Quantics Tensor Train for solving Gross-Pitaevskii equation

Fuente: arXiv
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Main Authors: Bou-Comas, Aleix, Płodzień, Marcin, Tagliacozzo, Luca, García-Ripoll, Juan José
Format: Preprint
Published: 2025
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author Bou-Comas, Aleix
Płodzień, Marcin
Tagliacozzo, Luca
García-Ripoll, Juan José
author_facet Bou-Comas, Aleix
Płodzień, Marcin
Tagliacozzo, Luca
García-Ripoll, Juan José
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2507_03134
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Quantics Tensor Train for solving Gross-Pitaevskii equation
Bou-Comas, Aleix
Płodzień, Marcin
Tagliacozzo, Luca
García-Ripoll, Juan José
Quantum Gases
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.
title Quantics Tensor Train for solving Gross-Pitaevskii equation
topic Quantum Gases
url https://arxiv.org/abs/2507.03134