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Can a Machine Infer Quantum Dynamics? Training a Recurrent Neural Network to Predict Quantum Trajectories from Raw Observation

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Can a Machine Infer Quantum Dynamics? Training a Recurrent Neural Network to Predict Quantum Trajectories from Raw Observation Can a machine infer quantum dynamics? Training a Recurrent Neural Network to Predict Quantum Trajectories from Raw Observation. arXiv:1811.12420 Emmanuel Flurin* S. Hacohen-Gourgy, L. Martin, I. Siddiqi Quantum Nanoelectronics Laboratory, UC Berkeley *Quantronics, CEA Saclay, France The Quantum Slot Machine intro A Quantum Information Processing Experiment Heralding Prep Quantum Evolution Tomo Readout 500 m intro Black Box Quantum Mechanics Preparation Evolution Measurement intro Black Box Quantum Mechanics Preparation Evolution Measurement Quantum mechanics gives intro Black Box Quantum Mechanics Preparation Evolution Measurement intro Black Box Quantum Mechanics Preparation Evolution Measurement intro Stochastic Quantum Evolution continuous measurement Preparation Evolution+ Measurement Continuous Monitoring Quantum mechanics gives intro Stochastic Quantum Evolution continuous measurement « POVM » Preparation Evolution+ Measurement measurement Continuous Monitoring backaction + coherent dynamics L.S. Martin Physical parameters have to be separately calibrated and fine-tuned intro Inferring Quantum Dynamics continuous measurement If one have a large set of instances Supervised Deep Learning learns no matter how complicated the problem is • language translation • medical diagnosis • image & speech recognition • LHC signal processing intro Inferring Quantum Dynamics Heralding Prep Evolution Tomo Readout Superconducting circuits provides instances per minutes Deep neural network can learn with no prior on quantum mechanics if spans a complete set of observable, is equivalent to the wave-function intro Inferring Quantum Dynamics Heralding Prep Evolution Tomo Readout preparation continuous settings measurement record data «translation» quantum trajectory Circuits Circuit Quantum Electro-Dynamics «matter» «light» energy energy Circuits Circuit Quantum Electro-Dynamics dispersive coupling energy energy Circuits Physical Implementation 1 cm χ 2⇡ 0.3 MHz ⇠ ⇥ Experiment Dispersive Measurement effective frequency refected phase measurement frequency Experiment Josephson Amplifier average measurement outcome STRONG vs. WEAK MEASUREMENT Trajectories Strong vs Weak Measurement average measurement outcome weak interaction Weak projective measurement ˆ POVM : ⌦Vt « Partial-Measurement Backaction and Nonclassical Weak Values in a Superconducting Circuit » Groen et al., PRL 2013 (Delft) STRONG vs. WEAK MEASUREMENT Trajectories Strong vs Weak Measurement average measurement outcome weak interaction Weak projective measurement integration ˆ time POVM : ⌦Vt weak interaction STRONG vs. WEAK MEASUREMENT Trajectories Strong vs Weak Measurement average measurement outcome weak interaction Weak projective measurement ˆ POVM : ⌦Vt integration time weak interaction Strong Trajectories Quantum Trajectories Bayesian inference What does the detector signal tell us? Generalized measurement operator Probability Bloch sphere Homodyne Voltage Trajectories Quantum Trajectories Experimental data: K. Murch et al., Nature 502 211 (2013). Trajectories Weak Measurement of a Driven Qubit JPA Trajectories Weak Measurement of a Driven Qubit non-QND measurement JPA preparation stochastic measurement quantum evolution Experiment 1.5 millions repetitions at a rate of 0.5 ms Recurent Neural Network Long Short Term Memory 32 neurones per layer 5,000 weights parameters 0.8 ms of GPU training per trace counts counts Neural Nets Deep Neural Network input state hidden states output state input output Neural Network are differentiable computers each layer is represented weight matrix neurones as a vector of neurones connecting each layer biases sigmoid activation function Neural Nets Deep Neural Network input state hidden states output state input output Cross-entropy loss function loss minimum when the distributiongradient of descent matches optimization with (backpropagation) measurement bit in the basis b prediction in the basisdata b y 0, 1 2 { } Neural Nets Deep Neural Network input state hidden states output state inputupdating all the weight matrices with gradient descent of the loss functionoutput loss backward propagationgradient descent optimization (backpropagation) (the chain rule for differentiation translates in matrix multiplications) data Neural Nets Deep Neural Network input state hidden states output state input output loss gradient descent optimization (backpropagation) tomography Neural Nets Neural Networks Architectures Convolutional Neural Network Recurrent Neural Network Spatially ordered data Time series • Image recognition • text generation • speech recognition (Amazon Alexa…) • language translation (Google translate…) space-like correlations time-like causal correlations Neural Nets Recurrent Neural Networks preparation settings inputed in ~h0 Neural Nets Recurrent Neural Networks gradient descent optimization loss data Neural Nets Recurrent Neural Networks: Example character-level language modeling input: current letter trained on « War and Peace » The sole importance of the crossing of the Berezina lies in the fact that it plainly and indubitably proved the fallacy of all the plans for cutting off the enemy's retreat and the soundness of the only possible line of action- -the one Kutuzov and the general mass of the army demanded- -namely, simply to follow the enem ? « y » output: most probable next letter [Karpathy, Andrej, Justin Johnson, and Li Fei-Fei. "Visualizing and understanding recurrent networks. » arXiv preprint arXiv:1506.02078 (2015).] Neural Nets Recurrent Neural Networks: Example Long range dependencies in RNN input: current letter output: most probable next letter [Karpathy, Andrej, Justin Johnson, and Li Fei-Fei. "Visualizing and understanding recurrent networks. » arXiv preprint arXiv:1506.02078 (2015).] RNN Learning Stochastic Quantum Dynamics Training set 6 preparation settings 6 measurement settings JPA 20 experiment durations Experiment preparation stochastic measurement 1.5 millions repetitions quantum evolution at a rate of 0.5 ms Recurent Neural Network Long Short Term Memory 32 neurones per layer 5,000 weights parameters 0.8 ms of GPU training per trace LSTM babysitting batchsize 1024 Prediction 10 epochs learning rate 10^{-3}->10^{-6} dropout 0.3->0 P (y Z) | quantum trajectory RNN Learning Stochastic Quantum Dynamics JPA Experiment 1.5 millions repetitions at a rate of 0.5 ms stochastic measurement preparation Recurent Neural Network quantum evolution strengthening Long Short Term Memory 32 neurones per layer 5,000 weights parameters 0.8 ms of GPU training per trace weakening Training set 6 preparation settings 6 measurement settings 20 experiment durations Prediction Recurrent Neural Network Neural Weights Update RNN Learning Stochastic Quantum Dynamics JPA Experiment 1.5 millions repetitions at a rate of 0.5 ms stochastic measurement preparation Recurent Neural Network quantum evolution strengthening Long Short Term Memory 32 neurones per layer 5,000 weights parameters 0.8 ms of GPU training per trace weakening Training set 6 preparation settings 6 measurement settings 20 experiment durations Prediction Recurrent Neural Network Neural Weights Update RNN Training continuous measurement 0 preparation measurement stochastic master equation RNN RNN Learning Quantum Mechanics probability continuous monitoring prep meas probability RNN Training ResultsValidation training validation 0.85 master equation RNN Tomography counts Predictions [Observing single quantum trajectories of a superconducting quantum bit Murch, Weber, Macklin, Siddiqi - Nature (2013)] RNN Training ResultsValidation training validation 0.85 master equation RNN counts Tomography [Observing single quantum trajectories of a superconducting quantum bit Predictions Murch, Weber, Macklin, Siddiqi - Nature (2013)] RNN Training Validation RNN Machine Prediction RNN Parameter Estimation & Sensing JPA prediction distribution RNN Parameter Estimation & Sensing JPA Drift map Dissipative evolution RNN Parameter Estimation & Sensing JPA Drift map Dephasing rate Rabi frequency Dissipative evolution RNN Parameter Estimation & Sensing JPA Drift map Diffusion map Dephasing rate Rabi frequency quantum efficiency Dissipative evolution Measurement back-action bi-RNN Prediction and retrodiction with bi-directional RNN Prediction preparation stochastic measurement quantum evolution Retrodiction [The two-state vector formalism of quantum mechanics Y Aharonov, L Vaidman (2002)] [Prediction and retrodiction for a continuously monitored superconducting qubit D. Tan, S. Weber, I. Siddiqi, K. Mølmer, K. W. Murch PRL (2015)] bi-RNN Prediction and retrodiction with bi-directional RNN forward prediction Prediction preparation stochastic measurement quantum evolution probability continuous monitoring Retrodiction probability [The two-state vector formalism of quantum mechanics Y Aharonov, L Vaidman (2002)] [Prediction and retrodiction for a continuously monitored superconducting qubit D. Tan, S. Weber, I. Siddiqi, K. Mølmer, K. W. Murch PRL (2015)] backward prediction bi-RNN Prediction and retrodiction with bi-directional RNN forward prediction Prediction y h ap r g omo preparation stochastic measurement T quantum evolution Backward Predictions probability continuous monitoring Retrodiction probability [The two-state vector formalism of quantum mechanics Y Aharonov, L Vaidman (2002)] [Prediction and retrodiction for a continuously monitored superconducting qubit D. Tan, S. Weber, I. Siddiqi, K. Mølmer, K. W. Murch PRL (2015)] backward prediction prediction 0 prep meas. bi-RNN State Tomography
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