Quantum-Classical Neural Networks for Solving Lindblad Master Equations
We propose a variational framework for solving Lindblad master equations by minimizing a residual cost function using a compositional ansatz obtained by combining a classical neural network with a parameterized quantum circuit.
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Key points
- Variational quantum algorithms have emerged as a promising approach for simulating open quantum systems, yet their expressive power and trainability remain poorly understood.
- Beyond the algorithmic formulation, we derive an upper bound for the covering number of the proposed compositional model and compare it with that of purely quantum neural networks.
- Our analysis shows that the classical parametrization enlarges the effective hypothesis class while providing finer control over its complexity, thereby establishing a theoretical connection between expressivity, covering numbers, effective dimension, and the barren plateau phenomenon.
- These results provide a unified variational and theoretical framework for the simulation of dissipative quantum dynamics using compositional quantum machine learning models.
Sources (1)
- [1]Quantum-Classical Neural Networks for Solving Lindblad Master EquationsarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 15, 09:59 PM
We propose a variational framework for solving Lindblad master equations by minimizing a residual cost function using a compositional ansatz obtained by combining a classical neural network with a parameterized quantum circuit.
Variational quantum algorithms have emerged as a promising approach for simulating open quantum systems, yet their expressive power and trainability remain poorly understood.
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