We investigate the interacting non-Hermitian Su-Schrieffer-Heeger (SSH) model, focusing on the interplay between topology and charge ordering. Using a real-space topological marker, charge correlations, and the complex many-body spectrum, we map out the phase diagram under periodic and open boundary conditions. We show that the topological marker remains a robust diagnostic of non-Hermitian topological phases in the presence of interactions and consistently signals their breakdown at the onset of a charge density wave (CDW). We further demonstrate that non-Hermiticity enhances interaction effects: While moderate changes occur under periodic boundary conditions, open boundary conditions lead to a pronounced amplification of staggered charge correlations near exceptional points. This enhancement arises from the accumulation of low-energy states near exceptional points, which promotes electronic instabilities and strengthens CDW tendencies.

The study of exoplanetary atmospheres traditionally relies on forward models to analytically compute the spectrum of an exoplanet by fine-tuning numerous chemical and physical parameters. However, the high-dimensionality of parameter space often results in a significant computational overhead. In this work, we introduce a novel approach to atmospheric retrieval leveraging on quantum extreme learning machines (QELMs), a quantum version of the classical Extreme Learning Machine (ELM) – a fast machine learning model typically used for regression and classification. Our method combines classical spectral patching and PCA-based dimensionality reduction with a factorized quantum reservoir that provides nonlinear features for the final linear retrieval map. We distinguish the classical PCA filtering used to mitigate noise in the input spectra from the readout-level robustness observed when the reservoir is executed on noisy quantum hardware. We demonstrate the robustness of our approach through a direct implementation on IBM Fez. The proposed QELM architecture highlights the potential of quantum computing in the analysis of astrophysical datasets, retrieving successfully the concentration of $CH_4$, $CO_2$, and $H_2O$, and the radius of over the $90$% of the dataset in the infinite statistics limit, while remaining robust under realistic noise conditions on IBM Fez, paving the way, in the near future, to faster, more efficient, and more accurate models for the study of exoplanetary atmospheres.

Device-independent quantum key distribution (DI-QKD) offers security with the smallest possible set of assumptions about the experimental setup. The challenge posed by its implementation could be tackled using routed Bell tests with entanglement swapping, or distant Bell state measurement (BSM) units. However, practical distances still require local tests with close-to-ideal violations. We propose a DI-QKD protocol based on multiple sources and measurement devices where, in each round, routed tests are performed on randomly selected local devices. The violation of local Bell tests is checked even when a successful BSM projection is achieved. By requiring that such conditional tests remain consistent with the overall one, we achieve improvements in the critical detection efficiencies of about  $4-12%$ for high visibilities. Our approach enables long-distance DI-QKD, with access to highly efficient loophole-free routing setups, and multiple local tests (possibly imperfect) with very high local detection efficiencies. Finally, we extend the concept of routing to dimension witnesses, where qubit-bounded sources send states to the BSM. This can be seen as a semi-device-independent extension of the aforementioned protocol.

Emergent collective excitations constitute a hallmark of interacting quantum many-body systems, yet in solid-state platforms their study has been largely limited by the constraints of linear-response probes and by finite momentum resolution. We propose to overcome these limitations by combining the spatial resolution of ultracold atomic systems with the nonlinear probing capabilities of two-dimensional spectroscopy (2DS). As a concrete illustration, we analyze momentum-resolved 2DS of the quantum sine-Gordon model describing the low-energy dynamics of two weakly coupled one-dimensional Bose-Einstein condensates. This approach reveals distinctive many-body signatures, most notably asymmetric cross-peaks reflecting the interplay between isolated ($B_2$ breather) and continuum ($B_1$ pair) modes. The protocol further enables direct characterization of anharmonicity and disorder, establishing momentum-resolved 2DS as both a powerful diagnostic for quantum simulators and a versatile probe of correlated quantum matter.