Simulating Quantum Many-Body States with Neural-Network Exponential Ansatz

Abstract: Preparing quantum many-body states on classical or quantum devices is a very challenging task that requires accounting for exponentially large Hilbert spaces. Although this complexity can be managed with exponential ans\"atze (such as in the coupled-cluster method), these approaches are often tailored to specific systems, which limits their universality. Recent work has shown that the contracted Schr\"odinger equation enables the construction of universal, formally exact exponential ans\"atze for quantum many-body physics. However, while the ansatz is capable of resolving arbitrary quantum systems, it still requires a full calculation of its parameters whenever the underlying Hamiltonian changes, even slightly. Here, inspired by recent progress in operator learning, we develop a surrogate neural network solver that generates the exponential ansatz parameters using the Hamiltonian parameters as inputs, eliminating the need for repetitive computations. We illustrate the effectiveness of this approach by training neural networks of several quantum many-body systems, including the Fermi-Hubbard model.