Bounding the depth of approximate t-designs
Abstract: A fundamental mystery of quantum information theory is the rate at which a random circuit architecture approaches a globally uniform distribution. This question not only describes the scrambling of random circuits, but has implications in many other aspects of physics, such as many-body quantum chaos or the dynamics of black holes. Previous works have proven that a one-dimensional brickwork architecture becomes an approximate t-design within a depth that is linear in system size and polynomial in t. In this talk, we will show how to reduce more general architectures to this one-dimensional case while keeping a linear bound in system size, by investigating the angles between the eigenspaces of different layers in the architecture. In addition, we will expand the regime where the t-polynomial bound can be reduced to a t-linear bound, by using a reduction of the one-dimensional staircase architecture.
Student Information: James Allen is a 7th year physics graduate student working with Bryan Clark on multiple areas of computational physics, with a focus on quantum information theory and tensor networks.
