooj vag tuaj yeem ua ib zaug lossis ob-qubit, nyob ntawm seb muaj pes tsawg qubits raug hloov dua siab tshiab.
Piv txwv ntawm quantum rooj vag:
Muaj ib lub tswvyim universal valve teeb, uas yog txaus los ua tej quantum xam. Piv txwv li, universal teeb muaj xws li lub rooj vag Hadamard, lub rooj vag hloov theem, lub rooj vag CNOT, thiab lub rooj vag Οβ8. Nrog lawv cov kev pab, koj tuaj yeem ua txhua qhov kev suav quantum ntawm cov qubits arbitrary.
Hauv tsab xov xwm no peb yuav tsis nyob hauv kev nthuav dav ntawm lub kaw lus ntawm quantum rooj vag; koj tuaj yeem nyeem ntxiv txog lawv thiab kev ua haujlwm zoo ntawm qubits, piv txwv li, . Lub ntsiab tseem ceeb yuav tsum nco ntsoov:
- Kev ua haujlwm ntawm quantum khoom xav tau kev tsim cov tswv yim tshiab (quantum rooj vag)
- Quantum rooj vag tuaj nyob rau hauv ib leeg-qubit thiab ob-qubit hom.
- Muaj cov rooj vag universal uas tuaj yeem siv los ua txhua qhov kev suav quantum
Kev sib raug zoo
Ib qho transistor tsis muaj txiaj ntsig zoo rau peb; txhawm rau ua tiav kev suav peb yuav tsum tau txuas ntau lub transistors rau ib leeg, uas yog, tsim cov semiconductor nti los ntawm ntau lab ntawm cov transistors uas tsim cov logical circuits, thiab, thaum kawg, tau txais lub processor niaj hnub hauv nws daim ntawv classic.
Ib qubit kuj tsis muaj txiaj ntsig rau peb (zoo, yog tias tsuas yog hauv cov ntsiab lus kev kawm),
Txhawm rau ua cov lej peb xav tau ib qho system ntawm qubits (quantum khoom)
uas, raws li peb twb tau hais lawm, yog tsim los ntawm entangling qubits nrog ib leeg kom cov kev hloov nyob rau hauv lawv lub xeev tshwm sim nyob rau hauv ib tug kev sib koom tes.
Algorithms
Cov txheej txheem algorithms uas tib neeg tau sau los txog niaj hnub no tsis tsim nyog rau kev siv ntawm quantum computer. Yog, feem ntau tsis xav tau. Quantum computers raws li rooj vag logic tshaj qubits yuav tsum tau tsim cov algorithms sib txawv kiag li, quantum algorithms. Ntawm qhov paub zoo tshaj plaws quantum algorithms, peb tuaj yeem paub qhov txawv:
- (factorization)
- (Kev tshawb nrhiav ceev hauv ib qho chaw khaws ntaub ntawv tsis tau xaj)
- ( teb rau lo lus nug, qhov ua haujlwm tas li lossis sib npaug)
Ntsiab Cai
Thiab qhov sib txawv tseem ceeb tshaj plaws yog txoj hauv kev ua haujlwm. Rau ib tug standard computer qhov no yog digital, nruj me ntsis txiav txim lub hauv paus ntsiab lus, raws li qhov tseeb hais tias yog hais tias peb teem ib co thawj lub xeev ntawm lub system thiab dhau nws los ntawm ib tug muab algorithm, ces cov txiaj ntsig ntawm kev xam yuav zoo ib yam, tsis muaj teeb meem pes tsawg zaus peb khiav qhov kev xam no. Qhov tseeb, tus cwj pwm no yog qhov peb xav tau los ntawm lub computer.
Quantum computer khiav rau analogue, probabilistic txoj cai. Qhov tshwm sim ntawm qhov muab algorithm ntawm ib lub xeev pib yog piv txwv los ntawm kev faib qhov tshwm sim kev ua tiav kawg ntawm cov algorithm ntxiv rau qhov ua tau yuam kev.
Qhov no probabilistic xwm ntawm quantum xam yog vim lub feem ntau probabilistic essence ntawm lub ntiaj teb no quantum. "Vajtswv tsis ua si tsuav nrog lub ntiaj teb.", hais tias qub Einstein, tab sis tag nrho cov kev sim thiab kev soj ntsuam kom deb li deb (nyob rau hauv lub scientific paradigm tam sim no) paub meej qhov opposite.
Physical implementations of qubits
Raws li peb twb tau hais lawm, tus qubit tuaj yeem sawv cev los ntawm quantum khoom, uas yog, lub cev khoom uas siv cov khoom quantum tau piav qhia saum toj no. Ntawd yog, kwv yees hais lus, txhua yam khoom siv lub cev uas muaj ob lub xeev thiab ob lub xeev no nyob rau hauv lub xeev ntawm superposition tuaj yeem siv los tsim lub computer quantum.
"Yog tias peb tuaj yeem tso lub atom rau hauv ob theem sib txawv thiab tswj lawv, ces koj muaj qubit. Yog tias peb tuaj yeem ua qhov no nrog ion, nws yog qubit. Nws zoo ib yam nrog tam sim no. Yog tias peb khiav nws clockwise thiab counterclockwise tib lub sijhawm, koj muaj qubit. "
muaj ΠΊ , nyob rau hauv uas tam sim no ntau yam ntawm lub cev kev siv ntawm qubit yog xam nyob rau hauv ntau nthuav dav, peb yuav tsuas sau cov feem ntau zoo-paub thiab ntau:
- thiab ntau lwm cov tswv yim txawv (anions, thiab lwm yam)
Ntawm tag nrho cov ntau yam no, feem ntau tsim yog thawj txoj kev tau txais qubits, raws li . , , thiab lwm tus thawj coj siv nws los tsim lawv lub tshuab.
Zoo, nyeem ntxiv ua tau qub od .
Cov hauv paus. Yuav ua li cas lub quantum computer ua haujlwm
Cov ntaub ntawv rau ntu no (ua haujlwm thiab duab) yog muab los ntawm kab lus .
Yog li, xav txog tias peb muaj cov haujlwm hauv qab no:
Muaj peb pawg neeg: (A)ndrey, (B)olodya thiab (C)erezha. Muaj ob lub tsheb tavxij (0 thiab 1).
Nws tseem paub tias:
- (A)ndrey, (B)olodya yog phooj ywg
- (A)ndrey, (C)erezha yog yeeb ncuab
- (B) olodya thiab (C)erezha yog yeeb ncuab
Kev Ua Haujlwm: Muab cov neeg nyob hauv tsheb tavxij thiaj li Max (cov phooj ywg) ΠΈ Min( yeeb ncuab)
Ntsuam xyuas: L = (ntau tus phooj ywg) - (ntau tus yeeb ncuab) rau txhua qhov kev xaiv chaw nyob
TSEEM CEEB: Piv txwv tias tsis muaj heuristics, tsis muaj kev daws teeb meem zoo. Hauv qhov no, qhov teeb meem tsuas yog daws tau los ntawm kev tshawb nrhiav tag nrho cov kev xaiv.
Kev daws ntawm ib lub computer tsis tu ncua
Yuav daws qhov teeb meem no li cas ntawm lub khoos phis tawj tsis tu ncua (super) (lossis pawg) - nws yog qhov tseeb tias koj yuav tsum tau voj los ntawm txhua qhov kev xaiv ua tau. Yog hais tias peb muaj ib tug multiprocessor system, ces peb yuav parallelize lub xam cov kev daws teeb meem nyob rau hauv ob peb processors thiab ces sau cov ntsiab lus.
Peb muaj 2 txoj kev xaiv chaw nyob (taxi 0 thiab tsheb tavxij 1) thiab 3 tus neeg. Qhov chaw daws teeb meem 2 x 3 = 8. Koj tuaj yeem mus dhau 8 txoj kev xaiv siv lub laij lej, qhov no tsis yog teeb meem. Tam sim no cia qhov teeb meem nyuaj - peb muaj 20 tus neeg thiab ob lub tsheb npav, qhov chaw daws teeb meem 2^20 = 1. Tsis muaj dab tsi nyuab thiab. Wb nce tus naj npawb ntawm cov neeg los ntawm 2.5 npaug - nqa 50 tus neeg thiab ob lub tsheb ciav hlau, qhov chaw daws teeb meem tam sim no Luas = 2 x 50 = 1.12 x 10^15. Lub computer zoo tib yam (super) twb pib muaj teeb meem loj. Wb ua kom neeg coob 2 zaug, 100 tus yuav muab rau peb lawm 1.2x10^30 kev xaiv tau.
Qhov ntawd yog nws, txoj haujlwm no tsis tuaj yeem suav nrog lub sijhawm tsim nyog.
Txuas lub supercomputer
Lub computer haib tshaj tam sim no yog tus naj npawb 1 ntawm uas yog , Productivity 122 . Cia peb xav tias peb xav tau 100 txoj haujlwm los suav ib qho kev xaiv, tom qab ntawd los daws qhov teeb meem rau 100 tus neeg peb yuav xav tau:
1.2 x 10^30 100) / 122 Γ 10 ^ 15 / (606024365) = np 3 x 10 x 37 y.
Raws li peb pom raws li qhov loj me ntawm cov ntaub ntawv thawj zaug nce, qhov chaw daws teeb meem loj hlob raws li txoj cai lij choj, nyob rau hauv cov ntaub ntawv dav dav, rau N cov khoom peb muaj 2^N cov kev xaiv kev daws teeb meem, uas rau qhov me me N (100) muab peb qhov tsis suav (ntawm qib thev naus laus zis tam sim no) qhov chaw daws teeb meem.
Puas muaj lwm txoj hauv kev? Raws li koj tau twv, yog, muaj.
Tab sis ua ntej peb nkag mus rau hauv yuav ua li cas thiab yog vim li cas quantum computers thiaj daws tau cov teeb meem zoo li no, cia peb siv sij hawm ib pliag los recap lawv yog dab tsi. qhov yuav faib. Tsis txhob ntshai, qhov no yog ib tsab xov xwm tshuaj xyuas, yuav tsis muaj ib qho nyuaj ua lej ntawm no, peb yuav ua nrog cov piv txwv classic nrog lub hnab thiab pob.
Tsuas yog me ntsis combinatorics, qhov yuav tshwm sim txoj kev xav thiab tus kws sim coj txawv txawv
Wb nqa ib lub hnab thiab muab tso rau hauv 1000 dawb thiab 1000 pob dub. Peb yuav ua ib qho kev sim - tshem tawm lub pob, sau cov xim, rov qab lub pob rau hauv lub hnab thiab sib tov cov khoom hauv lub hnab.
Qhov kev sim tau ua tiav 10 zaug, rub tawm 10 lub pob dub. Tej zaum? Heev. Cov qauv no puas muab peb lub tswv yim tsim nyog ntawm kev faib tawm hauv lub hnab? Obviously tsis. Dab tsi yuav tsum tau ua - txoj cai, prov ua qhov kev sim ib lab zaug thiab suav cov zaus ntawm cov pob dub thiab dawb. Peb tau, piv txwv li 49.95% dub thiab 50.05% dawb. Nyob rau hauv cov ntaub ntawv no, tus qauv ntawm kev faib tawm los ntawm qhov peb coj mus kuaj (tawm ib lub pob) twb ntau dua los yog tsawg dua.
Qhov tseem ceeb yog kom nkag siab qhov ntawd qhov kev sim nws tus kheej muaj qhov yuav tshwm sim, nrog ib qho qauv (pob) peb yuav tsis paub qhov tseeb qauv ntawm kev faib khoom, peb yuav tsum rov ua qhov kev sim ntau zaus thiab nruab nrab cov txiaj ntsig.
Cia peb ntxiv rau peb lub hnab 10 liab thiab 10 pob ntsuab ( yuam kev). Cia peb rov ua qhov kev sim 10 zaug. INrub tawm 5 liab thiab 5 ntsuab. Tej zaum? Yog lawm. Peb tuaj yeem hais qee yam txog qhov kev faib tawm tiag tiag - Tsis yog. Dab tsi yuav tsum tau ua - zoo, koj nkag siab.
Txhawm rau kom nkag siab txog cov qauv ntawm qhov kev faib tawm qhov tshwm sim, nws yog qhov yuav tsum tau rov ua piv txwv tus neeg tau txais txiaj ntsig los ntawm qhov kev faib tawm no thiab nruab nrab cov txiaj ntsig.
Txuas txoj kev xav nrog kev xyaum
Tam sim no es tsis txhob dub thiab dawb pob, cia peb nqa cov pob billiard thiab muab tso rau hauv ib lub hnab 1000 pob nrog tus lej 2, 1000 nrog tus lej 7 thiab 10 pob nrog lwm tus lej. Cia peb xav txog ib tus kws sim uas tau kawm hauv qhov ua haujlwm yooj yim tshaj plaws (tawm lub pob, sau tus lej, muab lub pob rov qab rau hauv lub hnab, sib tov cov khoom hauv lub hnab) thiab nws ua qhov no hauv 150 microseconds. Zoo, xws li ib tug sim ntawm ceev (tsis yog ib tug yeeb tshuaj advertisement !!!). Tom qab ntawd hauv 150 vib nas this nws yuav tuaj yeem ua peb qhov kev sim 1 lab zaug thiab muab peb cov txiaj ntsig nruab nrab.
Lawv zaum tus kws sim, muab ib lub hnab rau nws, tig mus, tos 150 vib nas this thiab tau txais:
tus naj npawb 2 - 49.5%, tus lej 7 - 49.5%, tus lej seem hauv tag nrho - 1%.
Yog lawm, peb lub hnab yog lub computer quantum nrog lub algorithm uas daws peb cov teeb meem, thiab cov pob yog cov kev daws teeb meem. Txij li thaum muaj ob txoj kev daws teeb meem, ces quantum computer yuav muab rau peb ib qho ntawm cov kev daws teeb meem no nrog qhov sib npaug, thiab 0.5% (10/2000) yuam kev, uas peb yuav tham txog tom qab.
Txhawm rau kom tau txais cov txiaj ntsig ntawm quantum computer, koj yuav tsum tau khiav lub quantum algorithm ntau zaus ntawm tib cov ntaub ntawv tawm tswv yim thiab qhov nruab nrab qhov tshwm sim.
Scalability ntawm quantum computer
Tam sim no xav txog tias rau ib txoj haujlwm uas muaj 100 tus neeg (daws qhov chaw 2^100 peb nco ntsoov qhov no), kuj muaj ob qho kev txiav txim kom raug xwb. Tom qab ntawd, yog tias peb muab 100 qubits thiab sau ib qho algorithm uas suav peb lub hom phiaj ua haujlwm (L, saib saum toj no) dhau cov qubits, ces peb yuav tau txais ib lub hnab uas yuav muaj 1000 pob nrog tus lej ntawm thawj cov lus teb raug, 1000 nrog tus naj npawb ntawm cov lus teb raug thib ob thiab 10 pob nrog lwm tus lej. Thiab nyob rau tib lub sijhawm 150 vib nas this peb tus kws sim yuav muab peb qhov kwv yees ntawm qhov tshwm sim ntawm cov lus teb raug.
Lub sijhawm ua tiav ntawm quantum algorithm (nrog qee qhov kev xav) tuaj yeem suav tias tsis tu ncua O (1) nrog rau qhov ntev ntawm qhov chaw daws teeb meem (2^N).
Thiab qhov no yog qhov tseeb ntawm lub quantum computer - runtime tsis tu ncua nyob rau hauv relation mus rau qhov nce zog txoj cai complexity ntawm kev daws qhov chaw yog qhov tseem ceeb.
Qubit thiab parallel worlds
Qhov no tshwm sim li cas? Dab tsi tso cai rau lub quantum computer ua kev suav sai sai? Nws yog txhua yam hais txog quantum xwm ntawm qubit.
Saib, peb tau hais tias qubit zoo li quantum khoom paub txog ib qho ntawm nws ob lub xeev thaum pom, tab sis nyob rau hauv "tsiaj qus" nws yog nyob rau hauv superpositions ntawm xeev, uas yog, nws yog nyob rau hauv ob qho tib si ntawm nws ciam teb ib txhij (nrog qee qhov tshwm sim).
Wb coj (A) ntuj thiab xav txog nws lub xeev (hauv lub tsheb twg nws yog - 0 lossis 1) raws li qubit. Tom qab ntawd peb muaj (hauv quantum chaw) ob lub ntiaj teb sib npaug,in ib (TABSIS) zaum hauv tsheb tavxij 0, hauv lwm lub ntiaj teb - hauv tsheb tavxij 1. Hauv ob lub tsheb tavxij tib lub sijhawm, tab sis nrog qee qhov tshwm sim ntawm kev pom nws hauv txhua tus ntawm lawv thaum saib.
Wb coj (B) hluas thiab cia peb xav txog nws lub xeev li qubit. Ob lub ntiaj teb sib npaug sib luag tshwm sim. Tab sis tam sim no cov khub ntawm lub ntiaj teb no (TABSIS) ΠΈ (AT) tsis txhob sib cuam tshuam. Yuav tsum tau ua dab tsi los tsim ntsig txog qhov system? Yog lawm, peb xav tau cov qubits no khi (confuse). Peb coj nws thiab tsis meej pem (A) nrog (B) - Peb tau txais quantum system ntawm ob qubits (A, B), realizing nyob rau hauv nws tus kheej plaub kev vam meej parallel worlds. Ntxiv (S) ergey thiab peb tau txais ib qho system ntawm peb qubits (ABC), siv yim kev vam meej parallel worlds.
Lub ntsiab lus ntawm quantum xam (kev siv cov saw hlau ntawm quantum rooj vag dhau ib qho kev sib txuas ntawm qubits) yog qhov tseeb tias qhov kev suav tshwm sim hauv txhua lub ntiaj teb sib luag ib txhij.
Thiab nws tsis muaj teeb meem pes tsawg ntawm lawv peb muaj, 2^3 lossis 2^100, lub quantum algorithm yuav raug tua nyob rau hauv lub sij hawm kawg ntawm tag nrho cov no parallel worlds thiab yuav muab peb cov txiaj ntsig, uas yog ib qho piv txwv los ntawm qhov tshwm sim ntawm qhov kev faib tawm ntawm cov algorithm cov lus teb.
Rau kev nkag siab zoo dua, ib tus tuaj yeem xav txog qhov ntawd quantum computer ntawm qib quantum khiav 2^N parallel solution processes, txhua tus ua haujlwm ntawm ib qho kev xaiv tau, tom qab ntawd sau cov txiaj ntsig ntawm kev ua haujlwm - thiab muab peb cov lus teb nyob rau hauv daim ntawv ntawm ib tug superposition ntawm kev daws (probability faib ntawm cov lus teb), uas peb coj mus kuaj ib zaug (rau txhua qhov kev sim).
Nco ntsoov lub sijhawm xav tau los ntawm peb tus kws sim (150 Β΅s) txhawm rau ua tiav qhov kev sim, qhov no yuav pab tau rau peb me ntsis ntxiv, thaum peb tham txog cov teeb meem tseem ceeb ntawm quantum computers thiab lub sijhawm decoherence.
Quantum algorithms
Raws li twb tau hais lawm, cov qauv txheej txheem raws li binary logic tsis muaj feem xyuam rau lub computer quantum siv quantum logic (quantum gates). Rau nws, nws yog qhov yuav tsum tau los nrog cov tshiab uas siv tag nrho cov peev txheej uas muaj nyob hauv quantum xwm ntawm kev suav.
Qhov zoo tshaj plaws algorithms niaj hnub no yog:
Tsis zoo li cov classical, quantum computers tsis yog universal.
Tsuas yog qee tus lej ntawm quantum algorithms tau pom txog tam sim no.
Π‘ΠΏΠ°ΡΠΈΠ±ΠΎ rau qhov txuas rau , qhov chaw uas, raws li tus sau (), cov neeg sawv cev zoo tshaj plaws ntawm lub ntiaj teb quantum-algorithmic tau sau thiab txuas ntxiv mus.
Hauv tsab xov xwm no peb yuav tsis txheeb xyuas quantum algorithms kom ntxaws; muaj ntau cov ntaub ntawv zoo heev hauv Is Taws Nem rau txhua theem ntawm kev nyuaj, tab sis peb tseem yuav tsum tau luv luv mus hla peb lub npe nrov tshaj plaws.
Shor lub algorithm.
Qhov nrov tshaj plaws quantum algorithm yog (tsim nyob rau hauv 1994 los ntawm English mathematician ), uas yog tsom rau kev daws qhov teeb meem ntawm cov lej ntawm cov lej rau hauv cov ntsiab lus tseem ceeb (qhov teeb meem ntawm kev faib tawm, sib cais logarithm).
Nws yog qhov algorithm no uas tau hais los ua piv txwv thaum lawv sau tias koj lub txhab nyiaj hauv tuam txhab thiab cov passwords yuav raug nyiag sai sai. Xav tias qhov ntev ntawm cov yuam sij siv niaj hnub no tsis tsawg dua 2048 khoom, lub sijhawm rau lub hau tseem tsis tau los.
Hnub no ntau tshaj li tus qauv. Qhov zoo tshaj plaws Factorization Cov txiaj ntsig nrog Shor's Algorithm - Tus lej ΠΈ , uas yog tsawg dua 2048 ntsis. Rau cov txiaj ntsig seem ntawm lub rooj, qhov sib txawv Kev suav, tab sis txawm tias qhov txiaj ntsig zoo tshaj plaws raws li cov txheej txheem no (291311) yog deb ntawm daim ntawv thov tiag tiag.
Koj tuaj yeem nyeem ntxiv txog Shor's algorithm, piv txwv li,. Hais txog kev coj ua - .
Ib qho ntawm complexity thiab xav tau lub hwj chim los ua tus lej 2048-ntsis yog lub computer nrog . Peb pw tsaug zog.
Grover's algorithm
- daws qhov teeb meem enumeration, uas yog, nrhiav kev daws rau qhov sib npaug F(X) = 1, qhov twg F los ntawm n sib txawv. Tau thov los ntawm ib tug American mathematician Π² .
Grover's algorithm tuaj yeem siv los nrhiav ΠΈ tus lej series. Tsis tas li ntawd, nws tuaj yeem siv los daws teeb meem los ntawm kev tshawb nrhiav tag nrho ntawm ntau txoj kev daws teeb meem. Qhov no yuav ua rau muaj kev nce nrawm dua piv rau classical algorithms, txawm tias tsis muab ""nyob rau hauv dav dav.
Koj tuaj yeem nyeem ntxiv, lossis ... Tsis tau Muaj kev piav qhia zoo ntawm cov txheej txheem siv cov piv txwv ntawm lub thawv thiab lub pob, tab sis, hmoov tsis, rau cov laj thawj tshaj li lwm tus tswj, qhov chaw no tsis qhib rau kuv los ntawm Russia. Yog koj muaj tseem raug thaiv, yog li ntawm no yog cov ntsiab lus luv luv:
Grover's algorithm. Xav txog tias koj muaj N daim ntawm cov lej kaw. Lawv tag nrho cov khoob tsuas yog ib qho, uas muaj lub pob. Koj txoj haujlwm: nrhiav tus naj npawb ntawm lub thawv uas lub pob nyob (qhov no tsis paub tus lej feem ntau txhais los ntawm tsab ntawv w).
Yuav daws qhov teeb meem no li cas? Txoj kev ruam tshaj plaws yog hloov pauv qhib lub thawv, thiab sai lossis tom qab koj yuav hla lub thawv nrog lub pob. Qhov nruab nrab, pes tsawg lub thawv yuav tsum tau kuaj ua ntej pom lub thawv nrog lub pob? Qhov nruab nrab, koj yuav tsum qhib ib nrab ntawm N / 2 lub thawv. Qhov tseem ceeb ntawm no yog tias yog tias peb nce cov thawv los ntawm 100 npaug, ces qhov nruab nrab ntawm cov thawv uas yuav tsum tau qhib ua ntej lub thawv nrog lub pob pom yuav nce los ntawm tib 100 npaug.
Tam sim no cia peb ua ib qho kev qhia ntxiv. Cia peb tsis txhob qhib lub thawv peb tus kheej nrog peb txhais tes thiab tshawb xyuas qhov muaj lub pob hauv txhua qhov, tab sis muaj qee tus neeg nruab nrab, cia peb hu nws Oracle. Peb qhia rau Oracle, "checkbox naj npawb 732," thiab Oracle ncaj ncees xyuas thiab teb, "tsis muaj pob nyob rau hauv lub thawv naj npawb 732." Tam sim no, es tsis txhob hais tias muaj pes tsawg lub thawv peb xav tau qhib qhov nruab nrab, peb hais tias "peb lub sijhawm nruab nrab peb yuav tsum mus rau Oracle li cas thiaj nrhiav tau tus naj npawb ntawm lub thawv nrog lub pob"
Nws hloov tawm tias yog tias peb txhais cov teeb meem no nrog lub thawv, pob thiab Oracle rau hauv quantum lus, peb tau txais txiaj ntsig zoo: txhawm rau nrhiav tus naj npawb ntawm lub thawv nrog lub pob ntawm N lub thawv, peb yuav tsum cuam tshuam Oracle nkaus xwb txog SQRT. (N) lub sijhawm!
Ntawd yog, qhov nyuaj ntawm txoj haujlwm tshawb nrhiav siv Grover's algorithm raug txo los ntawm lub hauv paus square ntawm lub sijhawm.
Deutsch-Jozi algorithm
Deutsch-Jozsa algorithm (tseem hu ua Deutsch-Jozsa algorithm) - [quantum algorithm](%D0%B0%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%BC), ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π½ΡΠΉ ΠΈ Π² , thiab tau dhau los ua ib qho piv txwv thawj ntawm algorithms tsim los ua kom tiav . _
Qhov teeb meem Deutsch-Jozsi yog los txiav txim seb qhov kev ua haujlwm ntawm ntau qhov sib txawv binary F(x1, x2, ... xn) yog qhov tsis tu ncua (yuav siv tus nqi 0 lossis 1 rau ib qho kev sib cav) lossis sib npaug (rau ib nrab ntawm lub npe nws siv. tus nqi 0, rau lwm ib nrab 1). Nyob rau hauv cov ntaub ntawv no, nws yog xam tau tias yog ib tug priori paub tias muaj nuj nqi yog ib tug tas mus li los yog balanced.
Koj kuj nyeem tau . Ib qho yooj yim piav qhia:
Lub Deutsch (Deutsch-Jozsi) algorithm yog raws li brute quab yuam, tab sis tso cai rau nws ua tau sai dua li niaj zaus. Xav txog tias muaj ib lub npib rau ntawm lub rooj thiab koj yuav tsum paub seb nws yog cuav los yog tsis. Txhawm rau ua qhov no, koj yuav tsum saib cov nyiaj npib ob zaug thiab txiav txim siab: "lub taub hau" thiab "tails" yog tiag, ob "lub taub hau", ob "tails" yog cuav. Yog li, yog tias koj siv Deutsch quantum algorithm, qhov kev txiav txim siab no tuaj yeem ua nrog ib saib - ntsuas.
Teeb meem ntawm quantum computers
Thaum tsim thiab ua haujlwm quantum computers, cov kws tshawb fawb thiab engineers ntsib ntau yam teeb meem, uas los txog rau niaj hnub no tau daws nrog ntau yam kev vam meej. Raws li () Cov teeb meem hauv qab no tuaj yeem txheeb xyuas:
- Kev nkag siab zoo rau ib puag ncig thiab kev cuam tshuam nrog ib puag ncig
- Ua kom yuam kev thaum muab xam
- Teeb meem nrog kev pib pib ntawm qubit xeev
- Teeb meem hauv kev tsim ntau lub tshuab qubit
Kuv xav kom nyeem cov kab lus "β, tshwj xeeb tshaj yog cov lus rau nws.
Cia peb npaj tag nrho cov teeb meem tseem ceeb rau hauv peb pawg loj thiab ua tib zoo saib ntawm lawv txhua tus:
Decoherence
.
Quantum xeev yam tsis yooj yim heevqubits nyob rau hauv lub xeev entangled yog heev unstable, ib qho kev cuam tshuam sab nraud tuaj yeem (thiab ua) rhuav tshem qhov kev sib txuas no. Ib qho kev hloov ntawm qhov kub thiab txias los ntawm qhov tsawg tshaj plaws ntawm ib lub degree, siab, ib tug random photon ya nyob ze - tag nrho cov no destabilizes peb lub cev.
Yuav kom daws tau qhov teeb meem no, qhov kub thiab txias sarcophagi yog tsim, nyob rau hauv uas qhov kub (-273.14 degrees Celsius) yog me ntsis saum toj kawg nkaus xoom, nrog rau qhov siab tshaj plaws cais ntawm lub sab hauv chamber nrog lub processor los ntawm tag nrho cov (muaj peev xwm) influences sab nraud ib puag ncig.
Lub neej ntev tshaj plaws ntawm quantum system ntawm ob peb entangled qubits, thaum lub sijhawm nws khaws nws cov khoom quantum thiab tuaj yeem siv rau kev suav, hu ua lub sijhawm decoherence.
Tam sim no, lub sij hawm decoherence nyob rau hauv qhov zoo tshaj plaws quantum daws yog nyob rau ntawm qhov kev txiav txim ntawm kaum thiab pua pua microseconds.
Muaj ib qho zoo kawg nkaus qhov twg koj tuaj yeem saib ntawm tag nrho cov tsim quantum systems. Kab lus no suav nrog tsuas yog ob tus txheej txheem saum toj kawg nkaus ua piv txwv - los ntawm IBM thiab los ntawm . Raws li peb tuaj yeem pom, lub sijhawm decoherence (T2) tsis tshaj 200 ΞΌs.
Kuv tsis pom cov ntaub ntawv tseeb ntawm Sycamore, tab sis feem ntau ob tug lej tau muab - 1 lab suav hauv 200 vib nas this, nyob rau hauv lwm qhov chaw - rau 130 vib nas this tsis poob ntawm kev tswj cov cim, thiab lwm yam.. Txawm li cas los xij, qhov no muab rau peb Lub sijhawm decoherence yog li 150 ΞΌs. Nco ntsoov peb sim nrog ib lub hnab? Zoo, nws nyob ntawm no.
| Lub npe computer | N Qubits | Max ua khub | T2 (Β΅s) |
| IBM Q System Ib | 20 | 6 | 70 |
| Google Sycamore | 53 | 4 | ~ 150-200 |
Decoherence ua hem peb nrog dab tsi?
Qhov teeb meem tseem ceeb yog tias tom qab 150 ΞΌs, peb lub khoos phis tawj ntawm N entangled qubits yuav pib tso tawm cov suab nrov dawb uas tsis muaj kev cuam tshuam txog kev faib tawm ntawm cov kev daws teeb meem raug.
Ntawd yog, peb xav tau:
- Initialize qubit system
- Ua ib qho kev suav (chain ntawm qhov rooj ua haujlwm)
- Nyeem qhov tshwm sim
Thiab ua txhua yam no hauv 150 microseconds. Kuv tsis muaj sijhawm - qhov tshwm sim tau hloov mus ua taub dag.
Tab sis qhov ntawd tsis yog tag nrhoβ¦
Tsis raug
Raws li peb tau hais, quantum txheej txheem thiab quantum xam yog probabilistic nyob rau hauv cov xwm, peb tsis tuaj yeem 100% tseeb ntawm txhua yam, tab sis tsuas yog nrog qee qhov tshwm sim. Qhov teeb meem yog ntxiv aggravated los ntawm qhov tseeb hais tias quantum xam yog yuam kev. Cov hom kev ua yuam kev hauv quantum suav yog:
- Decoherence yuam kev yog tshwm sim los ntawm cov complexity ntawm lub system thiab kev cuam tshuam nrog rau sab nraud ib puag ncig
- Gate xam yuam kev (vim lub quantum xwm ntawm xam)
- Qhov yuam kev hauv kev nyeem lub xeev kawg (qhov tshwm sim)
Qhov yuam kev cuam tshuam nrog decoherence, tshwm sim sai li sai tau thaum peb entangle peb qubits thiab pib ua xam. Qhov ntau qubits peb entangle, qhov system complex, thiab qhov yooj yim dua nws yog ua kom puas nws. Tsawg-kub sarcophagi, tiv thaiv chamber, tag nrho cov cuab yeej cuab tam no yog lub hom phiaj ntawm kev txo tus naj npawb ntawm qhov yuam kev thiab ncua sij hawm decoherence.
Rooj vag kev ua yuam kev - txhua qhov haujlwm ( rooj vag) ntawm qubits tuaj yeem, nrog qee qhov tshwm sim, xaus nrog kev ua yuam kev, thiab siv cov algorithm peb yuav tsum tau ua ntau pua lub rooj vag, yog li xav txog qhov peb tau txais thaum kawg ntawm kev ua tiav ntawm peb cov algorithm. Cov lus teb classic rau lo lus nug yog "Dab tsi yog qhov tshwm sim ntawm kev ntsib dinosaur hauv elevator?" - 50x50, koj yuav ntsib lossis tsis tau.
Txhawm rau ua kom qhov teeb meem loj dua, cov txheej txheem kev kho qhov yuam kev (kev sib piv ntawm kev suav thiab qhov nruab nrab) tsis ua haujlwm hauv lub ntiaj teb quantum vim tsis muaj kev sib tw. Rau nyob rau hauv quantum xam yuav tsum tau invented . Hais lus ntxhib, peb muab N qubits thiab ua 1 ntawm lawv logical qub nrog tus nqi yuam kev qis dua.
Tab sis ntawm no lwm qhov teeb meem tshwm sim - total qubits. Saib, cia peb hais tias peb muaj lub processor nrog 100 qubits, ntawm 80 qubits siv rau kev kho qhov yuam kev, ces peb tsuas muaj 20 sab laug rau kev suav.
Kev ua yuam kev hauv kev nyeem ntawv kawg - raws li peb nco qab, qhov tshwm sim ntawm quantum suav yog nthuav tawm rau peb hauv daim ntawv qhov yuav faib cov lus teb. Tab sis kev nyeem lub xeev kawg kuj tseem yuav ua tsis tiav nrog qhov yuam kev.
Ntawm qhov qub Muaj cov rooj sib piv ntawm cov processors los ntawm qib yuam kev. Rau kev sib piv, cia peb coj tib lub processors ib yam li hauv qhov piv txwv dhau los - IBM ΠΈ :
| Khoos phib tawj | 1-Qubit Gate Fidelity | 2-Qubit Gate Fidelity | Readout Fidelity |
| IBM Q System Ib | 99.96% | 98.31% | - |
| Google Sycamore | 99.84% | 99.38% | 96.2% |
nws yog yog ib qho kev ntsuas ntawm qhov zoo sib xws ntawm ob lub xeev quantum. Qhov loj ntawm qhov yuam kev tuaj yeem qhia tau hais tias yog 1-Fidelity. Raws li peb tuaj yeem pom, qhov yuam kev ntawm 2-qubit rooj vag thiab nyeem ntawv yuam kev yog qhov teeb meem tseem ceeb rau kev ua haujlwm nyuaj thiab ntev algorithms ntawm quantum computers uas twb muaj lawm.
Koj kuj nyeem tau xyoo los ntawm los daws qhov teeb meem ntawm kev kho qhov yuam kev.
Processor architecture
Hauv kev xav peb tsim thiab ua haujlwm circuits ntawm kaum ob ntawm entangled qubits, nyob rau hauv kev muaj tiag txhua yam yog nyuab dua. Tag nrho cov quantum chips (processors) uas twb muaj lawm yog tsim nyob rau hauv xws li ib txoj kev uas lawv muab tsis mob entanglement ntawm ib tug qubit tsuas yog nrog nws cov neeg nyob ze, uas tsis muaj ntau tshaj rau.
Yog tias peb xav tau 1st qubit, hais, nrog 12th, ces peb yuav tsum tau tsim kom muaj ib txoj hlua ntawm kev ua haujlwm quantum ntxiv, koom nrog qubits ntxiv, thiab lwm yam, uas ua rau nce qhov yuam kev tag nrho. Yog, thiab tsis txhob hnov ββqab txog lub sijhawm decoherence, tej zaum thaum lub sij hawm koj ua tiav txuas cov qubits rau hauv Circuit Court koj xav tau, lub sij hawm yuav xaus thiab tag nrho cov Circuit Court yuav tig mus rau hauv zoo dawb suab nrov generator.
Kuj tsis txhob hnov ββqab tias Lub architecture ntawm tag nrho cov quantum processors txawv, thiab cov kev pab cuam sau nyob rau hauv lub emulator nyob rau hauv lub "tag nrho-rau-tag nrho connectivity" hom yuav tsum tau "recompiled" rau hauv lub architecture ntawm ib tug tshwj xeeb nti. Muaj txawm los ua qhov haujlwm no.
Kev sib txuas siab tshaj plaws thiab cov lej siab tshaj plaws ntawm qubits rau tib lub chips sab saum toj:
| Lub npe computer | N Qubits | Max ua khub | T2 (Β΅s) |
| IBM Q System Ib | 20 | 6 | 70 |
| Google Sycamore | 53 | 4 | ~ 150-200 |
Thiab, rau kev sib piv, rooj nrog cov ntaub ntawv los ntawm cov tiam dhau los ntawm processors. Sib piv cov qubits, lub sijhawm decoherence thiab qhov ua yuam kev nrog qhov peb muaj tam sim no nrog cov tiam tshiab. Txawm li cas los xij, kev nce qib qeeb, tab sis txav mus.
Yog li ntawd,
- Tam sim no tsis muaj kev sib txuas tag nrho nrog> 6 qubits
- Txhawm rau entangle qubit 0s ntawm lub processor tiag, piv txwv li, qubit 15 yuav xav tau ntau lub kaum os ntxiv ua haujlwm
- Kev ua haujlwm ntau dua -> ntau qhov yuam kev -> muaj zog cuam tshuam ntawm decoherence
Cov txiaj ntsim tau los
Decoherence yog Procrustean txaj ntawm niaj hnub quantum xam. Peb yuav tsum haum txhua yam rau hauv 150 ΞΌs:
- Initialization ntawm lub xeev pib ntawm qubits
- xam qhov teeb meem siv quantum rooj vag
- Kho qhov yuam kev kom tau txais txiaj ntsig zoo
- Nyeem qhov tshwm sim
Txog tam sim no cov txiaj ntsig tau poob siab, txawm li cas los xij thov kom ua tiav 0.5s coherence tuav lub sijhawm ntawm quantum computer raws li :
Peb ntsuas lub sij hawm qubit coherence ntau tshaj 0.5 s, thiab nrog sib nqus shielding peb cia siab tias qhov no yuav txhim kho kom ntev dua 1000 s.
Koj tseem tuaj yeem nyeem txog cov tshuab no los yog piv txwv .
Qhov xwm txheej yog qhov nyuaj ntxiv los ntawm qhov tseeb tias thaum ua cov kev suav ua nyuaj nws yuav tsum siv quantum yuam kev kho circuits, uas tseem noj tau ob lub sijhawm thiab qubits.
Thiab thaum kawg, niaj hnub architectures tsis tso cai rau kev siv entanglement schemes zoo dua 1 ntawm 4 lossis 1 ntawm 6 ntawm tus nqi tsawg.
Txoj kev daws teeb meem
Txhawm rau daws cov teeb meem saum toj no, cov hauv qab no thiab cov txheej txheem tau siv tam sim no:
- Siv cryochambers uas tsis tshua muaj kub (10 mK (β273,14 Β° C))
- Siv cov processor units uas muaj kev tiv thaiv ntau tshaj plaws los ntawm kev cuam tshuam sab nraud
- Siv Quantum Error Correction Systems (Logic Qubit)
- Siv cov optimizers thaum programming circuits rau ib tug processor tshwj xeeb
Kev tshawb fawb tseem tab tom ua los txhawm rau txhawm rau txhim kho lub sijhawm decoherence, tshawb nrhiav tshiab (thiab txhim kho paub) kev siv lub cev ntawm quantum khoom, optimizing kho circuits, thiab lwm yam. Muaj kev vam meej (saib saum toj no ntawm cov yam ntxwv ntawm yav dhau los thiab niaj hnub no saum toj kawg nkaus chips), tab sis kom deb li deb nws yog qeeb, heev, qeeb heev.
D-Wave
D-Wave 2000Q 2000-qubit computer. Qhov chaw:
Amid Google tshaj tawm txog kev ua tiav quantum supremacy siv 53-qubit processor, ΠΈ los ntawm lub tuam txhab D-Wave, nyob rau hauv uas tus naj npawb ntawm qubits yog nyob rau hauv lub txhiab, yog me ntsis ruam. Zoo, tiag tiag, yog 53 qubits tau ua tiav quantum supremacy, ces dab tsi yog lub computer nrog 2048 qubits muaj peev xwm? Tab sis tsis yog txhua yam zoo li ntawd ...
Hauv luv luv (nrhiav los ntawm wiki):
Computers ua haujlwm ntawm txoj cai (), tuaj yeem daws qhov kev txwv tsis pub dhau ntawm cov teeb meem optimization, thiab tsis haum rau kev siv cov quantum algorithms thiab quantum rooj vag.
Yog xav paub ntxiv koj tuaj yeem nyeem, piv txwv li, , (ceev faj, yuav tsis qhib los ntawm Russia), los yog Π² los ntawm nws . Los ntawm txoj kev, kuv xav kom nyeem nws blog feem ntau, muaj ntau yam khoom zoo nyob ntawd
Feem ntau, txij thaum pib ntawm kev tshaj tawm, lub zej zog kev tshawb fawb muaj lus nug txog D-Wave computers. Piv txwv li, xyoo 2014, IBM tau nug qhov tseeb tias D-Wave Nws tau mus txog qhov uas nyob rau hauv 2015, Google, ua ke nrog NASA, yuav ib tug ntawm cov quantum computers thiab tom qab kev tshawb fawb. , yog lawm, lub computer ua haujlwm thiab xam qhov teeb meem sai dua li ib txwm muaj. Koj tuaj yeem nyeem ntxiv txog Google cov lus thiab, piv txwv li, .
Qhov loj tshaj plaws yog tias D-Wave computers, nrog lawv ntau pua thiab txhiab tus qubits, tsis tuaj yeem siv los xam thiab khiav quantum algorithms. Koj tsis tuaj yeem khiav Shor's algorithm rau lawv, piv txwv li. Txhua yam lawv ua tau yog siv qee yam quantum mechanisms los daws qhov teeb meem kev ua kom zoo. Peb tuaj yeem xav tias D-Wave yog quantum ASIC rau ib txoj haujlwm tshwj xeeb.
Ib me ntsis txog quantum computer emulation
Quantum suav tuaj yeem ua rau ntawm lub computer tsis tu ncua. Tseeb tiag, :
- Lub xeev ntawm qubit tuaj yeem yog tus lej complex, nyob ntawm 2x32 txog 2x64 khoom (8-16 bytes) nyob ntawm tus processor architecture
- Lub xeev ntawm N txuas qubits tuaj yeem sawv cev ua 2^N cov lej, piv txwv li. 2^(3+N) rau 32-ntsis architecture thiab 2^(4+N) rau 64-ntsis.
- Kev ua haujlwm quantum ntawm N qubits tuaj yeem sawv cev los ntawm 2^N x 2^N matrix
Tom qab ntawd:
- Txhawm rau khaws cov emulated xeev ntawm 10 qubits, 8 KB yog xav tau
- Txhawm rau khaws cov xeev ntawm 20 qubits koj xav tau 8 MB
- Txhawm rau khaws cov xeev ntawm 30 qubits, 8 GB yog xav tau
- 40 Terabytes xav tau los khaws cov xeev ntawm 8 qubits
- Txhawm rau khaws cov xeev ntawm 50 qubits, 8 Petabytes xav tau, thiab lwm yam.
Rau kev sib piv, () nqa tsuas yog 2.8 Petabytes ntawm lub cim xeeb.
- 49 qubit xa tawm xyoo tas los mus rau Suav teb loj tshaj plaws supercomputer ()
Qhov kev txwv ntawm simulating quantum computer ntawm classical systems yog txiav txim los ntawm tus nqi ntawm RAM yuav tsum tau khaws cia lub xeev ntawm qubits.
Kuv kuj pom zoo nyeem . Los ntawm muaj:
Los ntawm kev ua haujlwm - kom raug emulation ntawm 49-qubit Circuit Court uas muaj qee qhov 39 "cycles" (kev ywj pheej txheej ntawm rooj vag) 2^63 complex multiplications - 4 Pflops ntawm lub supercomputer rau 4 teev
Emulating 50+ qubit quantum computer ntawm classical systems yog suav tias yog tsis yooj yim sua nyob rau hauv lub sij hawm tsim nyog. Qhov no kuj yog vim li cas Google siv 53-qubit processor rau nws qhov kev sim quantum supremacy.
Quantum xam qhov tseem ceeb.
Wikipedia muab peb cov ntsiab lus hauv qab no ntawm quantum xam supremacy:
Quantum supremacy - muaj peev xwm pab kiag li lawm los daws cov teeb meem uas classical computers xyaum daws tsis tau.
Qhov tseeb, kev ua tiav quantum supremacy txhais tau hais tias, piv txwv li, kev ua haujlwm ntawm cov lej loj siv Shor algorithm tuaj yeem daws tau hauv lub sijhawm txaus, lossis cov tshuaj molecules nyuaj tuaj yeem ua raws li qib quantum, thiab lwm yam. Ntawd yog, lub sijhawm tshiab tau los txog.
Tab sis muaj qee qhov tsis txaus ntseeg hauv cov lus ntawm lub ntsiab lus, "uas classical computers xyaum daws tsis tau" Qhov tseeb, qhov no txhais tau hais tias yog tias koj tsim lub quantum computer ntawm 50+ qubits thiab khiav qee lub quantum circuit ntawm nws, ces, raws li peb tau tham saum toj no, qhov tshwm sim ntawm qhov Circuit Court no tsis tuaj yeem ua rau hauv lub computer tsis tu ncua. Qhov ntawd yog ib lub computer classical yuav tsis muaj peev xwm rov tsim dua qhov tshwm sim ntawm lub voj voog zoo li no.
Txawm hais tias qhov txiaj ntsig zoo li no yog qhov tseeb quantum supremacy lossis tsis yog ib lo lus nug philosophical. Tab sis nkag siab tias Google tau ua dab tsi thiab nws yog raws li dab tsi tsim nyog.
Google's Quantum Supremacy Statement
Sycamore 54-qubit processor
Yog li, thaum Lub Kaum Hli 2019, Google cov neeg tsim tawm tau tshaj tawm ib tsab xov xwm hauv kev tshaj tawm kev tshawb fawb Nature "" Cov kws sau ntawv tshaj tawm qhov ua tiav ntawm quantum supremacy thawj zaug hauv keeb kwm siv 54-qubit Sycamore processor.
Sycamore cov ntawv hauv online feem ntau xa mus rau 54-qubit processor lossis 53-qubit processor. Qhov tseeb yog tias raws li , tus processor lub cev muaj 54 qubits, tab sis ib qho ntawm lawv tsis ua haujlwm thiab tau raug tshem tawm ntawm kev pabcuam. Yog li, hauv kev muaj tiag peb muaj 53-qubit processor.
Hauv lub vev xaib tam sim ntawd cov ntaub ntawv ntawm lub ncauj lus no, qib uas txawv ntawm rau .
IBM's quantum computing team tom qab hais tias . Lub tuam txhab tau thov tias lub tshuab computer ib txwm siv los daws cov haujlwm no hauv qhov xwm txheej phem tshaj plaws hauv 2,5 hnub, thiab cov lus teb tshwm sim yuav raug ntau dua li ntawm quantum computer. Qhov kev txiav txim siab no tau ua los ntawm cov txiaj ntsig ntawm kev tshuaj ntsuam theoretical ntawm ntau txoj hauv kev optimization.
Thiab, ntawm chav kawm, hauv nws Kuv tsis tuaj yeem tsis quav ntsej cov lus no. Nws nrog rau txhua qhov txuas thiab raws li niaj zaus, lawv tsim nyog siv koj lub sijhawm. Hauv hub cov FAQ no, thiab nco ntsoov nyeem cov lus pom, muaj cov ntawv txuas mus rau cov ntaub ntawv ua ntej uas tau tawm hauv online ua ntej tshaj tawm.
Google ua li cas tiag? Rau kev nkag siab ntxaws, nyeem Aaronson, tab sis luv luv ntawm no:
Kuv tuaj yeem hais rau koj, tab sis kuv xav tias ruam heev. Kev suav yog raws li hauv qab no: tus neeg sim tsim ib qho kev sib tw quantum circuit C (piv txwv li, qhov sib txawv ntawm 1-qubit thiab 2-qubit rooj vag ntawm cov neeg nyob ze, nrog qhov tob ntawm, piv txwv li, 20, ua haujlwm ntawm 2D network ntawm n. = 50-60 qub). Tus kws sim ces xa C mus rau lub computer quantum, thiab hais kom nws siv C rau qhov pib ntawm 0, ntsuas qhov tshwm sim hauv {0,1} hauv paus, xa rov qab n-ntsis soj ntsuam ib ntus (txoj hlua), thiab rov ua ntau dua. txhiab lossis lab lub sijhawm. Thaum kawg, siv nws txoj kev paub txog C, tus kws sim ua qhov kev ntsuas ntsuas kom pom tias qhov tshwm sim zoo li qhov xav tau los ntawm quantum computer.
Luv luv heev:
- Ib qho kev sib txuas ntawm qhov ntev 20 ntawm 53 qubits yog tsim los ntawm cov rooj vag
- Lub voj voog pib nrog lub xeev pib [0β¦0] rau kev ua tiav
- Cov zis ntawm lub voj voog yog ib txoj hlua random me ntsis (piv txwv)
- Kev faib tawm ntawm qhov tshwm sim tsis yog random (kev cuam tshuam)
- Kev faib tawm ntawm cov qauv tau muab piv nrog qhov xav tau
- xaus Quantum Supremacy
Ntawd yog, Google tau siv qhov teeb meem hluavtaws ntawm 53-qubit processor, thiab ua raws nws cov lus thov kom ua tiav quantum supremacy ntawm qhov tseeb tias nws tsis tuaj yeem ua raws li cov txheej txheem ntawm cov txheej txheem hauv lub sijhawm tsim nyog.
Rau kev nkag siab - Tshooj lus no tsis nyob rau hauv ib qho kev txo qis Google qhov kev ua tiav, cov engineers zoo heev, thiab cov lus nug ntawm seb qhov no puas tuaj yeem suav tias yog quantum superiority los yog tsis, raws li tau hais ua ntej, yog kev xav ntau dua li engineering. Tab sis peb yuav tsum nkag siab tias tau ua tiav qhov kev suav zoo li no, peb tsis tau nce qib ib kauj ruam ntawm kev muaj peev xwm khiav Shor's algorithm ntawm 2048-ntsis tus lej.
Txoj kev xaus
Quantum computers thiab quantum suav yog ib qho kev cog lus zoo heev, cov tub ntxhais hluas thiab kom deb li deb tau siv thaj tsam me me ntawm cov ntaub ntawv thev naus laus zis.
Kev txhim kho ntawm quantum suav yuav (ib hnub) tso cai rau peb los daws cov teeb meem:
- Modeling complex lub cev systems nyob rau theem quantum
- Unsolvable nyob rau hauv ib lub computer tsis tu ncua vim xam complexity
Cov teeb meem tseem ceeb hauv kev tsim thiab ua haujlwm quantum computers:
- Decoherence
- Qhov yuam kev (decoherence thiab rooj vag)
- Processor architecture (tag nrho txuas qubit circuits)
Cov xwm txheej tam sim no:
- Qhov tseeb - qhov pib heev .
- Tseem tsis tau muaj kev ua lag luam tiag tiag (thiab nws tsis paub meej thaum twg yuav muaj)
Dab tsi tuaj yeem pab tau:
- Qee yam kev tshawb pom lub cev uas txo cov nqi ntawm kev xaim thiab kev khiav hauj lwm processors
- Tshawb nrhiav ib yam dab tsi uas yuav ua rau kom lub sij hawm decoherence los ntawm qhov kev txiav txim ntawm qhov loj thiab / lossis txo qhov yuam kev
Hauv kuv qhov kev xav (kev xav ntawm tus kheej nkaus xwb), Nyob rau hauv lub tam sim no scientific paradigm ntawm kev txawj ntse, peb yuav tsis muaj kev vam meej nyob rau hauv txoj kev loj hlob ntawm quantum technologies., ntawm no peb xav tau ib qho kev ua tau zoo hauv qee thaj tsam ntawm cov txheej txheem los yog siv kev tshawb fawb, uas yuav ua rau muaj kev cuam tshuam rau cov tswv yim tshiab thiab cov txheej txheem.
Lub sijhawm no, peb tau txais kev paub dhau los hauv quantum programming, sau thiab tsim quantum algorithms, sim cov tswv yim, thiab lwm yam. Peb tab tom tos txog kev tawg.
xaus
Hauv tsab xov xwm no, peb tau mus dhau lub ntsiab tseem ceeb hauv kev txhim kho quantum xam thiab quantum computers, tshuaj xyuas lub hauv paus ntsiab lus ntawm lawv txoj haujlwm, tshuaj xyuas cov teeb meem tseem ceeb ntawm cov engineers hauv kev txhim kho thiab kev ua haujlwm ntawm quantum processors, thiab tseem saib dab tsi multi-qubit. D-computers tiag tiag yog Wave thiab Google cov lus tshaj tawm tsis ntev los no ntawm kev ua tiav quantum supremacy.
Sab laug tom qab yog cov lus nug ntawm lub khoos phis tawj quantum (lus, txoj hauv kev, txoj hauv kev, thiab lwm yam) thiab cov lus nug ntsig txog kev siv lub cev tshwj xeeb ntawm cov txheej txheem, yuav ua li cas qubits tswj, txuas, nyeem, thiab lwm yam. Tej zaum qhov no yuav yog lub ntsiab lus ntawm tsab xov xwm tom ntej lossis kab lus.
Ua tsaug rau koj mloog, kuv vam tias tsab xov xwm no yuav muaj txiaj ntsig rau ib tus neeg.
(C)
Kev lees paub
rau cov ntaub ntawv pov thawj thiab cov lus pom ntawm cov ntawv nyeem, nrog rau cov ntawv
rau cov ntaub ntawv-nplua nuj cov lus ntawm , thiab tsis yog rau nws xwb, uas tau pab kuv txheeb xyuas qhov kev sib tw no.
Rau txhua tus kws sau ntawv ntawm cov ntawv thiab cov ntawv tshaj tawm uas nws cov ntaub ntawv tau siv los sau cov kab lus no.
Daim ntawv teev cov peev txheej
Cov Ntaub Ntawv Tam Sim No los ntawm [National Academies Press]
Cov khoom los ntawm Habr (nyob rau hauv random order)
Unsorted (tab sis tsis muaj tsawg nthuav) cov khoom hauv Internet
Cov chav kawm thiab cov lus qhuab qhia
Tau qhov twg los: www.hab.com