# Quantum Elastica

## TL;DR

This paper introduces a quantum method for solving optimization problems using the elastica problem as an example.

## Contribution

The novel approach combines forward and backward propagating wave solutions to handle boundary conditions.

## Key findings

- The method provides a new solution to the elastica problem.
- It opens pathways for applying quantum techniques to classical optimization challenges.

## Abstract

This paper presents a quantum method to tackle optimization challenges. Departing from the typical applications of quantum theory in particle physics, we demonstrate our approach using the elastica problem as a concrete example. The elastica, a classic variational problem extensively studied by mathematicians, serves as an ideal test case. Within quantum theory, our central innovation lies in the way we handle boundary conditions by combining forward and backward propagating wave solutions, a concept inspired by the superposition of forward and backward time-traveling particle waves in quantum mechanics. This approach not only provides a novel solution method for the elastica problem but also opens new pathways for applying quantum mathematical techniques to classical optimization challenges in other domains.