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arXiv:2109.14471

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

Nima Leclerc

Published Sep 29, 2021• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2109.14471

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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.
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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.
Numerous variational methods have been proposed for solving quantum many-body systems, but they often face exponentially increasing computational complexity as the Hilbert space dimension grows. To address this, we introduce a novel approach using quantum neural networks to simulate the dissipative dynamics of many-body open quantum systems. This method combines neural-network quantum state representation with the time-dependent variational principle, both implemented via quantum algorithms. This results in accurate open quantum dynamics described by the Lindblad quantum master equation, exemplified by the spin-boson and transverse field Ising models. Our approach avoids the computational expense of classical algorithms and demonstrates the potential advantages of quantum computing for many-body simulations. To reduce measurement errors, we introduce a projection reset procedure, which could benefit other quantum simulations. In addition, our approach can be extended to simulate non-Markovian quantum dynamics.
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Characterizing non-Markovian quantum dynamics is essential for accurately modeling open quantum systems, particularly in near-term quantum technologies. In this work, we develop a structure-preserving approach to characterizing non-Markovian evolution using the time-convolutionless (TCL) master equation, considering both linear and nonlinear formulations. To parameterize the master equation, we explore two distinct techniques: the Karhunen-Loeve (KL) expansion, which provides an optimal basis representation of the dynamics, and neural networks, which offer a data-driven approach to learning system-environment interactions. We demonstrate our methodology using experimental data from a superconducting qubit at the Quantum Device Integration Testbed (QuDIT) at Lawrence Livermore National Laboratory (LLNL). Our results show that while neural networks can capture complex dependencies, the KL expansion yields the most accurate predictions of the qubit's non-Markovian dynamics, highlighting its effectiveness in structure-preserving quantum system characterization. These findings provide valuable insights into efficient modeling strategies for open quantum systems, with implications for quantum control and error mitigation in near-term quantum processors.
Quantum computing requires the optimization of control pulses to achieve high-fidelity quantum gates. We propose a machine learning-based protocol to address the challenges of evaluating gradients and modeling complex system dynamics. By training a recurrent neural network (RNN) to predict qubit behavior, our approach enables efficient gradient-based pulse optimization without the need for a detailed system model. First, we sample qubit dynamics using random control pulses with weak prior assumptions. We then train the RNN on the system's observed responses, and use the trained model to optimize high-fidelity control pulses. We demonstrate the effectiveness of this approach through simulations on a single ST0ST_0ST0​ qubit.