Marek Gluza
NTU Singapore
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/9444128/slides_link22.png)
Dynamical structure factor of Rydberg arrays via quantum simulation
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/10197037/DSF1.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/10197037/DSF1.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/10197043/HL2.png)
How to get this
Dynamical structure factor
from this
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/10197042/HL1.png)
Rydberg
array
Our paper
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/10197060/DSF.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/10197066/Jens.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/10197077/JBV.jpeg)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/10197068/LB.jpeg)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/10197070/JH.jpeg)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/10197071/MG.jpeg)
Laura Baez:
DSF is key for quantum magnetism
Quantum simulators for quantum magnetism need to evaluate DSF!
How will it look for Rydberg atoms?
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/10197037/DSF1.png)
M. Goihl, J. Haferkamp, J. Bermejo-Vega, J. Eisert
What is DSF?
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/10197037/DSF1.png)
Frequency
Momentum
Excitation
No excitation
=
energy gap
Two-particle continuum
What is DSF?
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/10197037/DSF1.png)
Knap, Demler, et al., https://arxiv.org/abs/1307.0006
Probing real-space and time resolved correlation functions with many-body Ramsey interferometry
How to measure DSF?
you can measure this if not 0 by symmetry
you can measure this if not 0 by symmetry
How to measure DSF?
you can measure this if not 0 by symmetry
you can measure this if not 0 by symmetry
Fourier transform in space and time
How to measure DSF?
Fourier transform in space and time
E.g., If want 10% statistical error bar and 60 points (i-j,t) for Fourier transform then with 1 min preparation then it will take about 100 hours to run the experiment
If 1 second preparation then 100 minutes etc.
![](https://media1.giphy.com/media/smW5FBep69d3q/giphy.gif)
How well will it work?
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/10197167/DSF2.png)
How well will it work?
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/10197167/DSF2.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/10197168/DSF3.png)
Imperfections:
finite-size effects
finite quench duration
finite Fourier transform
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/10197169/DSF4.png)
Imprefection if state not the ground-state but finite-time adiabatic preparation
Correlation deviation continuously decreased and so DSF converges (quantitatively) fairly soon
(qualitatively: ok!)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/10197170/DSF5.png)
Imprefection if lattice is breathing
Correlation deviation is persistent and so DSF also deviates (quantitatively)
(qualitatively: ok!)
Complexity theory
raison d'être quantum simulation: compute what is hard to compute
it would be nice if the quantum simulated outcomes are useful
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/10197166/DSF1.png)
![](https://d2r55xnwy6nx47.cloudfront.net/uploads/2018/07/Problem_classes_2880lede.jpg)
P: Runs easily
BPP: Often runs easily
BQP: Often quantums easily
NP: Optimizes easily
![](https://d2r55xnwy6nx47.cloudfront.net/uploads/2018/07/Problem_classes_2880lede.jpg)
![](https://d2r55xnwy6nx47.cloudfront.net/uploads/2018/07/Problem_classes_2880lede.jpg)
QMA
![](https://d2r55xnwy6nx47.cloudfront.net/uploads/2018/07/Problem_classes_2880lede.jpg)
P: Runs easily
BPP: Often runs easily
BQP: Often quantums easily
NP: Optimizes easily
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/10197166/DSF1.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/10207065/Przechwycenie_obrazu_ekranu_2023-02-09_13-47-51.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/10197060/DSF.png)
"hardness( DSF approximation )"
=
"run( quantum computation )"
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/9741499/magic_ballbig.jpg)
![](https://d2r55xnwy6nx47.cloudfront.net/uploads/2018/07/Problem_classes_2880lede.jpg)
What else is there?
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/9441857/fig2.svg.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/9441865/thermal_entanglement_cost_L_20.pdf.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/9653308/J1B14_exact_LRDSF_alpha_3.png.png)
Material science?
0
0
0
0
C
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/9653292/simple_eigenstates_comparison_TFIM_J_2.pdf.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/9444128/slides_link22.png)
Diagonalization quantum algorithm
DSF of Rydberg arrays
Phonon tomography
Optical lattice tomography
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/9653526/WhatsApp_Image_2022-06-20_at_14.14.42.jpeg)
New quantum algorithm for diagonalization
no qubit overheads
no controlled-unitaries
0
0
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0
C
0
0
0
0
Simple
=
Easy
Doesn't spark joy :(
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/8692250/applesbananas.svg.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/8692250/applesbananas.svg.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/9352514/dplot_Fxt_i-v.pdf2.png)
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/9653284/Screenshot_from_2022-06-20_10-26-34.png)
Ask me anytime:
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0
0
C
![](https://s3.amazonaws.com/media-p.slid.es/uploads/1896016/images/9653292/simple_eigenstates_comparison_TFIM_J_2.pdf.png)
Fidelity witnesses
Tomography optical lattices
Tomography phonons
Proving statistical mechanics
Quantum simulating DSF
Holography in tensor networks
PEPS contraction average #P-hard
Quantum field machine
MBL l-bits
(click links at slides.com/marekgluza
Dynamical structure factor of Rydberg arrays
By Marek Gluza
Dynamical structure factor of Rydberg arrays
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