Q-Flow: Generative Modeling for Differential Equations of Open Quantum Dynamics with Normalizing Flows

• URL: http://arxiv.org/abs/2302.12235v2
• Date: Tue, 6 Jun 2023 22:00:01 GMT
• Title: Q-Flow: Generative Modeling for Differential Equations of Open Quantum Dynamics with Normalizing Flows
• Authors: Owen Dugan, Peter Y. Lu, Rumen Dangovski, Di Luo, Marin Solja\v{c}i\'c
• Abstract summary: We use a reformulation of open quantum system dynamics to a partial differential equation (PDE) for a corresponding probability distribution $Q$, the Husimi Q function. We develop novel methods for learning normalizing flow evolution governed by high-dimensional PDEs. Q-Flow is superior to conventional PDE solvers and state-of-the-art physics-informed neural network solvers.
• Score: 2.1199214954570653
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Studying the dynamics of open quantum systems can enable breakthroughs both in fundamental physics and applications to quantum engineering and quantum computation. Since the density matrix $\rho$, which is the fundamental description for the dynamics of such systems, is high-dimensional, customized deep generative neural networks have been instrumental in modeling $\rho$. However, the complex-valued nature and normalization constraints of $\rho$, as well as its complicated dynamics, prohibit a seamless connection between open quantum systems and the recent advances in deep generative modeling. Here we lift that limitation by utilizing a reformulation of open quantum system dynamics to a partial differential equation (PDE) for a corresponding probability distribution $Q$, the Husimi Q function. Thus, we model the Q function seamlessly with off-the-shelf deep generative models such as normalizing flows. Additionally, we develop novel methods for learning normalizing flow evolution governed by high-dimensional PDEs based on the Euler method and the application of the time-dependent variational principle. We name the resulting approach $Q$-$Flow$ and demonstrate the scalability and efficiency of Q-Flow on open quantum system simulations, including the dissipative harmonic oscillator and the dissipative bosonic model. Q-Flow is superior to conventional PDE solvers and state-of-the-art physics-informed neural network solvers, especially in high-dimensional systems.

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