Tensor network based machine learning of non-Markovian quantum processes

Abstract

We show how to learn structures of generic, non-Markovian, quantum stochastic processes using a tensor network based machine learning algorithm. We do this by representing the process as a matrix product operator (MPO) and train it with a database of local input states at different times and the corresponding time-nonlocal output state. In particular, we analyze a qubit coupled to an environment and predict output state of the system at different time, as well as reconstruct the full system process. We show how the bond dimension of the MPO, a measure of non-Markovianity, depends on the properties of the system, of the environment and of their interaction. Hence, this study opens the way to a possible experimental investigation into the process tensor and its properties.

5 pages, 3 figures

References in corpus (9)

• The density-matrix renormalization group in the age of matrix product states
• Randomized Benchmarking of Quantum Gates
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Efficient quantum state tomography
• Operational Markov condition for quantum processes
• Foundations and Measures of Quantum Non-Markovianity
• Demonstration of non-Markovian process characterisation and control on a quantum processor
• An introduction to operational quantum dynamics
• Quantum Markovianity as a supervised learning task

Cited by in corpus (38)

• Quantum stochastic processes and quantum non-Markovian phenomena
• Non-Markovian Quantum Process Tomography
• Collective Radiance of Giant Atoms in Non-Markovian Regime
• Quantum error mitigation via matrix product operators
• Riemannian geometry and automatic differentiation for optimization problems of quantum physics and quantum technologies
• Tensor networks for quantum machine learning
• Variational quantum process tomography
• Experimental characterisation of a non-Markovian quantum process
• Estimating the degree of non-Markovianity using machine learning
• Diagrammatic method for many-body non-Markovian dynamics: memory effects and entanglement transitions
• Probing non-Markovian quantum dynamics with data-driven analysis: Beyond "black-box" machine learning models
• A Pairwise Connected Tensor Network Representation of Path Integrals
• Extracting Quantum Dynamical Resources: Consumption of Non-Markovianity for Noise Reduction
• Ground state search by local and sequential updates of neural network quantum states
• Quantifying Non-Markovianity in Open Quantum Dynamics
• On the sampling complexity of open quantum systems
• Activating information backflow with the assistance of quantum SWITCH
• Towards a general framework of Randomized Benchmarking incorporating non-Markovian Noise
• From Non-Markovian Dissipation to Spatiotemporal Control of Quantum Nanodevices
• Reconstructing Non-Markovian Open Quantum Evolution From Multi-time Measurements
• Principles underlying efficient exciton transport unveiled by information-geometric analysis
• Randomised benchmarking for characterizing and forecasting correlated processes
• Capturing long-range memory structures with tree-geometry process tensors
• Density Matrix Renormalization Group Algorithm For Mixed Quantum States
• What can unitary sequences tell us about multi-time physics?
• Supervised Training of Neural-Network Quantum States for the Next Nearest Neighbor Ising model
• Relations between Markovian and non-Markovian correlations in multitime quantum processes
• Non-parametric Semi-Supervised Learning in Many-body Hilbert Space with Rescaled Logarithmic Fidelity
• Deep tensor networks with matrix product operators
• Input-Output Hierarchical Equations Of Motion
• Unifying non-Markovian characterisation with an efficient and self-consistent framework
• Understanding and utilizing the inner bonds of process tensors
• Efficient tensor networks for control-enhanced quantum metrology
• Tensor-Networks-based Learning of Probabilistic Cellular Automata Dynamics
• Scalable tensor network algorithm for quantum impurity problems
• Harnessing Quantum Dynamics for Robust and Scalable Quantum Extreme Learning Machines
• Estimating the degree of non-Markovianity using variational quantum circuits
• Process Tensor Approaches to Non-Markovian Quantum Dynamics