Ying Jer Kao-2

8/17/2019 Ying Jer Kao-2

1/90

Uni10

The Universal Tensor Network Library

Yun-Da Hsieh, Ying-Jer Kao

Center for Advanced Study in Theoretical Scienceand Department of PhysicsNational Taiwan University

http://www.uni10.org

Tensor Network W

orkshop: Algorithms and ApplicationsIOP, ACS, 2014-12-01~05

http://www.uni10.org/


2/90

Developers

Yun-Da Hsieh (National Taiwan University)Implementation of Uni10 (C++, CUDA, Python)

Pochung Chen (National Tsing-Hua University)

Design and testing

Tama Ma (Singapore National University)

Cross-platform build

Sukhbinder Singh (Macquarie University)Matlab wrapper


3/90

Tensor• A tensor is a multidimensional array

i = 1 ,

2 , 3 , … . ,

I

j=1, 2, 3,…., J

k = 1 ,

2 , 3 ,… . , K

A(i,j,k)

A(i,:,:)

A(:,j,:)

A(:,:,k)

A(:,5,1)

A(1,:,3)

A(1,3,:)


4/90

Tensors in Science

• Data analysis

• Signal and image processing

• Quantum Physics/Information

• Quantum Loop Gravity

• Quantum Chemistry

• Bioinformatics

• Computational neuroscience


5/90

Tensors in Science

• Data analysis

• Signal and image processing

• Quantum Physics/Information

• Quantum Loop Gravity

• Quantum Chemistry

• Bioinformatics

• Computational neuroscience


6/90

Graphical Representation


7/90


A =

A1A2

A3

.

.

.

AN

Aα

vector

!


8/90


A =

A1A2

A3

.

.

.

AN

Aα

vector

!

B =

B11 · · · B1n

.

.

.

...

.

.

.

Bm1 · · · Bmn

αβ

! "

matrix


9/90


A =

A1A2

A3

.

.

.

AN

Aα

vector

!

B =

B11 · · · B1n

.

.

.

...

.

.

.

Bm1 · · · Bmn

αβ

! "

matrix

! "

rank-3 tensor

C αβγ

#


10/90


A =

A1A2

A3

.

.

.

AN

Aα

vector

!

B =

B11 · · · B1n

.

.

.

...

.

.

.

Bm1 · · · Bmn

αβ

! "

matrix

! "

rank-3 tensor

C αβγ

#

!1

rank-n tensor

α1α2α3...αn

!2 !3…

!n


11/90


A =

A1A2

A3

.

.

.

AN

Aα

vector

!

B =

B11 · · · B1n

.

.

.

...

.

.

.

Bm1 · · · Bmn

αβ

! "

matrix

! "

rank-3 tensor

C αβγ

#

!1

rank-n tensor

α1α2α3...αn

!2 !3…

!n

S scalar


12/90


product of tensors (matrices)

• Internal lines are summed over• External lines are external indices

R

! " #SQ =

Qαβ =X

γ

Rαγ S γβ

! "


13/90




R

! " #SQ =

Qαβ =X

γ

Rαγ S γβ

! "

B

A C

D

Tr(ABCD)


14/90




R

! " #SQ =

Qαβ =X

γ

Rαγ S γβ

! "

B

A C

D

Tr(ABCD)

i

A B C

! "

j k

T ijk =

X

αβ

AαiBαβjC βk


15/90

Tensor Networks forQuantum Many-body Problems

PEPS

1D MERA

w1 2 3 w4

uux y

ρ (lower half)

ρ (upper half)

H

2D MERA

Things get messy when fermions are involved


16/90

Tensor Contraction

• Bookkeeping tensor indices istedious and error prone.

• Programming fermonic systemscan be complicated

• Minimize computation time and

memory usage

• Speed up computation withcompute accelerators (GPU, MIC)

!

" #

A

X

β

Aαβγ B

βµν

!

"

#

A

$

%

BBA


17/90

HardwareCPU, GPU

Low-Level LibrariesBLAS, LAPACK, CUDA, cuBLAS, Magma

Matlab, C++,Fortran, Python

Tensor Network ApplicationsDMRG, iTEBD, iPEPS, TRG, MERA, etc.


18/90

HardwareCPU, GPU

Low-Level LibrariesBLAS, LAPACK, CUDA, cuBLAS, Magma

Matlab, C++,Fortran, Python

Tensor Network ApplicationsDMRG, iTEBD, iPEPS, TRG, MERA, etc.

Uni10

Other tensor libraries: iTensor, TNT, SCON, NCON


19/90

Uni10• Fully implemented in objected-oriented C++

• Aimed toward applications in tensor network algorithms

• Provides basic tensor operations with easy-to-use interface

• A symmetric tensor class UniTensor (Abelian symmetry) withauxiliary classes for quantum numbers, Qnum , blocks Block and

bond labels, Bond and functions performing tensor operations.• A network class Network, where details of the graphical

representations of the networks are processed and stored.

• An engine to construct and analyze the contraction tree for a givennetwork.

• A heuristic algorithm to search for an optimal binary contractionorder based on the computational and memory constraints.

• Provides wrappers for Matlab (soon)and Python (pyUni10).

• Supports acceleration with Nvidia Cuda based GPU.

• Open source LGPL with cite-me license


20/90

A !

C

D

-1

-2

-3

-4

E

F

1

2

3

4

5

6

7

8

Network

Network

UniTensor Matrix

QnumBond Block

getBlock()

putBlock()

putTensor() launch()

UniTensor

2

1 3

4

Block

QnumBond

Q1

Q2

Q3

QaQb Qc

Qd

Matrix

UniTensor

2

1 3

4

Block

QnumBond

Q1

Q2

Q3

QaQb Qc

Qd

Matrix

UniTensor

2

1 3

4

Block

QnumBond

Q1

Q2

Q3

QaQb Qc

Qd

Matrix


21/90

Spin-1 Heisenberg Model

H = S1

· S2

1

2

3

4

S2S1

|S zi ∈ {|1i, |0i, | − 1i}

Construct symmetric basis


22/90

1 3

4

|1>|0>|-1>

|1>|0>|-1>


23/90

1 3

4

|1>|0>|-1>

|1>|0>|-1>

1 3

4

Sz=1

q#

q#


24/90

Qnum q0(0), q1(1), qm1(-1);

Bond bdr(BD_IN, [qm1, q0, q1]);

Bond bdc(BD_OUT, [qm1, q0, q1]);

UniTensor T([bdr, bdr, bdc, bdc]);

1 3

4

q#

q#

raw element block element

T.addRawElem(raw)


25/90

3

4

5

6

1

2

Ta Tb

Ta * Tb

Ta.addLabel([1, 2, 3, 4]);

Tb.addLabel([3, 4, 5, 6]);


26/90

UniTensor

• Operation• Tc = Ta * Tb;

•Tc = 2.13 * Ta;

• Tc = Ta + Tb;

• permute() and transpose()

•I / O

• write: Ta.save(“out”);

• read: UniTensor Ta(“out”);

• print: cout


27/90

UniTensor

• Operation• Tc = Ta * Tb;

•Tc = 2.13 * Ta;

• Tc = Ta + Tb;

• permute() and transpose()

•I / O

• write: Ta.save(“out”);

• read: UniTensor Ta(“out”);

• print: cout


28/90

Symmetries

U(1)

• Total Sz (spin systems)

• Total particle number (fermionic/bosonic systems)

Z2

• Parity

• Key to fermionic system


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Fermionic system

C1† C2† |0> = -C2† C1† |0>

|1,1> = - |1,1>

minus sign


30/90

A|0>

|1>

|0>

|1>1

2

4

3

p = 0

p = 1

Particle parity


31/90

0,0> 0,1> 1,0> 1,1>

0,0> 1 ! ! 2

0,1> ! 3 4 !

1,0> ! 5 6 !

1,1> 7 ! ! 8

A|0>

|1>

|0>

|1>1

2

4

3

p = 0

p = 1

Particle parity


32/90

Ta * Tb

A

1

2

3

4

B

5

6

minus sign!

4

3


33/90

A

1

2

B

5

6

minus sign!

3

4

[1, 2, 4, 3] [3, 4, 5, 6]

Before contraction:

Ta.permute([1, 2, 3, 4], 2)

[1, 2, 4, 3] —> [1, 2, 3, 4]

Ta * Tb

4

3


34/90

0,0> 0,1> 1,0> 1,1>

0,0> 1 ! ! 2

0,1> ! 3 4 !

1,0> ! 5 6 !

1,1> 7 ! ! 8

A|0>

|1>

|0>

|1>1

2

4

3


35/90

0,0> 0,1> 1,0> 1,1>

0,0> 1 ! ! -2

0,1> ! 3 4 !

1,0> ! 5 6 !

1,1> 7 ! ! -8

swap gates are added in permute()

A|0>

|1>

|0>

|1>1

2

4

3


36/90

UniTensor & Matrix

• Interactions:• T.qnums();

• T.getBlock(q3);

• T.putBlock(q3);

• Matrix operations:• M.eigh();

• M.svd();

• Mc = Ma * Mb;

• M.transpose();

getBlock(q3) putBlock(q3)

1 3

4

q1q2

q3

q4

"U VT

svd()

U * " * VT


37/90

Network

File for network connection: demo.txt

C: -1; 7 1D: -2; 2 8A: 1 2; 3 4B: 3 4; 5 6

E: 7 5; -3F: 6 8; -4ABCDEF

Network net(“demo.txt”)

A1

2

3

4

!

5

6

C7-1

D8

-2

E-3

F -4


38/90

Network

C: -1; 7 1D: -2; 2 8A: 1 2; 3 4B: 3 4; 5 6

E: 7 5; -3F: 6 8; -4ABCDEF

net

A1

2

3

4

!

5

6

C7-1

D8

-2

E-3

F -4


39/90

Network - putTensor

net.putTensor(0, C);

C: -1; 7 1D: -2; 2 8A: 1 2; 3 4B: 3 4; 5 6

E: 7 5; -3F: 6 8; -4ABCDEF

net

A1

2

3

4

!

5

6

C7-1

D8

-2

E-3

F -4

012345


40/90

Network - putTensor

net.putTensor(2, A);

C: -1; 7 1D: -2; 2 8A: 1 2; 3 4B: 3 4; 5 6

E: 7 5; -3F: 6 8; -4ABCDEF

net

A1

2

3

4

!

5

6

C7-1

D8

-2

E-3

F -4

012345


41/90

Network - launch

Tresult = net.launch();

C: -1; 7 1D: -2; 2 8A: 1 2; 3 4B: 3 4; 5 6E: 7 5; -3F: 6 8; -4ABCDEF

A1

2

3

4

!

5

6

C7-1

D8

-2

E-3

F -4

net


42/90

Network - reusable

net.putTensor(3, B’)Tresult = net.launch();

C: -1; 7 1D: -2; 2 8A: 1 2; 3 4B: 3 4; 5 6

E: 7 5; -3F: 6 8; -4ABCDEF

net

A1

2

3

4

!’5

6

C7-1

D8

-2

E-3

F -4

0123

45


43/90

Contraction order

C: -1; 7 1D: -2; 2 8

A: 1 2; 3 4B: 3 4; 5 6E: 7 5; -3F: 6 8; -4

CDABEF

A1

2

3

4 !

5

6

C7-1

D8

-2

E-3

F-4

Finding the optimal contraction order for a generaltensor network is NP-hard

C.-C. Lam, et al.,Parallel Processing Letters 07, 157 (1997).


44/90

Contraction order

C: -1; 7 1D: -2; 2 8

A: 1 2; 3 4B: 3 4; 5 6E: 7 5; -3F: 6 8; -4

CDABEF

A1

2

3

4 !

5

6

C7-1

D8

-2

E-3

F-4

Finding the optimal contraction order for a generaltensor network is NP-hard

C.-C. Lam, et al.,Parallel Processing Letters 07, 157 (1997).

Using heuristics


45/90

A B

C

E FD

Network - launch

(((A * B) * C) * E) * (D * F)

C: -1; 7 1

D: -2; 2 8A: 1 2; 3 4B: 3 4; 5 6E: 7 5; -3

F: 6 8; -4

CDABEF


46/90

A B

C

E FD

Network - launch

(((A * B) * C) * E) * (D * F)

C: -1; 7 1

D: -2; 2 8A: 1 2; 3 4B: 3 4; 5 6E: 7 5; -3

F: 6 8; -4

net.launch() CDABEF


47/90

A B

C

E FD

Network - launch

(((A * B) * C) * E) * (D * F)

C: -1; 7 1

D: -2; 2 8A: 1 2; 3 4B: 3 4; 5 6E: 7 5; -3

F: 6 8; -4

net.launch() CDABEF

Using heuristics to generate

an “optimal” binary contraction tree


48/90

Why binary?

Cost: abclmn

A

B C

a

b c

l

m

n

Dabc =

X

lmn

AalnBbmlC cnm


49/90

A

B C

a

b c

lm

n

pairwise contractions

A

B C

Cost: b c l m n + a b c l n

Cost: a b c l m n

(pairwise)

(direct sum)

pairwise is better if: (1 / a + 1 / m) < 1


50/90

A

B C

a

b c

lm

n


A

B C

(pairwise)

(direct sum)b c l n

Cost: b c l m n + a b c l n

Cost: a b c l m n

pairwise is better if: (1 / a + 1 / m) < 1

Intermediatetensor


51/90

A

B C

a

b c

l

m

n


A

B C

B

C A

C

A B

(1 / a + 1 / m) (1 / b + 1 / n) (1 / c + 1 / l )

b c l n a c l m a b m n

Time

Space


52/90

A B C D E F G

B D E A C F G

A G C FD EB

Nz

Nx Ny

getCost(Nz) =min( Cost(Nx * Ny) + getCost(Nx) + getCost(Ny) )

For all possible (Nx, Ny)(2n−1−

1)

n!(n− 1)!

2n−1Total:

Pfeifer et al., arXiv:1304.6112(2013)

a


53/90

A

B C

a

b c

l

m

n


A

B C

B

C A

C

A B

(1 / a + 1 / m) (1 / b + 1 / n) (1 / c + 1 / l )

b c l n a c l m a b m n

Time

Space

Assume:a=b=c

a


54/90

A

B C

a

b c

l

m

n


A

B C

Efficiency of B * C:(ElemNum(B) + ElemNum(C)) / ElemNum(B * C)

B * C: (lmb + nmc) / lnbc= m / nc + m / lb


55/90

Network

C: -1; 7 1D: -2; 2 8

A: 1 2; 3 4B: 3 4; 5 6E: 7 5; -3F: 6 8; -4

CDABEF

A

2

3 4

!

5 6

C

7

-1

D

8

-2

E- 3

F-4 Optimal contraction order: NP-hard


56/90

Network

C: -1; 7 1D: -2; 2 8

A: 1 2; 3 4B: 3 4; 5 6E: 7 5; -3F: 6 8; -4

CDABEF

A

2

3 4

!

5 6

C

7

-1

D

8

-2

E- 3

F-4 Use human intelligence


57/90

Network

C: -1; 7 1D: -2; 2 8

A: 1 2; 3 4B: 3 4; 5 6E: 7 5; -3F: 6 8; -4

CDABEF

A

2

3 4

!

5 6

C

7

-1

D

8

-2

E- 3

F-4

ORDER: ABCEDF

Give a suggested sequence of contraction

Use human intelligence


58/90

O[log(n)] ~ O[n]n!(n− 1)!

2n−1

A B

C

E FD

ORDER: ABCEDF

Not always optimal, but the algorithm is fast,

and several trials can give a better sequence.


59/90

Network - launch

A 1 2

3 4

!

5 6

C

7

- 1

D

8

- 2

E

- 3

F

- 4

ABCDEF


60/90

Network - launch

A 1 2

3 4

!

5 6

C

7

- 1

D

8

- 2

E

- 3

F

- 4

ABCDEF

A B


61/90

C

Network - launch

A 1 2

3 4

!

5 6

C

7

- 1

D

8

- 2

E

- 3

F

- 4

ABCDEF

A B


62/90

D

C

Network - launch

A 1 2

3 4

!

5 6

C

7

- 1

D

8

- 2

E

- 3

F

- 4

ABCDEF

A B


63/90

E

D

C

Network - launch

A 1 2

3 4

!

5 6

C

7

- 1

D

8

- 2

E

- 3

F

- 4

ABCDEF

A B


64/90

Network - launch

ABCDEF

E D

C

A B

A 1 2

3 4

!

5 6

C

7

- 1

D

8

- 2

E

- 3

F

- 4


65/90

Network - launch

ABCDEF

D

E

C

A B

A 1 2

3 4

!

5 6

C

7

- 1

D

8

- 2

E

- 3

F

- 4


66/90

A B

C

E FD

Network - launch

ABCDEF

(((A * B) * C) * E) * (D * F)

A 1 2

3 4

!

5 6

C

7

- 1

D

8

- 2

E

- 3

F

- 4


67/90

A B

C

E FD

Network - launch

C: -1; 7 1

D: -2; 2 8A: 1 2; 3 4B: 3 4; 5 6E: 7 5; -3F: 6 8; -4

net.launch()

CDABEF

ORDER: (((A * B) * C) * E) * (D * F)


68/90

A B

C

E FD

Network - launch

(((A * B) * C) * E) * (D * F)

C: -1; 7 1D: -2; 2 8

A: 1 2; 3 4B: 3 4; 5 6E: 7 5; -3F: 6 8; -4ABCDEF


69/90

A B

C

E FD

Network - launch

(((A * B) * C) * E) * (D * F)

C: -1; 7 1D: -2; 2 8

A: 1 2; 3 4B: 3 4; 5 6E: 7 5; -3F: 6 8; -4ABCDEF

for fermionic systemCDABEF != ABCEDF


70/90

A B

C

E FD

Network - launch

(((A * B) * C) * E) * (D * F)

C: -1; 7 1D: -2; 2 8

A: 1 2; 3 4B: 3 4; 5 6E: 7 5; -3F: 6 8; -4ABCDEF

for fermionic systemCDABEF != ABCEDF

CDABEF = net.launch()

E l C T f M t i


71/90

Example: Corner Transfer Matrix

h ÔiRomán Orús and Guifré Vidal, PRB 80, 094403 (2009)

• Used in iPEPS toestimate the environment

• Different bond dims• $ bd: boundary index • $ int: internal index • d : physical index

• Expectation value of an

operator

CTM

http://ctm.net/


72/90

CTM.net

C1: 1 2C2: 34 35

C3: 41 42

C4: 19 16

T1b: 1 20 3 4

T1a: 20 34 21 22

T2a: 35 38 36 37

T2b: 38 41 39 40

T3b: 42 33 31 32

T3a: 33 19 17 18

T4a: 16 13 14 15

T4b: 13 2 5 6

A1: 4 24 10 6 8

A1T: 3 23 9 5 7

B1: 22 37 27 24 25

B1T: 21 36 26 23 25

A2: 27 40 32 29 30

A2T: 26 39 31 28 30

B2: 10 29 18 15 12

B2T: 9 28 17 14 11O: 7 8 11 12

TOUT:

ORDER: C1 T1b T4b A1T A1 O B2T B2 T4a C4 T3a T1a B1T B1 A2T A2 T3b C2 T2a T2b C3

http://ctm.net/


73/90

Memory Requirement: 37846846304

Sum of memory usage: 47505684008

Maximun tensor:

elemNum: 4304672100

10 bonds and labels: 20, 13, 23, 24, 28, 17, 14, 29, 18, 15,

((((((((((((((((((((C1 T1b) T4b) A1T) A1) O) B2T)

B2) T4a) C4) T3a) T1a) B1T) B1) A2T) A2) T3b) C2) T2a) T2b) C3)


74/90



Maximun tensor:

elemNum: 425152800

9 bonds and labels: 20, 13, 23, 24, 10, 12, 28, 17, 14,


75/90



Maximun tensor:

elemNum: 425152800

9 bonds and labels: 20, 13, 23, 24, 10, 12, 28, 17, 14,



Maximun tensor:

elemNum: 4304672100

10 bonds and labels: 20, 13, 23, 24, 28, 17, 14, 29, 18, 15,

Memory Requirement:6 810 336 800 / 37 846 846 304 =

0.17994463119

Total Memory Usage

16 039 257 608 / 47 505 684 008 =0.33762817951


76/90

M e m o r y

U s a g e

Bond Dimension

!

8

"!

7

Courtesy: Marc Ziegler @ U Mainz

C d S l MERA


77/90

Code Sample: MERA

!"

!# !$

!%

!" !%

!# !$

&

"

% '

#

(

$

)

* +

"& ""

w1 w2

w†2

w†1

u†

u

Ascending operator:renormalization of a two-site operator

C d S l MERA


78/90

!"

!# !$

!%

&

"

%

'

# (

$

)

*

+

"& ""

w1 w2

w†2

w†1

u†

u Qnum q10(1, PRT_EVEN);

Qnum q_10(-1, PRT_EVEN);

Qnum q30(3, PRT_EVEN);

Qnum q_11(PRTF_ODD, -1, PRT_EVEN);

Qnum q11(PRTF_ODD, 1, PRT_EVEN);

Qnum q_31(PRTF_ODD, -3, PRT_EVEN);

#include "uni10.hpp"

Define quantum numbers

Code Sample: MERA

Code Sample: MERA


79/90

!"

!# !$

!%

&

"

%

'

# (

$

)

*

+

"& ""

w1 w2

w†

2w

†

1

u†

u

vector bonds;

vector qnums;

qnums.push_back(q10);

qnums.push_back(q_11);

Bond bdr(BD_IN, qnums);Bond bdc(BD_OUT, qnums);

bonds.push_back(bdr);

bonds.push_back(bdr);

bonds.push_back(bdc);


Assign quantum numbers to bonds

Code Sample: MERA

Code Sample MERA


80/90

!"

!# !$

!%

&

"

%

'

# (

$

)

*

+

"& ""

w1 w2

w†

2w

†

1

u†

u

Define Hamiltonian operator

double H_elem[] = {1.0/4, 0, 0, 0,

0, -1.0/4, 1.0/2, 0, 0, 1.0/2, -1.0/4, 0,

0, 0, 0, 1.0/4};

UniTensor H0(bonds, "Ob");

H0.addRawElem(H_elem);

Code Sample: MERA

Code Sample MERA


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!"

!# !$

!%

&

"

%

'

# (

$

)

*

+

"& ""

w1 w2

w†

2w

†

1

u†

u

vector qnums1;qnums1.push_back(q30);

qnums1.push_back(q11);



qnums1.push_back(q_10);




Bond bdr1(BD_IN, qnums1);

bonds.clear();

bonds.push_back(bdr1);




UniTensor W1(bonds, "W1");

W1.orthoRand();

UniTensor W1T = W1;

W1T.transpose();

Code Sample: MERA

Define w, w†

Code Sample: MERA


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!"

!# !$

!%

&

"

%

'

# (

$

)

*

+

"& ""

w1 w2

w

†2w

†1

u†

u

vector tens;

tens.push_back(&W1);

tens.push_back(&W2);

tens.push_back(&U);

tens.push_back(&H0);tens.push_back(&UT);

tens.push_back(&W1T);

tens.push_back(&W2T);

UniTensor H1, H2;

Network asdL(“AscendL.net", tens);

H1 = asdL.launch();

Code Sample: MERA

Assign tensors into network

Code Sample: MERA


83/90

!"

!# !$

!%

&

"

%

'

# (

$

)

*

+

"& ""

w1 w2

w†

2

w†

1

u†

u

W1: -1; 0 1 3

W2: -2; 7 10 11

U: 3 7; 4 8Ob: 1 4; 2 5

UT: 5 8; 6 9

W1T: 0 2 6; -3

W2T: 9 10 11; -4

TOUT:-1 -2; -3 -4

ORDER: (W1T ((W1 (Ob ((W2 * W2T) ( U, UT))))) )

AscendL.net

Code Sample: MERA

Code Sample: MERA


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!"

!# !$

!%

&

"

%

'

# (

$

)

*

+

"& ""

w1 w2

w†

2

w†

1

u†

u asdL.putTensor(0, &W1);

asdL.putTensor(1, &W2);asdL.putTensor(2, &U);

asdL.putTensor(3, &H0);

asdL.putTensor(4, &UT);

asdL.putTensor(5, &W1T);

asdL.putTensor(6, &W2T);

H2 = asdL.launch();


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pyUni10

• Programming in C++ is too hardcore.

• Need something that even a layman knows how toprogram.

• Take advantage of the beauty of Python.

• pyUni10: Wrapping the power of Uni10 with aeasy-to-program Python interface.

A l ti ith GPU


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Acceleration with GPU

GPU CPU

!

"

#

AA$

%

BB"

A l ti ith GPU


87/90

Acceleration with GPU

GPU CPU

!

#

AA * B$

%

Switching from CPU to GPU versionwithout any change in your functions

Unified API

Uni10


88/90

Uni10• Geared toward tensor network algorithms

• Reduce development time

• Behind-the-scene optimization

• Support for Python (pyUni10) and Matlab (soon)

• To do:

• GUI tools for network generation

• Non-abelian symmetries: SU(2)• OpenCL, MIC, Multi-GPU/Multi-node support

• Better search algorithm for contraction order (TensorContraction Engine, etc.)

http://uni10.org

N t k

http://uni10.org/


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A !

C

D

-1

-2

-3

-4

E

F

1

2

3

4

5

6

7

8

Network

Network

UniTensor Matrix

QnumBond Block

getBlock()

putBlock()

putTensor() launch()

UniTensor

2

1 3

4Block

QnumBond

Q1

Q2

Q3

QaQb Qc

Qd

Matrix

UniTensor

2

1 3

4Block

QnumBond

Q1

Q2

Q3

QaQb Qc

Qd

Matrix

UniTensor

2

1 3

4Block

QnumBond

Q1

Q2

Q3

QaQb Qc

Qd

Matrix

Memory Hierarchy


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Memory Hierarchy

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")+, -

.#$/0 123 45.#$/0 143 45.#$/0 1-3 45

.#$/0 123 -5.#$/0 143 -5.#$/0 1-3 -5

")+, 4

.#$/0 143 45

.#$/0 143 -5

.#$/0 143 25

.#$/0 1-3 45

.#$/0 1-3 -5

.#$/0 1-3 25

67)(&, .#$/0

8()9%#$/0 :7&)(,

'('$)*

67)(&,

8()9;7)(&, #$/

'('$)*

Documents

Ying Jer Kao-2