Learning Adaptive Quantum State Tomography with Neural Networks - - PowerPoint PPT Presentation

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Learning Adaptive Quantum State Tomography with Neural Networks - - PowerPoint PPT Presentation

Sep 25, 2023 473 likes •1.26k views

Learning Adaptive Quantum State Tomography with Neural Networks & Difg fgerentiable Programming Stanislav Fort Stanford University (prev. Google Research) sfort1@stanford.edu stanford.edu/~sfort1/ @stanislavfort Primarily based on arXiv

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Learning Adaptive Quantum State Tomography with Neural Networks & Difg fgerentiable Programming

Stanislav Fort

Stanford University (prev. Google Research) sfort1@stanford.edu stanford.edu/~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

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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

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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

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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

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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

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Differentiable programming

Heat 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 programming

Quantum 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 learning

Learning 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 learning

Learning 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 structure

How 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 tomography

Pure states first

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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA

Quantum state tomography

Pure states first

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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA

Quantum state tomography

Pure states first

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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA

Quantum state tomography

Pure states first

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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA

Quantum state tomography

Pure states first

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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA

Quantum state tomography

Pure states first

? ? ?

?

?

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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA

Quantum state tomography

Pure states first

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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA

Quantum state tomography

Pure states first

? ? ?

?

?

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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA

Quantum state tomography

Pure states first

? ? ?

?

?

( A d a p t i v i t y )

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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA

Quantum state tomography

Pure states first

? ? ?

?

?

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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA

Quantum state tomography

Pure states first

? ? ?

?

? ? ? ?

?

?

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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA

Quantum state tomography

Pure states first

? ? ?

?

? ? ? ?

?

? ? ? ?

?

?

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Stanislav Fort | Adaptive Quantum State Tomography with NNs and differentiable programming | 19 February 2020 | Stanford, USA

Quantum state tomography

Pure 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 tomography

Pure 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 tomography

Pure 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 tomography

What 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 matrices

Density matrices Pure 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 Tomography

Stage 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 Tomography

Stage 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 Tomography

Problem: 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 Tomography

Ferenc 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 Tomography

Ferenc 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 Tomography

Particle 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 Tomography

Particle 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 Tomography

Particle 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 approach

Yihui 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

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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) 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

  • ur 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