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We consider one-dimensional quantum walks in optical linear networks with synthetically introduced disorder and tunable system parameters allowing for the engineered realization of distinct topological phases. The option to directly monitor the walkers probability distribution makes this optical platform ideally suited for the experimental observation of the unique signatures of the one-dimensional topological Anderson transition. We analytically calculate the probability distribution describing the quantum critical walk in terms of a (time staggered) spin polarization signal and propose a concrete experimental protocol for its measurement. Numerical simulations back the realizability of our blueprint with current date experimental hardware.
The symmetries associated with discrete-time quantum walks (DTQWs) and the flexibilities in controlling their dynamical parameters allow to create a large number of topological phases. An interface in position space, which separates two regions with
Chains of superconducting circuit devices provide a natural platform for studies of synthetic bosonic quantum matter. Motivated by the recent experimental progress in realizing disordered and interacting chains of superconducting transmon devices, we
We present a large N solution of a microscopic model describing the Mott-Anderson transition on a finite-coordination Bethe lattice. Our results demonstrate that strong spatial fluctuations, due to Anderson localization effects, dramatically modify t
A continuous-time quantum walk is investigated on complex networks with the characteristic property of community structure, which is shared by most real-world networks. Motivated by the prospect of viable quantum networks, I focus on the effects of n
In this theoretical study, we analyze quantum walks on complex networks, which model network-based processes ranging from quantum computing to biology and even sociology. Specifically, we analytically relate the average long time probability distribu