Time-dependent Neural Galerkin Method for Quantum Dynamics

Understand

We introduce a classical computational method for quantum dynamics that relies on a global-in-time variational principle.

• Unlike conventional time-stepping approaches, our scheme computes the entire state trajectory over a finite time window by minimizing a loss function that enforces the Schr\"odinger's equation.
• The variational state is parametrized with a Galerkin-inspired ansatz based on a time-dependent linear combination of time-independent Neural Quantum States.
• This structure is particularly well-suited for exploring long-time dynamics and enables bounding the error with the exact evolution via the global loss function.