Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1808.01374 · New Journal of Physics

Modelling non-markovian quantum processes with recurrent neural networks

Leonardo Banchi, Edward Grant, Andrea Rocchetto, Simone Severini B

Published Dec 10, 2018• 73 citations
arXivHTMLPDF

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 (RNNs) 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 RNNs are accurate over different times and regimes.

DOI
10.1088/1367-2630/aaf749

Related papers

Modelling non-markovian quantum processes with recurrent neural networks

Leonardo Banchi, Edward Grant, Rocchetto, A +1 more

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 (RNNs) 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 RNNs are accurate over different times and regimes.

•Dec 1, 2018•70 citations

Predicting Dynamics of Transmon Qubit-Cavity Systems with Recurrent Neural Networks

Nima Leclerc

Developing accurate and computationally inexpensive models for the dynamics of open-quantum systems is critical in designing new qubit platforms by first understanding their mechanisms of decoherence and dephasing. Current models based on solutions to master equations are not sufficient in capturing the non-Markovian dynamics at play and suffer from large computational costs. Here, we present a method of overcoming this by using a recurrent neural network to obtain effective solutions to the Lindblad master equation for a coupled transmon qubit-cavity system. We present the training and testing performance of the model trained a simulated dataset and demonstrate its ability to map microscopic dissipative mechanisms to quantum observables.

arXiv:2109.14471•Sep 29, 2021•1 citation

Detecting Markovianity of quantum processes via recurrent neural networks

Angela Rosy Morgillo, Massimiliano Federico Sacchi, Chiara Macchiavello

Abstract We present a novel methodology utilizing recurrent neural networks (RNNs) to classify Markovian and non-Markovian quantum processes, leveraging time series data derived from Choi states. The model exhibits exceptional accuracy, surpassing 95%, across diverse scenarios, including dephasing and Pauli channels in an arbitrary basis, generalized amplitude damping dynamics, and even in the presence of noise. Additionally, the developed model shows efficient forecasting capabilities for the analyzed time series data. These results suggest the potential of RNNs in discerning and predicting the Markovian nature of quantum processes.

arXiv:2406.07226•Quantum Machine Intelligence•Mar 27, 2025•1 citation

Quantum neural networks for machine learning applied to the tracking and control of the dynamics of stochastic transmission lines

Harish Parthasarathy, Arti Vaish

In most of the machine learning problems based on classical neural networks, we try to identify a nonlinear system which may or may not have memory by adapting the weights of the neural network so that for the same input process applied to the system as well as to the neural network, the network output matches that of the true system output in the mean square sense or in the sense of some other metric on the space of output processes. If the network is feed forward, then this model can be used to simulate a memory-less nonlinear system. If however the actual system has memory and is described by a stochastic difference equation for its state followed by an output equation that is a function of the state, then we can use a recurrent neural network (RNN) whose state dynamics are described by a nonlinear difference equation involving weights as parameters and the state and weights of the RNN can be estimated from noisy measurements of the actual system output by means of the extended Kalman filter. If however, we are interested in estimating the joint probability density of a vector valued process like the transmission line current and voltage at different points along the line at all times, then a classical neural network will not work. This is because a probability density has several constraints like non-negativity and integrability to unity, and so on, and a classical neural network does not take care of these constraints.

CRC Press eBooks•Aug 18, 2023•1 citation

Modelling non-Markovian dynamics in photonic crystals with recurrent neural networks

Adam Burgess, Marian Florescu A

We develop a recurrent neural network framework to model the non-Markovian dynamics exhibited by two-level atoms interacting with the radiation reservoir of a photonic crystal. Despite the strong non-Markovianity of the atomic dynamics induced by the rapid spectral variation in photonic density of states of the photonic reservoir, our recurrent neural network approach is able to capture precise details in the atomic evolution, including the fractional steady-state atomic population inversion and spectral splitting of the atomic transition. We demonstrate the robustness of the recurrent neural network setup against reduced data sets and its effectiveness to deal with systems of increased complexity.

Optical Materials Express•May 30, 2021•8 citations

Completely-positive non-signalling non-Markovian dynamics

Serhii Kryhin, Vivishek Sudhir

We define non-Markovian quantum dynamics as evolution in which the current state depends on all past states, and completely characterize its structure under the assumptions of complete positivity and non-signalling. The resulting continuous-time dynamics is an integro-differential equation that augments the Gorini-Kossakowski-Sudarshan-Lindblad equation with a memory integral, and is capable of describing the quantum state of systems exposed to noise with any integrable power spectral density with no further approximations. We then establish a formalism to evaluate multi-time correlations of measurement outcomes in this general setting, obviating the need for a regression theorem. As an application, we derive the emission spectrum of a driven two-level system coupled to a non-Markovian bath: the familiar Mollow triplet acquires a frequency-dependent linewidth that encodes the memory of the bath. Our work provides a rigorous yet transparent description of the quantum state of non-Markovian systems, opening the door for state estimation and state-based quantum control beyond the Markovian regime.

quant-pharXiv:2605.03197•May 6, 2026•0 citations
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 (RNNs) 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 RNNs are accurate over different times and regimes.
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 (RNNs) 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 RNNs are accurate over different times and regimes.
Developing accurate and computationally inexpensive models for the dynamics of open-quantum systems is critical in designing new qubit platforms by first understanding their mechanisms of decoherence and dephasing. Current models based on solutions to master equations are not sufficient in capturing the non-Markovian dynamics at play and suffer from large computational costs. Here, we present a method of overcoming this by using a recurrent neural network to obtain effective solutions to the Lindblad master equation for a coupled transmon qubit-cavity system. We present the training and testing performance of the model trained a simulated dataset and demonstrate its ability to map microscopic dissipative mechanisms to quantum observables.
Abstract We present a novel methodology utilizing recurrent neural networks (RNNs) to classify Markovian and non-Markovian quantum processes, leveraging time series data derived from Choi states. The model exhibits exceptional accuracy, surpassing 95%, across diverse scenarios, including dephasing and Pauli channels in an arbitrary basis, generalized amplitude damping dynamics, and even in the presence of noise. Additionally, the developed model shows efficient forecasting capabilities for the analyzed time series data. These results suggest the potential of RNNs in discerning and predicting the Markovian nature of quantum processes.
In most of the machine learning problems based on classical neural networks, we try to identify a nonlinear system which may or may not have memory by adapting the weights of the neural network so that for the same input process applied to the system as well as to the neural network, the network output matches that of the true system output in the mean square sense or in the sense of some other metric on the space of output processes. If the network is feed forward, then this model can be used to simulate a memory-less nonlinear system. If however the actual system has memory and is described by a stochastic difference equation for its state followed by an output equation that is a function of the state, then we can use a recurrent neural network (RNN) whose state dynamics are described by a nonlinear difference equation involving weights as parameters and the state and weights of the RNN can be estimated from noisy measurements of the actual system output by means of the extended Kalman filter. If however, we are interested in estimating the joint probability density of a vector valued process like the transmission line current and voltage at different points along the line at all times, then a classical neural network will not work. This is because a probability density has several constraints like non-negativity and integrability to unity, and so on, and a classical neural network does not take care of these constraints.
We develop a recurrent neural network framework to model the non-Markovian dynamics exhibited by two-level atoms interacting with the radiation reservoir of a photonic crystal. Despite the strong non-Markovianity of the atomic dynamics induced by the rapid spectral variation in photonic density of states of the photonic reservoir, our recurrent neural network approach is able to capture precise details in the atomic evolution, including the fractional steady-state atomic population inversion and spectral splitting of the atomic transition. We demonstrate the robustness of the recurrent neural network setup against reduced data sets and its effectiveness to deal with systems of increased complexity.
We define non-Markovian quantum dynamics as evolution in which the current state depends on all past states, and completely characterize its structure under the assumptions of complete positivity and non-signalling. The resulting continuous-time dynamics is an integro-differential equation that augments the Gorini-Kossakowski-Sudarshan-Lindblad equation with a memory integral, and is capable of describing the quantum state of systems exposed to noise with any integrable power spectral density with no further approximations. We then establish a formalism to evaluate multi-time correlations of measurement outcomes in this general setting, obviating the need for a regression theorem. As an application, we derive the emission spectrum of a driven two-level system coupled to a non-Markovian bath: the familiar Mollow triplet acquires a frequency-dependent linewidth that encodes the memory of the bath. Our work provides a rigorous yet transparent description of the quantum state of non-Markovian systems, opening the door for state estimation and state-based quantum control beyond the Markovian regime.