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Center for Nonlinear Studies |
In the limit of large depth, random quantum circuits generally approach maximally random unitary operators. The approximate t-design depth captures the speed of this convergence, which can be interpreted as a rate of information scrambling or of thermalization. In this setting, a natural question is how the rate of scrambling depends on the geometric structure of the circuit. Previous work has established several upper bounds on the depths at which certain specific random quantum circuit ensembles approximate t-designs. I will discuss a technique to extend these bounds to arbitrary circuit architectures. The resulting bound, obtained via a reduction from arbitrary circuit architectures to the 1D brickwork architecture, depends on the details of the architecture only via the typical number of layers needed for a block of the circuit to form a connected graph over the sites. If time allows, we will discuss prospects for tightening this bound by improving either the reduction or the base case.
Bio:Daniel Belkin is a PhD student at the University of Illinois. He received his B.A. from Swarthmore College in physics with minors in engineering and mathematics in 2019. He proceeded to research neuromorphic computing at the University of Massachusetts and computational plasma physics at Lawrence Berkeley National Lab before joining Clark Research group at UIUC to study quantum information.
Host: Paolo Braccia (T-4)