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arXiv:2406.07226 · Quantum Machine Intelligence

Detecting Markovianity of quantum processes via recurrent neural networks

Angela Rosy Morgillo, Massimiliano Federico Sacchi, Chiara Macchiavello

Published Mar 27, 2025• 1 citation
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Abstract

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.

DOI
10.1007/s42484-025-00252-w

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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.
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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.
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Time series forecasting remains a significant challenge in various domains, including finance, weather prediction, and industrial process control. Traditional neural networks, particularly recurrent neural networks (RNNs), often struggle to effectively capture the intricate temporal dependencies inherent in time series data. This paper proposes a novel approach leveraging quantum-inspired algorithms to optimize RNNs for improved time series forecasting performance. Specifically, we explore the utilization of quantum annealing techniques to adjust the weights within an RNN architecture. This approach mimics key quantum principles, such as superposition and interference, to potentially enhance the network's ability to represent and predict complex temporal patterns. The core claim of this work is that classical neural networks, particularly RNNs, are limited in their ability to model temporal dependencies. We introduce a mechanism where quantum-inspired algorithms, particularly quantum annealing, are employed to optimize the weights of RNNs. The underlying principles of superposition and interference are leveraged to capture more complex temporal patterns. The results demonstrate the potential of this quantum-inspired approach to achieving superior forecasting accuracy compared to conventional RNNs.
we advance non-Markovian quantum process tomography through a novel neural network-based approach, effectively transforming experimental data into a process tensor represented by the Choi state. Our investigations validate that neural networks excel in reconstructing process tensors with superior precision and robustness against noise, particularly under the challenges of undersampling. The neural network model we present not only outstrips traditional linear inversion methods in computational efficiency and accuracy but also showcases remarkable generalization across varying environments. This study fully leverages causality constraints to reduce the number of parameters in process tensor prediction, significantly enhancing the training and data efficiency of neural networks in quantum process tomography. This work marks progress in quantum computing, leveraging the strengths of neural networks to robustly characterize and identify quantum processes, thereby broadening the horizons for practical quantum process tomography applications.
This paper is a survey on the use of fully-quantum digital recurrent neural networks (QRNNs) for time-series forecasting with real-world data. It discusses precedent QRNN papers, their methodology and evaluation strategies, and highlights that, despite their intuitive applicability to the problem, QRNNs haven't been rigorously evaluated with forecasting tasks. Finally, it presents some real-data forecasting experiment results and a couple examples of how experiment setup can affect the outcomes. These results serve to inform and motivate future work, with the goal of useful QRNN prediction.