QUROPE Quantum Information Processing and Communication in Europe

Discrete-time quantum walks allow Floquet topological insulator materials to be explored using controllable systems such as ultracold atoms in optical lattices. By numerical simulations, we study the robustness of topologically protected edge states in the presence of temporal disorder in one- and two-dimensional discrete-time quantum walks. We also develop a simple analytical model to gain further insight into the robustness of these edge states against either spin or spatial dephasing.

We discuss the dissipative preparation of p-wave superconductors in number-conserving one-dimensional fermionic systems. We focus on two setups: the first one entails a single wire coupled to a bath, whereas in the second one the environment is connected to a two-leg ladder. Both settings lead to stationary states which feature the bulk properties of a pwave superconductor, identified in this number-conserving setting through the long-distance behavior of the proper p-wave correlations.

We introduce a conceptually simple and experimentally feasible method to realize and detect photonic topological Chern insulators with a one-dimensional circuit quantum electrodynamics lattice. By periodically modulating the couplings in this lattice, we show that this one-dimensional model can be mapped into a two-dimensional Chern insulator model. In addition to allowing the study of photonic Chern insulators, this approach also provides a natural platform to realize experimentally Laughlin's pumping argument.

In this Letter we present, in a number conserving framework, a model of interacting fermions in a two-wire geometry supporting nonlocal zero-energy Majorana-like edge excitations. The model has an exactly solvable line, on varying the density of fermions, described by a topologically nontrivial ground state wave function. Away from the exactly solvable line we study the system by means of the numerical density matrix renormalization group.

Topological order has proven a useful concept to describe quantum phase transitions which are not captured by the Ginzburg-Landau type of symmetry-breaking order. However, lacking a local order parameter, topological order is hard to detect.

We analyze the robustness of a quantum memory based on Majorana modes in a Kitaev chain. We identify the optimal recovery operation acting on the memory in the presence of perturbations and evaluate its fidelity in different scenarios. We show that for time-dependent Hamiltonian perturbations that preserve the topological features, the memory is robust even if the perturbation contains frequencies that lie well above the gap. We identify the condition that is responsible for this feature. At the same time we find that the memory is unstable with respect to particle losses.