Section: New Results

Quantum Fast-Forwarding: Markov Chains and graph property testing

Participants: Alain Sarlette

This is the end of the PhD thesis of S.Apers, under supervision of A.Sarlette at Ghent University. In [11], we propose a quantum algorithmic routine, called Quantum Fast-Forwarding, which allows to simulate a Markov chain quadratically faster on a quantum computer than on a classical one. The key novelty, from an application point of view, is that we can achieve this acceleration not only for reaching the asymptotic distribution, but also for any intermediate time that one would be interested in. Such transient behaviors of Markov chains are important in algorithmic context, for instance to distinguish clusters in graphs. We explicitly work out those applications on graph properties.