We show that informational completeness, while sufficient to have a bijection between ideal measurement probabilities and quantum states, does not guarantee statistically stable reconstruction from finite measurement data. To address this problem, we develop a general estimation theory for continuous-variable systems in which stable reconstructibility is characterized by the POVM effects forming a measurement frame. Informational completeness is therefore necessary, but not sufficient, for stable reconstruction. Our framework is based on measurement frames in a $σ$-regularized operator geometry, where the reference state σ encodes prior information about relevant features of the measured states. For any fixed measurement scheme, observables may be inaccessible, weakly reconstructible only through estimators with divergent variance, or stably reconstructible by finite-variance unbiased estimators. The relevant regime is determined by the range of the POVM synthesis operator. Our framework provides practical methods for constructing estimators and gives an operational interpretation of singular quasiprobability distributions, including the Glauber-Sudarshan P representation: quasiprobabilities act as unbiased estimators for associated observables, and their singularities reflect a pathological feature of the corresponding measurement: its lack of loewr frame bound. We furthermore show how this formalism naturally provides operational regularization procedures tied to prior information. Overall, our framework provides a unified view of continuous-variable tomography, quasiprobability representations, and classical-shadow estimation.

Simulating open quantum systems on digital quantum computers typically relies on the use of auxiliary qubits, resulting in overheads of noisy multi-qubit gates, that severely limit execution on near-term hardware. In this work, we explore the simulation of non-Markovian dynamics as well as memory channels leveraging the method of trajectory mixing, valid for mixed unitary channels. This allows to drastically reduce circuit depth, trading entangling gates for a statistical mixture of independent, pure state trajectories. Using a realistic noise model calibrated to modern quantum processors, we show the benefits of this approach, yielding higher state fidelity and better preservation of quantum correlations. This shows the possibility of simulating long-time non-Markovian evolutions with low noise and limited resources.

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.