Abstract

Quantum computers have the potential to drastically change the way we do computations and could help us solve some of the most complex problems. Their applications could range from physics simulations to drug development and even finance. In this project, I explored how quantum computing could be used to solve Green’s functions, which are important tools in physics used to predict how some quantum systems will respond to different conditions.

When considering complex cases, calculating Green’s function with a classical computer can be very time-consuming due to the heavy computational effort required. To investigate this, I developed two versions of an algorithm: one using classical computing and another using the computational power of quantum computing. The algorithm relies on Chebyshev polynomials, a special type of mathematical pattern.

I then tested the quantum version of the algorithm on a simulator, which mimics how a real quantum computer operates. The results showed that the quantum method successfully produced the same results as the classical one. This suggests that quantum computing could eventually be a powerful tool for solving Green’s function, especially in cases where traditional methods struggle.