Related papers: An Optimal Framework for Constructing Lie-Algebra …
Sparse tensor algebra is challenging to efficiently parallelize due to the irregular, data-dependent, and potentially skewed structure of sparse computation. We propose the first partitioning algorithm that provably load balances the…
Recent advances in quantum computing devices have brought attention to hybrid quantum-classical algorithms like the Variational Quantum Eigensolver (VQE) as a potential route to practical quantum advantage in chemistry. However, it is not…
The utility of effective model spaces in quantum simulations of non-relativistic quantum many-body systems is explored in the context of the Lipkin-Meshkov-Glick model of interacting fermions. We introduce an iterative…
Quantum computing has the potential to improve our ability to solve certain optimization problems that are computationally difficult for classical computers, by offering new algorithmic approaches that may provide speedups under specific…
Quantum computers have the potential to solve some important industrial and scientific problems with greater efficiency than classical computers. While most current realizations focus on two-level qubits, the underlying physics used in most…
Computational quantum chemistry plays a critical role in drug discovery, chemical synthesis, and materials science. While first-principles methods, such as density functional theory (DFT), provide high accuracy in modeling electronic…
Accurately capturing electron correlation in large-scale molecular systems remains one of the foremost challenges in quantum chemistry and a primary driver for the development of quantum algorithms. Classical configuration-interaction…
Current gate-based quantum computers have the potential to provide a computational advantage if algorithms use quantum hardware efficiently. To make combinatorial optimization more efficient, we introduce the Filtering Variational Quantum…
Derived brackets provide a mechanism for generating algebraic structures from graded Lie superalgebras, with applications in Poisson geometry, mathematical physics, and the theory of algebroids. In this paper, we present a complete…
Applications of algebras in physics are related to the connection of measurable observables to relevant elements of the algebras, usually the generators. However, in the determination of the generators in Lie algebras there is place for…
Variational quantum eigensolvers (VQEs) are leading candidates to demonstrate near-term quantum advantage. Here, we conduct density-matrix simulations of leading gate-based VQEs for a range of molecules. We numerically quantify their level…
The Variational Quantum Eigensolver (VQE) algorithm is gaining interest for its potential use in near-term quantum devices. In the VQE algorithm, parameterized quantum circuits (PQCs) are employed to prepare quantum states, which are then…
Parity compilation is the challenge of laying out the required constraints for the parity mapping in a local way. We present the first constructive compilation algorithm for the parity architecture using plaquettes for arbitrary…
Variational quantum eigensolvers (VQEs) are among the most promising quantum algorithms for solving electronic structure problems in quantum chemistry, particularly during the Noisy Intermediate-Scale Quantum (NISQ) era. In this study, we…
Variational Quantum Eigensolvers (VQEs) are a powerful class of hybrid quantum-classical algorithms designed to approximate the ground state of a quantum system described by its Hamiltonian. VQEs hold promise for various applications,…
Basic properties of Lie-orthogonal operators on a finite-dimensional Lie algebra are studied. In particular, the center, the radical and the components of the ascending central series prove to be invariant with respect to any Lie-orthogonal…
Adaptive quantum design identifies the best broken-symmetry configurations of atoms and molecules that enable a desired target function response. In this work, numerical optimization is used to design atomic clusters with specified…
We present quantum algorithms, for Hamiltonians of linear combinations of local unitary operators, for Hamiltonian matrix-vector products and for preconditioning with the inverse of shifted reduced Hamiltonian operator that contributes to…
Analytical and practical evidence indicates the advantage of quantum computing solutions over classical alternatives. Quantum-based heuristics relying on the variational quantum eigensolver (VQE) and the quantum approximate optimization…
We present a new algorithm for constructing a Chevalley basis for any Chevalley Lie algebra over a finite field. This is a necessary component for some constructive recognition algorithms of exceptional quasisimple groups of Lie type. When…