Upgrade to Pro
— share decks privately, control downloads, hide ads and more …
Speaker Deck
Features
Speaker Deck
PRO
Sign in
Sign up for free
Search
Search
Qubism: self-similar visualization of a many-bo...
Search
Piotr Migdał
January 10, 2013
Science
1
320
Qubism: self-similar visualization of a many-body wavefunction
Article, code and more:
http://qubism.wikidot.com/
Piotr Migdał
January 10, 2013
Tweet
Share
More Decks by Piotr Migdał
See All by Piotr Migdał
Detecting trypophobia triggers (with deep learning)
pmigdal
1
240
Teaching Machine Learning
pmigdal
7
1.5k
A game needs to framework
pmigdal
1
170
Visualizing word coincidences
pmigdal
1
70
Dreams, Drugs and ConvNets
pmigdal
1
860
{Machine, Deep} Learning for software engineers
pmigdal
1
2.1k
Lightning talk - Teaching machine learning
pmigdal
0
1.7k
Interaktywna wizualizacja danych w d3.js
pmigdal
2
640
Gry naukowe, moja gra kwantowa
pmigdal
0
220
Other Decks in Science
See All in Science
最適化超入門
tkm2261
14
3.5k
小杉考司(専修大学)
kosugitti
2
620
Causal discovery based on non-Gaussianity and nonlinearity
sshimizu2006
0
230
マテリアルズ・インフォマティクスの先端で起きていること / What's Happening at the Cutting Edge of Materials Informatics
snhryt
1
190
生成AI による論文執筆サポートの手引き(ワークショップ) / A guide to supporting dissertation writing with generative AI (workshop)
ks91
PRO
0
400
(論文読み)贈り物の交換による地位の競争と社会構造の変化 - 文化人類学への統計物理学的アプローチ -
__ymgc__
1
180
白金鉱業Meetup Vol.16_数理最適化案件のはじめかた・すすめかた
brainpadpr
3
1.4k
第61回コンピュータビジョン勉強会「BioCLIP: A Vision Foundation Model for the Tree of Life」
x_ttyszk
1
1.6k
06_浅井雄一郎_株式会社浅井農園代表取締役社長_紹介資料.pdf
sip3ristex
0
180
【健康&筋肉と生産性向上の関連性】 【Google Cloudを企業で運用する際の知識】 をお届け
yasumuusan
0
470
Visual Analytics for R&D Intelligence @Funding the Commons & DeSci Tokyo 2024
hayataka88
0
140
All-in-One Bioinformatics Platform Realized with Snowflake ~ From In Silico Drug Discovery, Disease Variant Analysis, to Single-Cell RNA-seq
ktatsuya
0
310
Featured
See All Featured
CoffeeScript is Beautiful & I Never Want to Write Plain JavaScript Again
sstephenson
160
15k
Art, The Web, and Tiny UX
lynnandtonic
298
20k
"I'm Feeling Lucky" - Building Great Search Experiences for Today's Users (#IAC19)
danielanewman
227
22k
Designing on Purpose - Digital PM Summit 2013
jponch
117
7.1k
I Don’t Have Time: Getting Over the Fear to Launch Your Podcast
jcasabona
32
2.1k
Code Review Best Practice
trishagee
67
18k
Writing Fast Ruby
sferik
628
61k
How GitHub (no longer) Works
holman
314
140k
Thoughts on Productivity
jonyablonski
69
4.5k
Performance Is Good for Brains [We Love Speed 2024]
tammyeverts
7
650
Unsuck your backbone
ammeep
669
57k
Fantastic passwords and where to find them - at NoRuKo
philnash
51
3k
Transcript
self-similar visualization of many-body wavefunctions QUBISM: presented by: Piotr Migdał
(ICFO, Barcelona)
Don’t take plots for granted!
None
None
bar chart - William Playfair (1786) scatter plot - Francis
Galton (a century later)
Dmitri Mendeleev | Periodic Table of Elements (1869) periodic table
- Dimitri Mendeleev (1869)
Back to the quantum world
↵|"i + |#i
↵|"i + |#i ⇠ = ↵| i + |•i
↵|"i + |#i ⇠ = ↵| i + |•i ⇠
= ↵|0i + |1i
↵|"i + |#i ⇠ = ↵| i + |•i ⇠
= ↵|0i + |1i ↵00 |00i + ↵01 |01i + ↵10 |10i + ↵11 |11i
↵|"i + |#i ⇠ = ↵| i + |•i ⇠
= ↵|0i + |1i ↵00 |00i + ↵01 |01i + ↵10 |10i + ↵11 |11i ↵000 |000i + ↵001 |001i + ↵010 |010i + ↵011 |011i + ↵100 |100i + ↵101 |101i + ↵110 |110i + ↵111 |111i
↵|"i + |#i ⇠ = ↵| i + |•i ⇠
= ↵|0i + |1i 2n complex parameters ↵00 |00i + ↵01 |01i + ↵10 |10i + ↵11 |11i ↵000 |000i + ↵001 |001i + ↵010 |010i + ↵011 |011i + ↵100 |100i + ↵101 |101i + ↵110 |110i + ↵111 |111i
None
None
00 01 10 11
00 01 10 11 00 01 00 01 10 11
10 11 00 01 00 01 10 11 10 11
00 01 10 11 00 01 10 11 00 01
10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 00 01 10 11 10 11 00 01 00 01 10 11 10 11
00 01 10 11 00 01 10 11 00 01
10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 00 01 10 11 10 11 00 01 00 01 10 11 10 11 |101000i
00 01 10 11 00 01 10 11 00 01
10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 00 01 10 11 10 11 00 01 00 01 10 11 10 11 |101000i
00 01 10 11 00 01 10 11 00 01
10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 00 01 10 11 10 11 00 01 00 01 10 11 10 11 |101000i
00 01 10 11 00 01 10 11 00 01
10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 00 01 10 11 10 11 00 01 00 01 10 11 10 11 |101000i
00 01 10 11 00 01 10 11 00 01
10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 00 01 10 11 10 11 00 01 00 01 10 11 10 11 |101000i
00 01 10 11 00 01 10 11 00 01
10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 00 01 10 11 10 11 00 01 00 01 10 11 10 11 FM: 000000... FM: 111111...
00 01 10 11 00 01 10 11 00 01
10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 10 11 00 01 00 01 10 11 10 11 00 01 00 01 10 11 10 11 FM: 000000... FM: 111111... AFM: 010101... AFM: 101010...
Examples
Dicke state |01i + |10i p 2
Dicke state |01i + |10i p 2 00 10 01
11
Dicke state (|0011i + |0101i +|0110i + |1001i +|1010i +
|1100i) / p 6
Dicke state particles zeros ones 6 3 3
Dicke state particles zeros ones 8 4 4
Dicke state particles zeros ones 10 5 5
Dicke state particles zeros ones 12 6 6
Dicke state particles zeros ones 14 7 7
Product state (↵|0i + |1i)n
Heisenberg AFM X ~ Si · ~ Si+1 (periodic boundary
cond.)
Heisenberg AFM (1,2) (3,4) (5,6) (7,8) ... X ~ Si
· ~ Si+1 (periodic boundary cond.)
Heisenberg AFM (1,2) (3,4) (5,6) (7,8) ... (n,1) (2,3) (4,5)
(6,7) ... X ~ Si · ~ Si+1 (periodic boundary cond.)
Heisenberg AFM (1,2) (3,4) (5,6) (7,8) ... (n,1) (2,3) (4,5)
(6,7) ... X ~ Si · ~ Si+1 (open boundary cond.)
It works for any qudit 1D spin chains
-- -0 -+ 0- 00 0+ +- +0 ++ +
qutrits (spin-1) 0 -
AKLT state Affleck, Lieb, Kennedy and Tasaki (| +i +
|00i + | + i)/ p 3 + 1 3 ⇣ ~ Si · ~ Si+1 ⌘2 X ~ Si · ~ Si+1
AKLT state particles 4 Affleck, Lieb, Kennedy and Tasaki +
1 3 ⇣ ~ Si · ~ Si+1 ⌘2 X ~ Si · ~ Si+1
AKLT state Affleck, Lieb, Kennedy and Tasaki + 1 3
⇣ ~ Si · ~ Si+1 ⌘2 X ~ Si · ~ Si+1 particles 6
AKLT state Affleck, Lieb, Kennedy and Tasaki + 1 3
⇣ ~ Si · ~ Si+1 ⌘2 X ~ Si · ~ Si+1 particles 8
AKLT state Affleck, Lieb, Kennedy and Tasaki + 1 3
⇣ ~ Si · ~ Si+1 ⌘2 X ~ Si · ~ Si+1 particles 10
Alternative qubistic schemes
00 01 11 10 anti-ferromagnetic ferromagnetic
Heisenberg AFM X ~ Si · ~ Si+1
X z i z i+1 X x i Ising transverse
field
X z i z i+1 X x i Ising transverse
field = 1
X z i z i+1 X x i Ising transverse
field
X z i z i+1 X x i Ising transverse
field = 1
None
Product state
Product state Dicke half-filled
Product state Dicke half-filled Ising transverse field (ground state)
Product state Dicke half-filled Ising transverse field (ground state) Heisenberg
(ground state)
You can see entanglement
entanglement: (1,2) vs (3,4,5,6,7,8,9,...)
entanglement: (1,2) vs (3,4,5,6,7,8,9,...) Schmidt rank: A A A A
1 (not entangled)
entanglement: (1,2) vs (3,4,5,6,7,8,9,...) Schmidt rank: A A A A
1 (not entangled) A B B C 3 (entangled!)
entanglement: (1,2,3,4) vs (5,6,7,8,9,...) Schmidt rank:
entanglement: (1,2,3,4) vs (5,6,7,8,9,...) Schmidt rank: A A A A
A A A A A A A A A A A A 1 (not entangled)
entanglement: (1,2,3,4) vs (5,6,7,8,9,...) Schmidt rank: A A A A
A A A A A A A A A A A A 1 (not entangled) A
A B B B B entanglement: (1,2,3,4) vs (5,6,7,8,9,...) Schmidt
rank: A A A A A A A A A A A A A A A A 1 (not entangled) A
A B B B B entanglement: (1,2,3,4) vs (5,6,7,8,9,...) Schmidt
rank: A A A A A A A A A A A A A A A A 1 (not entangled) A B B C B C C B C C C A
A B B B B entanglement: (1,2,3,4) vs (5,6,7,8,9,...) Schmidt
rank: A A A A A A A A A A A A A A A A 1 (not entangled) A B B C B C C D B C C D C D D A B B C B C C B C C C A
A B B B B entanglement: (1,2,3,4) vs (5,6,7,8,9,...) Schmidt
rank: A A A A A A A A A A A A A A A A 1 (not entangled) A B B C B C C D B C C D C D D A B B C B C C B C C C A 5 (entangled!) A B B C B C C D B C C D C D D E
{|0i, |1i}⌦4 {|+i, | i}⌦4 ⌦4 x ⌦4 z Schmidt
number: 1 2 2 3 4 |0000i |GHZi |Wi Dicke half-filling
Renyi fractal dimension (and box counting)
AKLT ground state also works for qutrits (e.g. spin-1) log(4)
log(3) ⇡ 1 . 26 and its fractal dimension
0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8
1 1.2 1.4 1.6 dq arctan(K) q=0 q=0.5 q=1 q=2 q =104 X ( i ) z ( i +1) z ( i ) x Ising transverse field surface-like line-like point-like
0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8
1 1.2 1.4 1.6 dq arctan(K) q=0 q=0.5 q=1 q=2 q =104 X ( i ) z ( i +1) z ( i ) x Ising transverse field = 1 surface-like line-like point-like
And how about going the other way?
Jose I. Latorre, arXiv:quant-ph/0510031 (2005) QPEG! matrix product states for
image compression JPEG?
Javier Rodriguez-Laguna Piotr Migdał Miguel Ibanez Berganza Maciej Lewenstein German
Sierra
http://qubism.wikidot.com/ Thanks! paper, code, etc: J.Rodriguez-Laguna, P. Migdał, M. Ibánez
Berganza, M. Lewenstein and G. Sierra. Qubism: self-similar visualization of many-body wavefunctions. New J. Phys. 14, 053028 (2012), arXiv:1112.3560.
None