A Hybrid Classical-Quantum framework for solving Free Boundary Value Problems and Applications in Modeling Electric Contact Phenomena

TL;DR

This paper introduces a hybrid classical-quantum framework leveraging quantum algorithms to solve heat transfer problems with free boundaries, demonstrating its effectiveness through experiments on IBM Quantum hardware.

Contribution

It presents a novel hybrid classical-quantum approach for solving Stefan type free boundary problems, including inverse problems, using the HHL quantum algorithm.

Findings

Successful implementation on IBM Quantum Machine

Accurate solutions for inverse Stefan problems

Demonstrated potential of quantum algorithms in heat transfer modeling

Abstract

In this paper we elaborate a hybrid classical-quantum framework which allows one to model and solve heat and mass transfer problems occurring in electric contacts. We utilize special functions and Harrow-Hassidim-Lloyd (HHL) quantum algorithm for finding temperature and arc flux functions exactly and approximately for the Stefan type problems. The Stefan type problems we are considering are based on the Generalized Heat Equation with free boundaries. As examples we consider exact and approximate solutions of inverse one-phase and two-phase Stefan problems. An Inverse Generalized One-Phase Stefan Problem is considered as a model problem. Computational experiments were conducted and demonstrated on IBM Quantum Machine.