Non-Hermitian shortcuts to adiabaticity based on physics-informed neural networks
Abstract
Physics-informed neural networks (PINNs) represent a methodology that integrates physical equations into neural networks. By incorporating the residuals of physical equations as part of the loss function, PINNs enable the network to learn data features while simultaneously satisfying the constraints imposed by physical laws. The underlying principle of PINNs involves using optimization algorithms to iteratively update the network parameters until the value of a specified physics-informed loss function decreases to an acceptable level, thereby driving the network towards the solution of the differential equations. This approach is not merely a tool but serves as a bridge integrating scientific computing with artificial intelligence, offering novel paradigms for modeling and predicting complex systems. In this paper, we propose a non-Hermitian shortcut to adiabaticity (STA) scheme based on physics-informed neural networks. We utilize the physics-informed neural networks to solve parameterized differential equations, employing the neural networks as an approximating function for the quantum adiabatic evolution process. This provides an interpretable and end-to-end framework (termed STAPINNs) for control-field optimization, distinct from traditional gradient-based approaches like gradient ascent pulse engineering (GRAPE), which require pre-defined pulse parameterization. The parameterized differential equations, along with various physical constraints, are incorporated into the…
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