A topological quantum computer is a type of computer that uses quantum physics to process information faster and more efficiently than traditional computers. It works by using the way particles interact with each other when arranged in a certain way so that information can be moved across the system quickly. The particles are arranged into what are called 'topological clusters', which are like groups of particles that interact with each other in a specific way. By changing the arrangement of the clusters, information can be transported quickly, allowing for much faster computing than traditional computers.