Chunhao Wang, PhD candidate
David R. Cheriton School of Computer Science
We give a dissipative quantum search algorithm that is based on a novel dissipative query model. If there are $N$ items and $M$ of them are marked, this algorithm performs a fixed-point quantum search using $O(\sqrt{N/M}\log(1/\epsilon))$ queries with error bounded by $\epsilon$. In addition, we present a continuous-time version of this algorithm in terms of Lindblad evolution.
Chunhao Wang, PhD candidate
David R. Cheriton School of Computer Science
We present a quantum algorithm for simulating the dynamics of Hamiltonians that are not necessarily sparse. Our algorithm is based on the assumption that the entries of the Hamiltonian are stored in a data structure that allows for the efficient preparation of states that encode the rows of the Hamiltonian. We use a linear combination of quantum walks to achieve a poly-logarithmic dependence on the precision.