Modelling Non-Markovian Quantum Processes with Recurrent Neural Networks

Abstract

Quantum systems interacting with an unknown environment are notoriously difficult to model, especially in presence of non-Markovian and non-perturbative effects. Here we introduce a neural network based approach, which has the mathematical simplicity of the Gorini-Kossakowski-Sudarshan-Lindblad master equation, but is able to model non-Markovian effects in different regimes. This is achieved by using recurrent neural networks for defining Lindblad operators that can keep track of memory effects. Building upon this framework, we also introduce a neural network architecture that is able to reproduce the entire quantum evolution, given an initial state. As an application we study how to train these models for quantum process tomography, showing that recurrent neural networks are accurate over different times and regimes.

arXiv comment10 pages, 8 figures

References in corpus (43)

• Deep Learning in Neural Networks: An Overview
• Quantum Machine Learning
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Machine learning phases of matter
• Non-Markovian dynamics in open quantum systems
• An introduction to quantum machine learning
• Open Quantum Systems. An Introduction
• A class of quantum many-body states that can be efficiently simulated
• Many-body quantum state tomography with neural networks
• Learning phase transitions by confusion
• Quantum machine learning: a classical perspective
• On the degree of non-Markovianity of quantum evolution
• General non-Markovian dynamics of open quantum systems
• Non-Markovian quantum processes: complete framework and efficient characterisation
• Stochastic wave function method for non-Markovian quantum master equations
• Reinforcement Learning in Different Phases of Quantum Control
• Active learning machine learns to create new quantum experiments
• Deep learning in color: towards automated quark/gluon jet discrimination
• Non-Markovian quantum dynamics: local versus non-local
• Equivalence of restricted Boltzmann machines and tensor network states
• Hamiltonian Learning and Certification Using Quantum Resources
• Non-Markovian Dynamical Maps: Numerical Processing of Open Quantum Trajectories
• Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
• Markovian and non-Markovian dynamics in quantum and classical systems
• Collision-model-based approach to non-Markovian quantum dynamics
• Master equations for correlated quantum channels
• Machine Learning Assisted Many-Body Entanglement Measurement
• Energy transfer in structured and unstructured environments: master equations beyond the Born-Markov approximations
• Quantum process tomography and Linblad estimation of a solid state qubit
• Non-Markovianity and System-Environment Correlations in a microscopic collision model
• Simulation of indivisible qubit channels in collision models
• System-environment correlations and Markovian embedding of quantum non-Markovian dynamics
• Collision models in quantum optics
• Designing High-Fidelity Single-Shot Three-Qubit Gates: A Machine Learning Approach
• Quantum State and Process Tomography of Energy Transfer Systems via Ultrafast Spectroscopy
• Learning hard quantum distributions with variational autoencoders
• Quantum gate learning in engineered qubit networks: Toffoli gate with always-on interactions
• Using Recurrent Neural Networks to Optimize Dynamical Decoupling for Quantum Memory
• A practical, unitary simulator for non-Markovian complex processes
• Genetic Algorithms for Digital Quantum Simulations
• Tomographically reconstructed master equations for any open quantum dynamics
• An analytical continuation approach for evaluating emission lineshapes of molecular aggregates and the adequacy of multichromophoric Förster theory
• A tomographic approach to non-Markovian master equations

Cited by in corpus (41)

• Machine learning and the physical sciences
• Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
• Learning Quantum Systems
• Model-Free Quantum Control with Reinforcement Learning
• Machine learning non-Markovian quantum dynamics
• Reinforcement learning approach to non-equilibrium quantum thermodynamics
• Tensor network based machine learning of non-Markovian quantum processes
• Riemannian geometry and automatic differentiation for optimization problems of quantum physics and quantum technologies
• Artificial Intelligence for Quantum Computing
• Predicting non-Markovian superconducting qubit dynamics from tomographic reconstruction
• Learning Quantum Hamiltonians from Single-qubit Measurements
• A comparative study of different machine learning methods for dissipative quantum dynamics
• Solving the Liouvillian Gap with Artificial Neural Networks
• Estimating the degree of non-Markovianity using machine learning
• QGOpt: Riemannian optimization for quantum technologies
• Gradient-descent quantum process tomography by learning Kraus operators
• One-shot trajectory learning of open quantum systems dynamics
• Probing non-Markovian quantum dynamics with data-driven analysis: Beyond "black-box" machine learning models
• Non-Markovian Memory Strength Bounds Quantum Process Recoverability
• Spectral Density Classification For Environment Spectroscopy
• Machine learning for excitation energy transfer dynamics
• Ground state search by local and sequential updates of neural network quantum states
• Time-dependent atomic magnetometry with a recurrent neural network
• QD3SET-1: A Database with Quantum Dissipative Dynamics Data Sets
• Deep learning of many-body observables and quantum information scrambling
• MLQD: A package for machine learning-based quantum dissipative dynamics
• Machine Learning for Estimation and Control of Quantum Systems
• Open Ising Model Perturbed by Classical Colored Noises
• Inferring interpretable dynamical generators of local quantum observables from projective measurements through machine learning
• Noise Classification in Three-Level Quantum Networks by Machine Learning
• Hamiltonian Learning using Machine Learning Models Trained with Continuous Measurements
• Supervised Training of Neural-Network Quantum States for the Next Nearest Neighbor Ising model
• Differentiable master equation solver for quantum device characterisation
• Predicting quantum evolutions of excitation energy transfer in a light-harvesting complex using multi-optimized recurrent neural networks
• Limitations of strong coupling in non-Markovian quantum thermometry
• Learning the dynamics of Markovian open quantum systems from experimental data
• Simulation of Open Quantum Dynamics with Bootstrap-Based Long Short-Term Memory Recurrent Neural Network
• Detecting Markovianity of Quantum Processes via Recurrent Neural Networks
• Dual Map Framework for Noise Characterization of Quantum Computers
• Quantum Noise Sensing by generating Fake Noise
• Data-Driven Time Propagation of Quantum Systems with Neural Networks