Quantum computers, if they are built, will almost surely lead to paradigm shifts throughout science and engineering. This is because quantum computers are better able to simulate quantum mechanical systems than classical computers. Surprisingly, they will also be capable of solving certain problems from mathematics that appear to have nothing to do with quantum physics (e.g. factoring integers into products of primes) more quickly than classical computers. But it's not entirely clear which mathematical problems are amenable to quantum speed-ups. In this project, we will explore the feasibility of using quantum algorithms to detect knots.
More precisely, we will perform computational experiments that will help us determine if the quantum phase estimation protocol can be used to compute the Khovanov homology of knots more quickly than known classical algorithms.
Advanced linear algebra and Python