Talks

I will present an efficient quantum algorithm for an additive approximation of the famous Tutte polynomial of any planar graph at any point. The Tutte polynomial captures an extremely wide range of interesting combinatorial properties of graphs, including the partition function of the q-state Potts model. This provides a new class of quantum complete problems. Our methods generalize the recent AJL algorithm for the approximation of the Jones polynomial; instead of using unitary representations, we allow non-unitarity, which seems counter intuitive in the quantum world. Significant contribution of this is a proof that non-unitary operators can be used for universal quantum computation.