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DARTMOUTH COLLEGE PHYSICS AND ASTRONOMY

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Presentation on theme: "DARTMOUTH COLLEGE PHYSICS AND ASTRONOMY"— Presentation transcript:

1 DARTMOUTH COLLEGE PHYSICS AND ASTRONOMY
WHITFIELD GROUP DARTMOUTH COLLEGE  PHYSICS AND ASTRONOMY Ψ

2 Approximating Matrix Product States with Machine Learning
Sam Greydanus, James Whitfield 4/25/2019

3 Objective Obtain a compressed representation of a system of entangled particles 4/25/2019 Document reference

4 What is entanglement? Simplest case, 2 sites
Cannot describe one without the other Bell state Simplest case, 2 sites 4/25/2019 opentextbc.ca/chemistry/ wikimedia commons

5 opentextbc.ca/chemistry/
What is entanglement? 4/25/2019 opentextbc.ca/chemistry/ Wikimedia commons

6 What is entanglement? More generally… n-site cases How to partition?
s1, s2, …, sN How to partition? N=8 4/25/2019 wikimedia commons phys.org/news/

7 Why is entanglement useful?
Find lowest energy state Makes computation hard… 1. dwavesys.com/blog 4/25/2019

8 Curse of dimensionality
Hamiltonian N entangled sites -> 2N dimensional matrix Simulation is hard Memory, computation 4/25/2019

9 A better idea: Matrix Product States
Most entanglements are local 1D vs 2D and up How to find compressed representation? 4/25/2019 phys.org/news/

10 Computing MPS Density Matrix Renormalization Group (DMRG)
Machine learning? 4/25/2019

11 1. Density Matrix Renormalization Groups
1D algorithm Finite, infinite 4/25/2019

12 1. Density Matrix Renormalization Groups
Enlarge system 4/25/2019

13 1. Density Matrix Renormalization Groups
Compute Hblock This is the DMRG step! 4/25/2019

14 1. Density Matrix Renormalization Groups
min 4/25/2019

15 1. Density Matrix Renormalization Groups
Rotate and truncate any operator! 4/25/2019

16 1. Density Matrix Renormalization Groups
4/25/2019 1. cond-mat/ v2

17 2. Deep Learning “…multilayer feedforward networks…are capable of approximating any Borel measurable function from one finite dimensional space to another to any desired degree of accuracy” (Stinchcombe and White 1989) 4/25/2019 doi: / (89)

18 2. Deep Learning Neural networks 4/25/2019 1. greydanus.github.io

19 2. Deep Learning Neural nets as function approximators Is small
Arbitrary function of any dimension Is small 4/25/2019

20 2. Deep Learning Our training objective We know how to solve this!
4/25/2019

21 Progress Finished To do Working finite DMRG Working infinite DMRG
Get MPS from DMRG Get MPS for AKLT state Approximate MPS with NN Evaluate model 2D case? Profit  4/25/2019

22 DARTMOUTH COLLEGE PHYSICS AND ASTRONOMY
WHITFIELD GROUP DARTMOUTH COLLEGE  PHYSICS AND ASTRONOMY Ψ

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