Related papers: An Optimal Framework for Constructing Lie-Algebra …
Accurate prediction of protein active-site structures remains a central challenge in structural biology, particularly for short and flexible peptide fragments where conventional and simulation-based methods often fail. Here, we present a…
A simple yet general method for constructing basis sets for molecular electronic structure calculations is presented. These basis sets consist of atomic natural orbitals from a multi-configurational self-consistent field calculation…
Quantum algorithms offer a compelling new avenue for addressing difficult NP-complete optimization problems, such as the Generalized Assignment Problem (GAP). Given the operational constraints of contemporary Noisy Intermediate-Scale…
Determining the physically accessible unitary dynamics of a quantum system under finite Hamiltonian resources is a central problem in quantum control and Hamiltonian engineering. Dynamical Lie algebras (DLAs) provide the fundamental link…
Machine-learning potentials (MLPs) for atomistic simulations are a promising alternative to conventional classical potentials. Current approaches rely on descriptors of the local atomic environment with dimensions that increase…
We provide an integration of the universal, perturbative explicitly correlated [2]$_\text{R12}$-correction in the context of the Variational Quantum Eigensolver (VQE). This approach is able to increase the accuracy of the underlying…
Measurement-based quantum computing (MBQC) is a promising approach to reducing circuit depth in noisy intermediate-scale quantum algorithms such as the Variational Quantum Eigensolver (VQE). Unlike gate-based computing, MBQC employs local…
Variational quantum approaches have shown great promise in finding near-optimal solutions to computationally challenging tasks. Nonetheless, enforcing constraints in a disciplined fashion has been largely unexplored. To address this gap,…
Current quantum computers are limited in the number of qubits and coherence time, constraining the algorithms executable with sufficient fidelity. The variational quantum eigensolver (VQE) is an algorithm to find an approximate ground state…
We consider the reduced quasi-classical self-dual Yang-Mills equation (rYME) and two recently found (Jahnov\'{a} and Voj\v{c}\'{a}k, 2024) invertible recursion operators $\mathcal{R}^q$ and $\mathcal{R}^m$ for its full-fledged (in a given…
In the noisy-intermediate-scale-quantum era, Variational Quantum Eigensolver (VQE) is a promising method to study ground state properties in quantum chemistry, materials science, and condensed physics. However, general quantum eigensolvers…
Lie groups, and therefore Lie algebras, are fundamental structures in quantum physics that determine the space of possible trajectories of evolving systems. However, classification and characterization methods for these structures are often…
Analytical methods underpin geotechnical engineering practice, yet their implementation remains fragmented across error-prone spreadsheets and opaque proprietary software. While Large Language Models (LLMs) offer transformative potential…
In view of controlling finite dimensional open quantum systems, we provide a unified Lie-semigroup framework describing the structure of completely positive trace-preserving maps. It allows (i) to identify the Kossakowski-Lindblad…
Quantum computing is entering a transformative phase with the emergence of logical quantum processors, which hold the potential to tackle complex problems beyond classical capabilities. While significant progress has been made, applying…
Electronic structure calculations on small systems such as H$_2$, H$_2$O, LiH, and BeH$_2$ with chemical accuracy are still a challenge for the current generation of the noisy intermediate-scale quantum (NISQ) devices. One of the reasons is…
Non-Hermitian operators naturally arise in the description of open quantum systems, which exhibit features such as resonances and decay processes, where the associated eigenvalues are complex. Standard quantum algorithms, including the…
Every non-solvable and non-semisimple quadratic Lie algebra can be obtained as a double extension of a solvable quadratic Lie algebra. Thanks to a partial classification of nilpotent Lie algebras and this result, we can design different…
The elements of the wide class of quantum universal enveloping algebras are prooved to be Hopf algebras $H$ with spectrum $Q(H)$ in the category of groups. Such quantum algebras are quantum groups for simply connected solvable Lie groups…
Variational quantum eigensolver~(VQE) typically optimizes variational parameters in a quantum circuit to prepare eigenstates for a quantum system. Its applications to many problems may involve a group of Hamiltonians, e.g., Hamiltonian of a…