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Learning Adaptive Quantum State Tomography with
Neural Networks & Differentiable Programming
Stanislav FortStanford University (prev. Google Research)
[email protected]/~sfort1/
@stanislavfort
Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Primarily based on arXiv 1812.06693
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Primarily based on arXiv 1812.06693, in review
Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Primarily based on arXiv 1812.06693, in review
![Page 4: Stanislav Fort with Neural Net works & Differentiable Programmingstanford.edu/~yquek/Slides/NAQST_slides.pdf · 2020. 4. 28. · Stanislav Fort Stanford University (prev. Google Research)](https://reader035.vdocument.in/reader035/viewer/2022081622/613a915e0051793c8c011d91/html5/thumbnails/4.jpg)
AI, ML, DL & differentiable programming
Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
● Artificial intelligence: The science of making machines smart
● Machine learning: Machines getting smart from data
● Deep learning: Machines getting smart from data using deep neural networks as functional approximators
● Differentiable programming:Taking partial derivatives through programs, not restricted to deep neural networks as functions
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AI, ML, DL & differentiable programming
Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
● Artificial intelligence: The science of making machines smart
● Machine learning: Machines getting smart from data
● Deep learning: Machines getting smart from data using deep neural networks as functional approximators
● Differentiable programming:Taking partial derivatives through programs, not restricted to deep neural networks as functions
![Page 6: Stanislav Fort with Neural Net works & Differentiable Programmingstanford.edu/~yquek/Slides/NAQST_slides.pdf · 2020. 4. 28. · Stanislav Fort Stanford University (prev. Google Research)](https://reader035.vdocument.in/reader035/viewer/2022081622/613a915e0051793c8c011d91/html5/thumbnails/6.jpg)
AI, ML, DL & differentiable programming
Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
● Artificial intelligence: The science of making machines smart
● Machine learning: Machines getting smart from data
● Deep learning: Machines getting smart from data using deep neural networks as functional approximators
● Differentiable programming:Taking partial derivatives through programs, not restricted to deep neural networks as functions
![Page 7: Stanislav Fort with Neural Net works & Differentiable Programmingstanford.edu/~yquek/Slides/NAQST_slides.pdf · 2020. 4. 28. · Stanislav Fort Stanford University (prev. Google Research)](https://reader035.vdocument.in/reader035/viewer/2022081622/613a915e0051793c8c011d91/html5/thumbnails/7.jpg)
AI, ML, DL & differentiable programming
Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
● Artificial intelligence: The science of making machines smart
● Machine learning: Machines getting smart from data
● Deep learning: Machines getting smart from data using deep neural networks as functional approximators
● Differentiable programming:Taking partial derivatives through programs, not restricted to deep neural networks as functions
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Differentiable programmingHeat equation example
Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
∂
∂ temperature field
Bridging ML &scientific computing
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Differentiable programmingQuantum games example
Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
∂
∂ quantum game strategy
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Writing down a solution vs learning a solution
Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
f( )= “tortoise”
Bubble sort (explicit)
Image classification(learned)
Translation(much better when learned)
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Writing down a solution vs learning a solution
Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Even solving symbolic math
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Machine learningLearning to get faster (& better) heuristics
Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
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Machine learningLearning to get faster (& better) heuristics
Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
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Network & data structureHow to induce the correct learning prior?
Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Quantum state tomography
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Quantum state tomographyPure states first
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Quantum state tomographyPure states first
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Quantum state tomographyPure states first
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Quantum state tomographyPure states first
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Quantum state tomographyPure states first
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Quantum state tomographyPure states first
? ??
??
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Quantum state tomographyPure states first
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Quantum state tomographyPure states first
? ??
??
![Page 24: Stanislav Fort with Neural Net works & Differentiable Programmingstanford.edu/~yquek/Slides/NAQST_slides.pdf · 2020. 4. 28. · Stanislav Fort Stanford University (prev. Google Research)](https://reader035.vdocument.in/reader035/viewer/2022081622/613a915e0051793c8c011d91/html5/thumbnails/24.jpg)
Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Quantum state tomographyPure states first
? ??
??
(Adaptivity)
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Quantum state tomographyPure states first
? ????
![Page 26: Stanislav Fort with Neural Net works & Differentiable Programmingstanford.edu/~yquek/Slides/NAQST_slides.pdf · 2020. 4. 28. · Stanislav Fort Stanford University (prev. Google Research)](https://reader035.vdocument.in/reader035/viewer/2022081622/613a915e0051793c8c011d91/html5/thumbnails/26.jpg)
Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Quantum state tomographyPure states first
? ??????
???
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Quantum state tomographyPure states first
? ??????
?????
???
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Quantum state tomographyPure states first
? ??????
?????
?????
???
N
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Quantum state tomographyPure states first
? ????? ????? ????? ??
??
N
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Quantum state tomographyPure states first
? ????? ????? ????? ??
??
N
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Quantum state tomographyWhat is difficult?
? ????? ????? ????? ??
??
N
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Pure states → density matricesDensity matricesPure states
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
What do we care about?
1) How precisely can you reconstruct the unknown state, given N copies of the unknown state?
2) How much compute does it take?
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Regular Quantum State Tomography
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Regular Quantum State TomographyStage 1: Take measurements
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Regular Quantum State TomographyStage 2: Process them
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Regular Quantum State TomographyProblem: Measurements expensive
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Adaptive Quantum State TomographyFerenc Huszár, Neil M. T. Houlsby. Adaptive Bayesian Quantum Tomography, arXiv 1107.0895
Stage 1: Take measurements up to t
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Adaptive Quantum State TomographyFerenc Huszár, Neil M. T. Houlsby. Adaptive Bayesian Quantum Tomography, arXiv 1107.0895
Stage 2: Determine the next POVM
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Adaptive Quantum State TomographyParticle bank maintaining and update
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Adaptive Quantum State TomographyParticle bank maintaining and update
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Adaptive Quantum State TomographyParticle bank resampling
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Adaptive Quantum State Tomography
Problem: Computationally expensive
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)
Our approachYihui Quek*, Stanislav Fort*, Hui Khoon Ng. Adaptive Quantum State Tomography with Neural Networks, arXiv 1812.06693
Advantages:- Parametrized state ansatz is not
required- Exponential computational speedup- Learned directly from simulated data- Can retrain within hours- Any POVM types- Different noise models- Learned distance measure, update rule
etc.
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Custom recurrent architecture - off the shelf doesn’t work
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Custom recurrent architecture - off the shelf doesn’t work
Train: Differentiable quantum simulator provides measurement results
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Custom recurrent architecture - off the shelf doesn’t work
Train: Differentiable quantum simulator provides measurement results
Test: Experimenter provides measurement results
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Inside the RNN cell - where the magic happens
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Inside the RNN cell - where the magic happens
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Inside the RNN cell - where the magic happens
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Inside the RNN cell - where the magic happens
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Inside the RNN cell - where the magic happens
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Inside the RNN cell - where the magic happens
Veil of ignorance =
gradient stop
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Inside the RNN cell - where the magic happens
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Inside the RNN cell - where the magic happens
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Inside the RNN cell - where the magic happens
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Inside the RNN cell - where the magic happens
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Inside the RNN cell - where the magic happens
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Inside the RNN cell - where the magic happens
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Inside the RNN cell - where the magic happens
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Inside the RNN cell - where the magic happens
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Inside the RNN cell - where the magic happens
![Page 63: Stanislav Fort with Neural Net works & Differentiable Programmingstanford.edu/~yquek/Slides/NAQST_slides.pdf · 2020. 4. 28. · Stanislav Fort Stanford University (prev. Google Research)](https://reader035.vdocument.in/reader035/viewer/2022081622/613a915e0051793c8c011d91/html5/thumbnails/63.jpg)
Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Inside the RNN cell - where the magic happens
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Different paradigm from ABQT
● No explicit Bayesian interpretation - weights are just weights
● Automatically learned NN similarity metric for resampling and weight updates
● Resampling is fast ● End-to-end training minimizing arbitrary human
choices
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)How is it trained? 2 notions of “time”
Inference step
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)How is it trained? 2 notions of “time”
Backprop step
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Numerical experiments - what can be varied?
1) Single-qubit POVM type: 2 (basis POVM), 3, 4 (SIC), and 6 (Pauli) legs per qubit subspace
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Numerical experiments - what can be varied?
1) Single-qubit POVM type: 2 (basis POVM), 3, 4 (SIC), and 6 (Pauli) legs per qubit subspace
2) POVM Adaptivity: Adaptive or random measurements? What are the benefits?
3) 3) Reconstruction algorithm: Standard QST, ABQT, or our NA-QST
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Reconstruction accuracy and time to compute
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Reconstruction accuracy and time to compute
Number of measurements
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Reconstruction accuracy and time to compute
Reconstruction error
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Reconstruction accuracy and time to compute
NA-QST is:
1) Equal in reconstruction accuracy
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Reconstruction accuracy and time to compute
NA-QST is:
1) Equal in reconstruction accuracy
2) Orders of magnitude faster!
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Reconstruction accuracy and time to compute
NA-QST is:
1) Equal in reconstruction accuracy
2) Orders of magnitude faster!
3) Time complexity scales better
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)Time complexity scaling: polynomial to logarithmic
NA-QST: logarithmic time scaling
ABQT: polynomial time scaling
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Neural Adaptive Quantum State Tomography (NA-QST)When does adaptivity help?
Conclusions:
- 2 legs (basis): Adaptivity helps a lot
- 3 legs: Adaptive helps slightly
- 4 legs and above (informationally complete): Adaptivity does not make any difference
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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA
Takeaways and thank you!We designed, implemented, and tested an end-to-end trainable, deep learning powered algorithm called Neural Adaptive Quantum State Tomography (NA-QST)
NA-QST is:1) Fast to train (hours on a laptop)
2) Very fast to run (poly → log)3) Accurate in reconstruction (~SOTA)4) Flexible (noise, different POVMs etc)
Future: Retraining for downstream products involving the density matrix
Primarily based on arXiv 1812.06693