Many particle quantum walks - David Feder

The quantum walk (QW) is the quantum mechanical extension of the classical random walk, where the quantum particle (the walker) can be considered to follow many trajectories simultaneously. The quantum walker can often traverse graphs more quickly than using any classical scheme, an advantage that can be harnessed for fast quantum algorithms. Motivated by recent experiments on ultracold atoms in optical lattices, I will explore the properties of many particle quantum walks. I will discuss two main results. First, these walks can provide in situ experimental signatures of both the Mott-insulator phase transition and fermionization. Second, a duality between many-particle and single-particle quantum walks reveals that a quantum walker can fully traverse certain one and two-dimensional weighted graphs in constant time, even when the number of vertices grows exponentially, hitting the output vertex with 100\% probability.