Quantum-Inspired Solver for Simulating Material Deformations

TL;DR

This paper demonstrates that tensor networks, inspired by quantum mechanics, can efficiently simulate large-scale material deformations by solving linear elasticity equations, offering exponential improvements in computational resources.

Contribution

The study introduces a quantum-inspired tensor network approach for simulating material deformations, achieving significant efficiency gains over traditional methods.

Findings

Solved linear elasticity equations with billions of degrees of freedom

Achieved exponential reductions in memory and computational time

Validated practical viability of tensor networks for material simulation

Abstract

This paper explores the application of tensor networks (TNs) to the simulation of material deformations within the framework of linear elasticity. Material simulations are essential computational tools extensively used in both academic research and industrial applications. TNs, originally developed in quantum mechanics, have recently shown promise in solving partial differential equations (PDEs) due to their potential for exponential speedups over classical algorithms. Our study successfully employs TNs to solve linear elasticity equations with billions of degrees of freedom, achieving exponential reductions in both memory usage and computational time. These results demonstrate the practical viability of TNs as a powerful classical backend for executing quantum-inspired algorithms with significant efficiency gains. This work is based on our research conducted with IKERLAN.