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We develop generalized bounds for quantum single-parameter estimation problems for which the coupling to the parameter is described by intrinsic multi-system interactions. For a Hamiltonian with $k$-system parameter-sensitive terms, the…
Computational molecular modeling and visualization has seen significant progress in recent years with sev- eral molecular modeling and visualization software systems in use today. Nevertheless the molecular biology community lacks…
There is a prevalent effort to achieve quantum-enhanced metrology using criticality. However, the extent to which estimation precision is enhanced through criticality still needs further exploration under the constraint of finite time…
High precision measurements are essential to solve major scientific and technological challenges, from gravitational wave detection to healthcare diagnostics. Quantum sensing delivers greater precision, but an in-depth optimisation of…
We generalize many results concerning the tractability of SAT and #SAT on bounded treewidth CNF-formula in the context of Quantified Boolean Formulas (QBF). To this end, we start by studying the notion of width for OBDD and observe that the…
Integrating high-dimensional biological data into data-driven mechanistic modeling requires rigorous practical identifiability to ensure interpretability and generalizability. However, coordinate identifiability analysis often suffers from…
In this paper a variation of the classic vector quantization problem is considered. In the standard formulation, a quantizer is designed to minimize the distortion between input and output when the number of reconstruction points is fixed.…
Big data processing systems often employ batched updates and data sketches to estimate certain properties of large data. For example, a CountMin sketch approximates the frequencies at which elements occur in a data stream, and a batched…
We consider the general problem of estimating an unknown control parameter of an open quantum system. We establish a direct relation between the evolution of both system and environment and the precision with which the parameter can be…
Using mathematical models to assist in the interpretation of experiments is becoming increasingly important in research across applied mathematics, and in particular in biology and ecology. In this context, accurate parameter estimation is…
The paper investigates the techniques of quantum computation in metrological predictions, with a particular emphasis on enhancing prediction potential through variational parameter estimation. The applicability of quantum simulations and…
As quantum technologies advance, the ability to generate increasingly large quantum states has experienced rapid development. In this context, the verification and estimation of large entangled systems represents one of the main challenges…
Machine learning models can generalize well on real-world datasets. According to the manifold hypothesis, this is possible because datasets lie on a latent manifold with small intrinsic dimension (ID). There exist many methods for ID…
The attainability of the quantum Cram\'er-Rao bound [QCR], the ultimate limit in the precision of the estimation of a physical parameter, requires the saturation of the quantum information bound [QIB]. This occurs when the Fisher…
We introduce a new kind of quantum measurement that is defined to be symmetric in the sense of uniform Fisher information across a set of parameters that injectively represent pure quantum states in the neighborhood of a fiducial pure…
Quantization for probability distributions concerns the best approximation of a $d$-dimensional probability distribution $P$ by a discrete probability with a given number $n$ of supporting points. In this paper, we have considered a…
Gradient-based optimization is a key ingredient of variational quantum algorithms, with applications ranging from quantum machine learning to quantum chemistry and simulation. The parameter-shift rule provides a hardware-friendly method for…
Beneficial to advanced computing devices, models with massive parameters are increasingly employed to extract more information to enhance the precision in describing and predicting the patterns of objective systems. This phenomenon is…
Entanglement is widely regarded as an essential resource for a number of tasks and can in some cases be quantified by figures of merit related to those tasks. In quantum metrology, this is showcased by the connections between the quantum…
Embedding vectors are widely used for representing unstructured data and searching through it for semantically similar items. However, the large size of these vectors, due to their high-dimensionality, creates problems for modern vector…