Solving the Gross-Pitaevskii Equation with Quantic Tensor Trains: Ground States and Nonlinear Dynamics

TL;DR

This paper introduces a tensor network approach using the quantic tensor train format to efficiently solve the Gross-Pitaevskii equation, enabling high-resolution simulations of Bose-Einstein condensates with reduced computational cost.

Contribution

The authors develop a novel QTT-based framework for solving the GPE, combining TDVP and gradient descent to handle nonlinearities efficiently, outperforming traditional methods.

Findings

Accurate simulation of BEC ground states and dynamics

Demonstrated vortex lattice formation and breathing modes

Stable long-time evolution with reduced computational resources

Abstract

We develop a tensor network framework based on the quantic tensor train (QTT) format to efficiently solve the Gross-Pitaevskii equation (GPE), which governs Bose-Einstein condensates under mean-field theory. By adapting time-dependent variational principle (TDVP) and gradient descent methods, we accurately handle the GPE's nonlinearities within the QTT structure. Our approach enables high-resolution simulations with drastically reduced computational cost. We benchmark ground states and dynamics of BECs--including vortex lattice formation and breathing modes--demonstrating superior performance over conventional grid-based methods and stable long-time evolution due to saturating bond dimensions. This establishes QTT as a powerful tool for nonlinear quantum simulations.