**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.