Quantics Tensor Train for solving Gross-Pitaevskii equation

TL;DR

This paper introduces a quantum-inspired tensor train method for efficiently solving the one-dimensional Gross-Pitaevskii equation, enabling accurate simulations with significantly reduced computational resources.

Contribution

The authors develop a novel QTT-based framework with algorithms for ground state and real-time dynamics, extending the capabilities of classical simulations of nonlinear Schrödinger equations.

Findings

Achieves exponential reduction in computational resources compared to standard methods.

Successfully captures diverse physical scenarios including long-range interactions.

Maintains quantitative accuracy within the compressed tensor network representation.

Abstract

We present a quantum-inspired solver for the one-dimensional Gross-Pitaevskii equation in the Quantics Tensor-Train (QTT) representation. By evolving the system entirely within a low-rank tensor manifold, the method sidesteps the memory and runtime barriers that limit conventional finite-difference and spectral schemes. Two complementary algorithms are developed: an imaginary-time projector that drives the condensate toward its variational ground state and a rank-adapted fourth-order Runge-Kutta integrator for real-time dynamics. The framework captures a broad range of physical scenarios - including barrier-confined condensates, quasi-random potentials, long-range dipolar interactions, and multicomponent spinor dynamics - without leaving the compressed representation. Relative to standard discretizations, the QTT approach achieves an exponential reduction in computational resources while retaining quantitative accuracy, thereby extending the practicable regime of Gross-Pitaevskii simulations on classical hardware. These results position tensor networks as a practical bridge between high-performance classical computing and prospective quantum hardware for the numerical treatment of nonlinear Schrodinger-type partial differential equations.