Neural Simulated Classical and Quantum Annealing
Transcript of Neural Simulated Classical and Quantum Annealing
Mohamed Hibat-Allah
Neural Simulated Classical and
Quantum Annealing
AQC, June 2021
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Joint work with
RoelandWiersema
JuanCarrasquilla
EstelleInack
Roger Melko
Mohamed Hibat-Allah, Estelle Inack, Roeland Wiersema, Roger G. Melko, Juan Carrasquilla, Variational Neural Annealing, arXiv:2101.10154.
Neural Simulated Classical and Quantum Annealing
Question?
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Can we solve real-world Optimization Problems using
< Neural Networks | Annealing >?
Neural Simulated Classical and Quantum Annealing
Question?
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Can we solve real-world Optimization Problems using
Recurrent Neural Networks by taking advantage of Simulated
(Classical and Quantum) Annealing?
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Outline
o 1 - Recurrent Neural Networks (RNN).
o 2 - Variational Classical Annealing with RNNs.
o 3 - Variational Quantum Annealing with RNNs.
o 4 - Promising results on prototypical models.
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1 - Recurrent Neural Networks
Neural Simulated Classical and Quantum Annealing
Recurrent Neural Networks (RNNs)
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Very powerful at generating sequential data.
• Speech recognition, machine translation, times series reconstruction.
Neural Simulated Classical and Quantum Annealing
Recurrent Neural Networks (RNNs)
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Very powerful at generating sequential data.
• Speech recognition, machine translation, times series reconstruction.
-Juan Carrasquilla, Giacomo Torlai, Roger G. Melko, Leandro Aolita
Reconstructing quantum states with generative models, Nature Machine Intelligence, 2019.
-Mohamed Hibat-Allah, Martin Ganahl, Lauren E. Hayward, Roger G. Melko, Juan Carrasquilla, Recurrent Neural Network Wave Functions,
PRReasearch, 2020.
-Christopher Roth, Iterative Retraining of Quantum Spin Models using Recurrent Neural Networks,
2020.
RNNs and Quantum-many body physics
Neural Simulated Classical and Quantum Annealing
RNN Wave Functions
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Neural Simulated Classical and Quantum Annealing
Recurrent Neural Network Wave Functions,
PRReasearch, Jun 2020.
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RNN Wave Functions
Neural Simulated Classical and Quantum Annealing
Recurrent Neural Network Wave Functions,
PRReasearch, Jun 2020.
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RNN Wave Functions
Neural Simulated Classical and Quantum Annealing
Recurrent Neural Network Wave Functions,
PRReasearch, Jun 2020.
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RNN Wave Functions
Neural Simulated Classical and Quantum Annealing
Recurrent Neural Network Wave Functions,
PRReasearch, Jun 2020.
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RNN Wave Functions
An approximation of the ground state is found!
Recurrent Neural Network Wave Functions,
PRReasearch, Jun 2020.
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2 - Variational Classical Annealing (VCA)
with RNNs
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-Goal: Find ground state of a target (classical) Hamiltonian:
Simulated Classical Annealing
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-Goal: Find ground state of a target (classical) Hamiltonian:
Simulated Classical Annealing
-Examples:
• Spin glass models.
• Traveling salesman problems.
• Protein folding problems,…
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-Goal: Find ground state of a target (classical) Hamiltonian:
Simulated Classical Annealing
Entropy term (thermal fluctuations)
-Free Energy:
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Simulated Classical Annealing
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High-Temperature Regime
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Warmup Phase
𝐅𝐑𝐍𝐍 from a randomly initialized RNN
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Warmup Phase
Gradient descent
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Warmup Phase
Gradient descent
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Warmup Phase
Gradient descent
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Warmup Phase
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Annealing Step
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Training Step
Gradient descent
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Close to zero temperature
Gradient descent
Global minimum
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Optimization at T = 0
Gradient descent
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Gradient descent
Optimization at T = 0
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Gradient descent
Optimization at T = 0
Local minimum
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3 - Variational Quantum Annealing (VQA)
with RNN Wave Functions
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RNNwave function
Variational Quantum Annealing with RNNs
Initial Hamiltonian:
“Ground state is simple”
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Gradient descent
Warmup phase
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Gradient descent
Warmup phase
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Gradient descent
Warmup phase
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Annealing Step
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Annealing Step
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Training Step
Gradient descent
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Training Step
Gradient descent
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Annealing Step
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Training Step
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Variational Quantum Annealing (VQA)
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Variational Quantum Annealing (VQA)
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Variational Quantum Annealing (VQA)
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Variational Quantum Annealing (VQA)
Ground state of target Hamiltonian is found!
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The Variational Adiabatic Theorem
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is sufficient to guarantee:
Under a set of assumptions [1], a total number of gradient steps:
[1] Variational Neural Annealing, 2101.10154
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The Variational Adiabatic Theorem
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Conclusions:
[1] Variational Neural Annealing, 2101.10154
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4 - Results on spin-glass models
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Spin Ising glass in 2D
Edwards-Anderson model:
The couplings are drawn from random uniform distribution in
the range [-1,1)
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Spin Ising glass in 2D (N = 10x10 spins)
Edwards-Anderson model:
Residual energy:
Variational Classical Annealing (VCA)
• 𝐓(𝐭) = 𝐓𝟎 𝟏 − 𝐭/𝐍𝐚𝐧𝐧𝐞𝐚𝐥𝐢𝐧𝐠
Variational Quantum Annealing (VQA)
• 𝐁𝐱(𝐭) = 𝐁𝐱𝟎 𝟏 − 𝐭/𝐍𝐚𝐧𝐧𝐞𝐚𝐥𝐢𝐧𝐠
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Spin Ising glass in 2D (N = 10x10 spins)
Variational Classical Annealing (VCA)
• 𝐓(𝐭) = 𝐓𝟎 𝟏 − 𝐭/𝐍𝐚𝐧𝐧𝐞𝐚𝐥𝐢𝐧𝐠
Variational Quantum Annealing (VQA)
• 𝐁𝐱(𝒕) = 𝐁𝐱𝟎 𝟏 − 𝐭/𝐍𝐚𝐧𝐧𝐞𝐚𝐥𝐢𝐧𝐠
Classical-Quantum Optimization (CQO)
• 𝐓 = 𝟎, 𝐁𝐱 = 𝟎
Edwards-Anderson model:
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Spin Ising glass in 2D (N = 40x40 spins)
SA: Simulated Annealing.
SQA: Path-Integral Quantum Monte Carlo.
Edwards-Anderson model:
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Sampling advantage of RNNs
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SA and SQAMetropolis sampling
VCA (RNNs)Autoregressive (exact) sampling
Fully-connected spin glasses (N = 100 spins)
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The couplings are drawn from a gaussian distribution with
mean 0 and variance 1.
Sherrington-Kirkpatrick model:
Residual energy:
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Takeaways
o We can use neural networks to emulate Classical and Quantum Annealing to
solve optimization problems.
o Neural Machine Translation (RNNs) meets Classical and Quantum Annealing.
o VCA is superior compared to VQA.
o VCA is superior compared to SA and SQA.
Neural Simulated Classical and Quantum Annealing
More results: Variational Neural Annealing, arXiv:2101.10154.
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Thank you for your attention!
Neural Simulated Classical and Quantum Annealing
o We can use neural networks to emulate Classical and Quantum Annealing to
solve optimization problems.
o Neural Machine Translation (RNNs) meets Classical and Quantum Annealing.
o VCA is superior compared to VQA.
o VCA is superior compared to SA and SQA.
More results: Variational Neural Annealing, arXiv:2101.10154.