Applications of the Hubbard wheel: Quantum non-demolition readout and the role of disorder in an ensemble of qubits

Easily realizable and scalable setups involving a center site with extensively scaling coordination number are important in quantum information. Recent work on a system of hardcore bosons on a wheel geometry, known to form a Bose-Einstein condensate, introduced a mechanism stabilizing a one-dimensional quantum many-body phase in the presence of nearest-neighbor interactions via the protection of an emergent Z₂ symmetry. In this talk, I'll discuss the effect of further perturbations, relevant in more realistic setups in quantum simulation and central spin systems. Furthermore, I'll introduce a probe site for quantum non-demolition readout of many-particle states, allowing to predict the state of the BEC on the wheel. These novel theoretical insights will facilitate experimental realizations and interesting applications in various quantum platforms.