stanislav fort with neural net works & differentiable...

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

mailto:[email protected]

Primarily based on arXiv 1812.06693, in review


AI, ML, DL & differentiable programming


● 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

Differentiable programmingHeat equation example


∂

∂ temperature field

Bridging ML &scientific computing

Differentiable programmingQuantum games example


∂

∂ quantum game strategy

Writing down a solution vs learning a solution


f( )= “tortoise”

Bubble sort (explicit)

Image classification(learned)

Translation(much better when learned)

Writing down a solution vs learning a solution


Even solving symbolic math

Machine learningLearning to get faster (& better) heuristics


Network & data structureHow to induce the correct learning prior?



Quantum state tomography


Quantum state tomographyPure states first



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(Adaptivity)



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Quantum state tomographyWhat is difficult?

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N


Pure states → density matricesDensity matricesPure states


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?


Regular Quantum State Tomography


Regular Quantum State TomographyStage 1: Take measurements


Regular Quantum State TomographyStage 2: Process them


Regular Quantum State TomographyProblem: Measurements expensive


Adaptive Quantum State TomographyFerenc Huszár, Neil M. T. Houlsby. Adaptive Bayesian Quantum Tomography, arXiv 1107.0895

Stage 1: Take measurements up to t


Adaptive Quantum State TomographyFerenc Huszár, Neil M. T. Houlsby. Adaptive Bayesian Quantum Tomography, arXiv 1107.0895

Stage 2: Determine the next POVM


Adaptive Quantum State TomographyParticle bank maintaining and update


Adaptive Quantum State TomographyParticle bank resampling


Adaptive Quantum State Tomography

Problem: Computationally expensive


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.


Neural Adaptive Quantum State Tomography (NA-QST)Custom recurrent architecture - off the shelf doesn’t work



Train: Differentiable quantum simulator provides measurement results



Train: Differentiable quantum simulator provides measurement results

Test: Experimenter provides measurement results


Neural Adaptive Quantum State Tomography (NA-QST)Inside the RNN cell - where the magic happens



Veil of ignorance =

gradient stop


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


Neural Adaptive Quantum State Tomography (NA-QST)How is it trained? 2 notions of “time”

Inference step


Neural Adaptive Quantum State Tomography (NA-QST)How is it trained? 2 notions of “time”

Backprop step


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


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


Neural Adaptive Quantum State Tomography (NA-QST)Reconstruction accuracy and time to compute



Number of measurements



Reconstruction error



NA-QST is:

1) Equal in reconstruction accuracy



NA-QST is:


2) Orders of magnitude faster!



NA-QST is:


2) Orders of magnitude faster!

3) Time complexity scales better


Neural Adaptive Quantum State Tomography (NA-QST)Time complexity scaling: polynomial to logarithmic

NA-QST: logarithmic time scaling

ABQT: polynomial time scaling


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


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

stanislav fort with neural net works & differentiable...

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