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Measuring entanglement is a demanding task in the field of quantum computation and quantum information theory. Recently, some authors experimentally demonstrated an embedding quantum simulator, using it to efficiently measure two-qubit…
The Lattice Boltzmann Method (LBM) is a computational technique of Computational Fluid Dynamics (CFD) that has gained popularity due to its high parallelism and ability to handle complex geometries with minimal effort. Although LBM…
In this note, we first recall the nonconvex problem setting and introduce the optimal PAGE algorithm (Li et al., ICML'21). Then we provide a simple and clean convergence analysis of PAGE for achieving optimal convergence rates. Moreover,…
We introduce new formulations of the quantum Cram\'{e}r-Rao bound (QCRB) and the Holevo Cram\'{e}r-Rao bound (HCRB) in multi-parameter quantum metrology via purification, where we show their values for any mixed state are connected to that…
An introduction to the Quantum Chemistry Package (QCP), implemented in the computer algebra system Maple, is presented. The QCP combines sophisticated electronic structure methods and Maple's easy-to-use graphical interface to enable…
In a recent publication we showed that permutation symmetry reduces the numerical complexity of Lindblad quantum master equations for identical multi-level systems from exponential to polynomial scaling. This is important for open system…
Rigid registration of multi-view and multi-platform LiDAR scans is a fundamental problem in 3D mapping, robotic navigation, and large-scale urban modeling applications. Data acquisition with LiDAR sensors involves scanning multiple areas…
Umbrella sampling is an efficient method for the calculation of free energy changes of a system along well-defined reaction coordinates. However, when multiple parallel channels along the reaction coordinate or hidden barriers in directions…
We address the relative paucity of empirical testing of learning algorithms (of any type) by introducing a new public-domain, Modular, Optimal Learning Testing Environment (MOLTE) for Bayesian ranking and selection problem, stochastic…
Measuring software complexity plays an important role to meet the demands of complex software. The cyclomatic complexity is one of most used and renowned metric among the other three proposed and researched metrics that are namely: Line of…
Large Language Models (LLMs) like LLaMA, Mistral, and Gemma are increasingly used in decision-critical domains such as healthcare, law, and finance, yet their reliability remains uncertain. They often make overconfident errors, degrade…
Quantum computing has recently exhibited great potentials in predicting chemical properties for various applications in drug discovery, material design, and catalyst optimization. Progress has been made in simulating small molecules, such…
Semidefinite programming (SDP) is widely acknowledged as one of the most effective methods for deriving the tightest lower bounds of the optimal power flow (OPF) problems. In this paper, an enhanced semidefinite relaxation model that…
In multi-parameter quantum metrology, the resource of entanglement can lead to an increase in efficiency of the estimation process. Entanglement can be used in the state preparation stage, or the measurement stage, or both, to harness this…
We present a finitely convergent cutting-plane algorithm for solving a general mixed-integer convex program given an oracle for solving a general convex program. This method is extended to solve a family of two-stage mixed-integer convex…
Mixture proportion estimation (MPE) is the problem of estimating the weight of a component distribution in a mixture, given samples from the mixture and component. This problem constitutes a key part in many "weakly supervised learning"…
Machine learning (ML) is increasingly becoming a common tool in computational chemistry. At the same time, the rapid development of ML methods requires a flexible software framework for designing custom workflows. MLatom 3 is a program…
Fault-tolerant quantum computation promises to solve outstanding problems in quantum chemistry within the next decade. Realizing this promise requires scalable tools that allow users to translate descriptions of electronic structure…
We propose a multi-criteria Composite Index Method (CIM) to compare the performance of alternative approaches to solving an optimization problem. The CIM is convenient in those situations when neither approach dominates the other when…
In quantum metrology, entangled states of many-particle systems are investigated to enhance measurement precision of the most precise clocks and field sensors. While single-parameter quantum metrology is well established, many metrological…