Mladen Paviciˇ c:´ Graﬁ cko raˇ cunanjeˇ kvantno-mehanickih … · 2011-02-22 · su sami kvantni sistemi. Zatim, jedino kvantni sistemi, koji su hardware kvantnih kompjutera,

Mladen Pavicic: Graficko racunanjekvantno-mehanickih nelinearnih jednadžbi

Projekt:Kvantno racunanje: paralelnost i vizualizacija(082-0982562-3160); voditelj: M. Pavicic

Program: Distrada i znanstvena vizualizacija(0982562); voditelj: Karolj Skalae-Science day, IRB 17.12.2009

Prof. dr. sc. Mladen Pavicic, Katedra za fiziku, Gradjevinski fakultet u Zagrebu

[email protected] ; Web: http://m3k.grad.hr/pavicic

Mladen Pavicic: Graficko racunanje kvantno-mehanickih nelinearnih jednadzbi – p. 1

Pozadina

Gatesova ideja: Riješiti probleme sirovom silom.


Pozadina


Medjutim: Moore: Hoops! Sorry!:


Pozadina



1993 1996 1999 2002 20050.1

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Pozadina



1993 1996 1999 2002 20050.1

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Intel CPU introductions: 486-50 MHz Jun 1991, DX2-66 Aug 92, P(entium)-100 Mar 94,P-133 Jun 95, P-200 Jun 96, PII-300 May 97, PII-450 Aug 98, PIII-733 Oct 99, PIII-1.0 GHz

Mar 00, P4-1.7 Apr 01, P4-2.0 Aug 01, P4-2.53 May 02, P4-2.8 Aug 02, P4-3.0 Apr 03,P4-3.4 Apr 04, P4-3.6 Jun 04, P4-3.8 Nov 04.


Problem

Pripreme i mjerenja stanja kvantnih sistema ne možemosimulirati klasicnim sistemima.


Problem

Pripreme i mjerenja stanja kvantnih sistema ne možemosimulirati klasicnim sistemima.Npr., jedini stvarni generator nasumicno generiranih brojevasu sami kvantni sistemi. Zatim, jedino kvantni sistemi, kojisu hardware kvantnih kompjutera, mogu direktno simuliratikvantne probleme. Klasicni hardware ih može samorješavati preko binarnog koda jednadžbi.


Problem

Pripreme i mjerenja stanja kvantnih sistema ne možemosimulirati klasicnim sistemima.Npr., jedini stvarni generator nasumicno generiranih brojevasu sami kvantni sistemi. Zatim, jedino kvantni sistemi, kojisu hardware kvantnih kompjutera, mogu direktno simuliratikvantne probleme. Klasicni hardware ih može samorješavati preko binarnog koda jednadžbi.

Izracunavanje orijentacija uredjaja zapripremu i mjerenje kvantnih stanja tražimasivno racunanje pomocu clustera i grida.Rezultati su premnogobrojni → primijen-juje se 2D, 3D i 4D graficka vizualizacija.Priprema stanja koja su iskljucivo kvantna:Kochen-Specker-ova stanja.


PHYSICAL REVIEW A69, 062311 (2004)


Multiparty entanglement in graph states


M. Hein, J. Eisert, and H. J. Briegel


Institut für Physik, Uni Potsdam


Blackett Lab., Imperial College, London


Orthogonal Spins

We have to measure spins in 3, 4, 5, . . . dimensions.


Orthogonal Spins

We have to measure spins in 3, 4, 5, . . . dimensions. Ofcourse in a Hilbert space. It corresponds to outgoing portsin our 3-dim lab.


Orthogonal Spins

We have to measure spins in 3, 4, 5, . . . dimensions. Ofcourse in a Hilbert space. It corresponds to outgoing portsin our 3-dim lab. Vectors are orthogonal ⇒ nonlinearequations

aB · aC = aB1aC1 + aB2aC2 + aB3aC3 + aB4aC4 = 0,

aB · aD = aB1aD1 + aB2aD2 + aB3aD3 + aB4aD4 = 0,

aB · aE = aB1aE1 + aB2aE2 + aB3aE3 + aB4aE4 = 0,

aC · aD = aC1aD1 + aC2aD2 + aC3aD3 + aC4aD4 = 0,

aC · aE = aC1aE1 + aC2aE2 + aC3aE3 + aC4aE4 = 0,

aD · aE = aD1aE1 + aD2aE2 + aD3aE3 + aD4aE4 = 0.


Mission Impossible

To solve these equations for all possible combinations for atleast 18 vectors (no solutions below 18) we would need amillion ages of the universe on all today’s processors on theGlobe working in parallel.


Mission Impossible

To solve these equations for all possible combinations for atleast 18 vectors (no solutions below 18) we would need amillion ages of the universe on all today’s processors on theGlobe working in parallel.

D3,1 D3,2

D4,3 D4,4

Figure 1: Generation tree for MMP diagrams with

loops of size 5 for 3-dim vectors.

1

Use MMP hyper-graphs instead ofequations.


Exponential ⇒ Polynomial

We first “translate” nonlinear equations into linearhypergraphs.



We first “translate” nonlinear equations into linearhypergraphs.Next, we impose conditions on generation of hypergraphs.Generation proves to be statistically polynomially complex(SPC).



We first “translate” nonlinear equations into linearhypergraphs.Next, we impose conditions on generation of hypergraphs.Generation proves to be statistically polynomially complex(SPC).We filter the obtained hypergraphs by additions conditions.The procedure is also SPC.



We first “translate” nonlinear equations into linearhypergraphs.Next, we impose conditions on generation of hypergraphs.Generation proves to be statistically polynomially complex(SPC).We filter the obtained hypergraphs by additions conditions.The procedure is also SPC.In the end we translate a rather “small” number (millions) ofhypergraphs back into equations and solve them by meansof interval analysis method. Its programs are SPC as well.


David A. Richter


Western Michigan University


P.K.Aravind


Worcester Polytechnic Institute


Norman D. Megill, Boston Information Group

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Solutions

\ 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 total

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19 1 1

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22 1 9 36 23 12 3 1 85

23 2 19 76 79 58 27 11 3 1 276

24 1 6 39 137 187 188 136 83 40+ 1 18 6 2 1 845

total 1 2 8 24 65 139 228 248 216 147 86 42 18 6 2 1 1233


Solutions

\ 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 total

18 1 1

19 1 1

20 1 4+ 1 1 7

21 2 11 4 1 18

22 1 9 36 23 12 3 1 85

23 2 19 76 79 58 27 11 3 1 276

24 1 6 39 137 187 188 136 83 40+ 1 18 6 2 1 845

total 1 2 8 24 65 139 228 248 216 147 86 42 18 6 2 1 1233

Boxed in red are the solutionspreviously found by humans.


Solutions

\ 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 total

18 1 1

19 1 1

20 1 4+ 1 1 7

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22 1 9 36 23 12 3 1 85

23 2 19 76 79 58 27 11 3 1 276

24 1 6 39 137 187 188 136 83 40+ 1 18 6 2 1 845

total 1 2 8 24 65 139 228 248 216 147 86 42 18 6 2 1 1233

Boxed in red are the solutionspreviously found by humans.

It would take over 150 years togenerate all the solutions on a sin-gle PC


Brendan D. McKay, Australian National Univ.

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A i Danko Bosanac, IRB . . .

je na projektu, ali u njegovim drugim teorijskim dijelovima, ane na konkretnim clusterskim i grid racunanjima.



PARALELIZAM & VIZUALIZACIJA . . .

. . . ili kako paralelno vizualizirano grid racunanje gradikvantnu—inherentno paralelnu—simulaciju.

Hvala!


Documents

Mladen Paviciˇ c:´ Graﬁ cko raˇ cunanjeˇ kvantno-mehanickih … · 2011-02-22 · su sami kvantni sistemi. Zatim, jedino kvantni sistemi, koji su hardware kvantnih kompjutera,