Universal Neural Propagator: Learning Time Evolution in Many-Body Quantum Systems

TL;DR

The paper introduces the Universal Neural Propagator (UNP), a model that learns to predict quantum many-body dynamics across various initial states and driving protocols, enabling transferable and scalable simulations.

Contribution

A novel unified neural model that predicts quantum dynamics across protocols and states, trained self-supervised, and scalable beyond exact diagonalization.

Findings

UNP accurately predicts dynamics in a 2D driven Ising model.

UNP demonstrates transferability across initial states and protocols.

UNP remains accurate at larger system sizes beyond exact methods.

Abstract

Conventional approaches to simulating quantum many-body dynamics produce a single trajectory: if the Hamiltonian or the initial state is changed, the computation must be re-performed. Recent efforts toward foundation models have begun to address this limitation, yet existing methods transfer across either Hamiltonians or initial states, but not both. In this work, we introduce the Universal Neural Propagator (UNP), a single, unified model that learns the functional mapping from driving protocols to time-evolution propagators. Trained in an entirely self-supervised way, a single UNP model predicts dynamics across a function space of driving protocols and an exponentially large Hilbert space of initial states simultaneously. We benchmark on a two-dimensional driven Ising model and demonstrate the UNP's accuracy and transferability across product and entangled initial states, as well as for both in- and out-of-distribution driving protocols. The UNP remains accurate at system sizes beyond exact diagonalization, and can be efficiently fine-tuned across all initial states using observable data. By shifting the object of learning from quantum states to operators, this work opens a route toward transferable simulation of driven quantum matter.