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arXiv:1811.12420 · Physical Review X

Using a Recurrent Neural Network to Reconstruct Quantum Dynamics of a Superconducting Qubit from Physical Observations

Emmanuel Flurin, Leigh S. Martin, Shay Hacohen-Gourgy, Irfan A. Siddiqi

Published Jan 9, 2020• 88 citations
arXivHTMLPDF

Abstract

At its core, quantum mechanics is a theory developed to describe fundamental observations in the spectroscopy of solids and gases.Despite these practical roots, however, quantum theory is infamous for being highly counterintuitive, largely due to its intrinsically probabilistic nature.Neural networks have recently emerged as a powerful tool that can extract nontrivial correlations in vast datasets.These networks routinely outperform state-of-the-art techniques in language translation, medical diagnosis, and image recognition.It remains to be seen if neural networks can be trained to predict stochastic quantum evolution without a priori specifying the rules of quantum theory.Here, we demonstrate that a recurrent neural network can be trained in real time to infer the individual quantum trajectories associated with the evolution of a superconducting qubit under unitary evolution, decoherence, and continuous measurement from physical observations only.The network extracts the system Hamiltonian, measurement operators, and physical parameters.It is also able to perform tomography of an unknown initial state without any prior calibration.This method has the potential to greatly simplify and enhance tasks in quantum systems such as noise characterization, parameter estimation, feedback, and optimization of quantum control.

DOI
10.1103/physrevx.10.011006

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At its core, quantum mechanics is a theory developed to describe fundamental observations in the spectroscopy of solids and gases.Despite these practical roots, however, quantum theory is infamous for being highly counterintuitive, largely due to its intrinsically probabilistic nature.Neural networks have recently emerged as a powerful tool that can extract nontrivial correlations in vast datasets.These networks routinely outperform state-of-the-art techniques in language translation, medical diagnosis, and image recognition.It remains to be seen if neural networks can be trained to predict stochastic quantum evolution without a priori specifying the rules of quantum theory.Here, we demonstrate that a recurrent neural network can be trained in real time to infer the individual quantum trajectories associated with the evolution of a superconducting qubit under unitary evolution, decoherence, and continuous measurement from physical observations only.The network extracts the system Hamiltonian, measurement operators, and physical parameters.It is also able to perform tomography of an unknown initial state without any prior calibration.This method has the potential to greatly simplify and enhance tasks in quantum systems such as noise characterization, parameter estimation, feedback, and optimization of quantum control.
Weak measurements of a superconducting qubit produce noisy voltage signals that are weakly correlated with the qubit state.To recover individual quantum trajectories from these noisy signals, traditional methods require slow qubit dynamics and substantial prior information in the form of calibration experiments.Monitoring rapid qubit dynamics, e.g., during quantum gates, requires more complicated methods with increased demand for prior information.Here, we experimentally demonstrate an alternative method for accurately tracking rapidly driven superconducting qubit trajectories that uses a long short-term memory (LSTM) artificial neural network with minimal prior information.Despite few training assumptions, the LSTM produces trajectories that include qubit-readout resonator correlations due to a finite detection bandwidth.In addition to revealing rotated measurement eigenstates and a reduced measurement rate in agreement with theory for a fixed drive, the trained LSTM also correctly reconstructs evolution for an unknown drive with rapid modulation.Our work enables new applications of weak measurements with faster or initially unknown qubit dynamics, such as the diagnosis of coherent errors in quantum gates.
The problem of reconstructing an unknown time-dependent Hamiltonian of a two-level quantum system from its observed dynamics is considered. A method based on a neural network in the Neural ODE framework is proposed, where the continuous evolution of the quantum state is modeled by integrating the Schrodinger equation with a parametric Hamiltonian model implemented by the network. The input data consist of measured time series of the expectation values of Pauli operators for a qubit. The network is trained by minimizing the difference between the experimentally observed and simulated trajectories of quantum observables. Using the example of spin dynamics in a time-varying magnetic field, it is shown that the proposed approach allows accurate reconstruction of the parameters of the time-dependent Hamiltonian without interrupting the quantum evolution. The results demonstrate that the Neural ODE model provides continuous handling of the time parameter and robust reconstruction of system dynamics under conditions of limited data and noise.
Abstract The problem of reconstructing an unknown time-dependent Hamiltonian of a two-level quantum system from data on the system’s dynamics is considered. A method based on a neural network within the Neural ODE framework is proposed, in which the continuous evolution of the quantum state is modeled by integrating the Schrödinger equation with a parametric Hamiltonian model implemented by the network. As input data, measured time series of the expectation values of Pauli operators for a qubit are used. The network is trained by minimizing the difference between the experimentally observed and modeled trajectories of quantum observables. Using the example of simulating spin dynamics in a time-varying magnetic field, it is shown that the proposed approach enables high-accuracy reconstruction of the time-dependent Hamiltonian parameters without interrupting the quantum evolution. The results demonstrate that the Neural ODE model provides continuous tracking of the time parameter and reliable reconstruction of the system’s dynamics under conditions of limited data and noise.
In the Hamiltonian-based quantum dynamics, to estimate Hamiltonians from the measured data is a vital topic.In this work, we propose a recurrent neural network to learn the target Hamiltonians from the temporal records of single-qubit measurements, which does not require the ground states and only measures single-qubit observables.It is applicable on both time-independent and time-dependent Hamiltonians and can simultaneously capture the magnitude and sign of Hamiltonian parameters.Taking the Hamiltonians with the nearest-neighbor interactions as numerical examples, we trained our recurrent neural networks to learn different types of Hamiltonians with high accuracy.The study also shows that our method has good robustness against the measurement noise and decoherence effect.Therefore, it has widespread applications in estimating the parameters of quantum devices and characterizing the Hamiltonian-based quantum dynamics.
Machine learning (ML) is a promising approach for performing challenging quantum-information tasks such as device characterization, calibration, and control.ML models can train directly on the data produced by a quantum device while remaining agnostic to the quantum nature of the learning task.However, these generic models lack physical interpretability and usually require large datasets in order to learn accurately.Here we incorporate features of quantum mechanics in the design of our ML approach to characterize the dynamics of a quantum device and learn device parameters.This physics-inspired approach outperforms physics-agnostic recurrent neural networks trained on numerically generated and experimental data obtained from continuous weak measurement of a driven superconducting transmon qubit.This demonstration shows how leveraging domain knowledge improves the accuracy and efficiency of this characterization task, thus laying the groundwork for more scalable characterization techniques.
Neural networks have emerged as a powerful way to approach many practical problems in quantum physics. In this work, we illustrate the power of deep learning to predict the dynamics of a quantum many-body system, where the training is based purely on monitoring expectation values of observables under random driving . The trained recurrent network is able to produce accurate predictions for driving trajectories entirely different than those observed during training. As a proof of principle, here we train the network on numerical data generated from spin models, showing that it can learn the dynamics of observables of interest without needing information about the full quantum state. This allows our approach to be applied eventually to actual experimental data generated from a quantum many-body system that might be open, noisy, or disordered, without any need for a detailed understanding of the system. This scheme provides considerable speedup for rapid explorations and pulse optimization. Remarkably, we show the network is able to extrapolate the dynamics to times longer than those it has been trained on, as well as to the infinite-system-size limit.