kvanturi kompiuteri
DESCRIPTION
Tsu 2007. kvanturi kompiuteri. gia giorgaZe [email protected]. gamomTvleli mowyobiloba, romelic kvanturi fizikis kanonebiT muSaobs. gamoTvla = algoriTmi + gamomTvleli mowyobiloba. - PowerPoint PPT PresentationTRANSCRIPT
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kvanturi kompiuteri
gia giorgaZegia [email protected]@jinr.ru
TsuTsu 2007 2007
gamomTvleli mowyobiloba, romelic kvanturi fizikis kanonebiT muSaobs
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gamoTvla = algoriTmi +
gamomTvleli mowyobiloba
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mocemulia diofanturi mocemulia diofanturi gantoleba ucnobTa nebismieri gantoleba ucnobTa nebismieri
ricxviTa da mTeli koeficientebiT. ricxviTa da mTeli koeficientebiT. miuTiToT meTodze, romlis miuTiToT meTodze, romlis
saSualebiTac operaciaTa sasruli saSualebiTac operaciaTa sasruli raodenobis Semdeg gairkveva, raodenobis Semdeg gairkveva,
amoxsnadia Tu ara es amoxsnadia Tu ara es
gantoleba mTel ricxvebSi.gantoleba mTel ricxvebSi.
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daviT hilberti, 1900 weli, agvisto. maTematikosTa me-2
saerTaSoriso kongresi, parizi.
hilbertis me-10 problema mocemulia diofanturi gantoleba ucnobTa nebismieri ricxviTa da mTeli
koeficientebiT. miuTiToT meTodze (proceduraze), romlis saSualebiTac
operaciaTa sasruli raodenobis Semdeg gairkveva, amoxsnadia Tu ara es gantoleba mTel ricxvebSi.
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algoriTmi kurt giodeli, alan tiuringi, emil
posti, alonzo CiorCi... tiuringis manqana, postis
manqana, λ-aRricxva, nawilobriv rekursiuli funqciebi...
yvela zemoT moyvanili aparati erTmaneTis eqvivalenturia.
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iuri matiaseviCi
Диофантовость перечислимых множеств. Доклады АН СССР, 1970
Teorema. ar arsebobs zogadi algoriTmi, romelic gaarkvevs diofanturi gantoleba amoxsnadia Tu ara mTel ricxvebSi
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amocanaTa ori klasi:
arsebobs algoriTmi
ar arsebobs algoriTmi
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algoriTmebi:
rTuli – NP-klasis, eqponencialuri...
polinomialuri, wrfivi
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(gamoTvlebis) sirTulis Teoria
problema: samarTliania Tu ara P=NP toloba?
me-20 saukunis 70-iani wlebi: s. kuki, p.karpi, l.levini
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kvanturi sistemis dinamika aRiwereba Sredingeris gantolebiT.
zogadi Teoriazogadi Teoria
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zogadi Teoriazogadi Teoria
• mdgomareobaTa sivrce mdgomareobaTa sivrce sasrulganzomilebiani hilbertis sivrceasasrulganzomilebiani hilbertis sivrcea
• evoluciis operatori am sivrcis elementebze evoluciis operatori am sivrcis elementebze (veqtorebze) moqmedeben rogorc wrfivi (veqtorebze) moqmedeben rogorc wrfivi operatorebi operatorebi
• ori damoukidebeli kvanturi sistemis ori damoukidebeli kvanturi sistemis mdgomareobaTa sivrce, rogorc erTi mdgomareobaTa sivrce, rogorc erTi sistemisa, aris TiToeuli sistemis sistemisa, aris TiToeuli sistemis mdgomareobaTa sivrcis tenzoruli namravli mdgomareobaTa sivrcis tenzoruli namravli
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kvanturi kompiuteri
U2
Ui
UN
kvanturi registeri
U1
geitebi gazoma
HdtiU i exp
sistemis evolucia, dinamika
iU geitebis generacia
sistemis evolucia emorCileba kvanturi fizikis kanonebs
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Eelementaruli kvanturi geitebiEelementaruli kvanturi geitebi
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uolS-adamaris operatoriuolS-adamaris operatori
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H H10 10 ii ee 1sin0cos
11
10
01
00
11
10
01
00
ie
11
00
i
i
e
e
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isini miiRebian Semdegi kargad cnobili hamiltonianidan:
sxva elementaruli geitebisxva elementaruli geitebi
)()(ˆ tBtH
sadac B aris 3D veqtori da
),,( zyx
10
01,
0
0,
01
10zyx i
i
x
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kvanturi paralelizmikvanturi paralelizmi
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http://www-math.mit.edu/~shor/http://www-math.mit.edu/~shor/
• Teorema.Teorema. diskretuli furies diskretuli furies gardaqmnisaTvis arsebobs gardaqmnisaTvis arsebobs polinomialuri algoriTmipolinomialuri algoriTmi
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operators ewodeba gadaxlarTvis operatori, Tu aseTia veqtori.
gadaxlarTul mdgomareobebs ar aqvT klasikuri analogi!
2222: CCCCG
2-qubits ewodeba gadaxlarTuli, Tu is ar iSleba 1-qubitebis tenzorul
namravlad.
veqtori gadaxlarTulia maSin da mxolod maSin, Tu sruldeba toloba
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kvanturi biti anu qubiti
2
V
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Qqubitis mdgomareobaTa sivrce2-ganzomilebiani sfero
erTi mdgomareobidan meoreSi gadasvla xdeba unitaruli operatoris saSualebiT
sferos nebismieri wertili SesaZlo mdgomareobaa
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elementaruli geitebierT an or qubitze moqmedi unitaruli
operatorebi arian elementaruli geitebi
arsebobs elementaruli geitebis sas-ruli raodenoba, romelic gamoTvle-bisaTvis saWiro yvela geits iZleva.
yvela 1-geiti gadaxlarTvis operator-Tan erTad iZleva kvanturi gamoTvlebis baziss.
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sawyis mdgomareobaze geitebis moqmedebis erT-erTi SesaZlo sqema
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magaliTi: belis mdgomareobebi
gadaxlarTvis operators aqvs saxe
standartul bazisze misi moqmedeba
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1 dinamika:
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2 dinamika:
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3 dinamika:
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4 dinamika:
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5 dinamika:
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6 dinamika:
)cos1(2
1
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7 dinamika:
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8 dinamika:
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9 dinamika:
)cos1()cos1(2
1)cos1(
2
1
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kvanturi kompiuteris kvanturi kompiuteris fizikuri realizaciafizikuri realizacia
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kvanturi kompiuteris fizikuri kvanturi kompiuteris fizikuri realizaciarealizacia
ionebis CamWeriionebis CamWeribirTvuli magnituri rezonansibirTvuli magnituri rezonansikvanturi wertilebikvanturi wertilebizegamtaruli elementebizegamtaruli elementebi
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literatura
M.Nielsen, I.Chuang.
Quantum computation and quantum information. Cambridge,2002
Квантовые вычисления. Современная математика и ее приложения, т.44, 2007
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gmadlobT yuradRebisTvis!gmadlobT yuradRebisTvis!
gisurvebT gisurvebT warmatebebs!warmatebebs!