Related papers: Electronic Structure Calculatins and the Ising Mac…
A promising approach to achieve computational supremacy over the classical von Neumann architecture explores classical and quantum hardware as Ising machines. The minimisation of the Ising Hamiltonian is known to be NP-hard problem for…
Computation with the Ising model is central to future computing technologies like quantum annealing, adiabatic quantum computing, and thermodynamic classical computing. Traditionally, computed values have been equated with ground states.…
The methods which are actively used for electronic structure calculations of low-lying states of heavy- and superheavy-element compounds are briefly described. The advantages and disadvantages of calculations with the Dirac-Coulomb-Breit…
We show that a rectangular collocation method, equivalent to evaluating all matrix elements with a quadrature-like scheme and using more points than basis functions, is an effective approach for solving the electronic Schr\"odinger equation…
We describe an efficient approximation algorithm for evaluating the ground-state energy of the classical Ising Hamiltonian with linear terms on an arbitrary planar graph. The running time of the algorithm grows linearly with the number of…
We compare convergence of isogeometric analysis (IGA), a spline modification of finite element method (FEM), with FEM in the context of our real space code for ab-initio electronic structure calculations of non-periodic systems. The…
An approximate relativistic two-component Hamiltonian for use in molecular electronic structure calculations is derived in the form of a sum of fixed atom-centered kinetic and spin-orbit operators added to the non-relativistic Hamiltonian.…
Recent years have shown steady progress in research towards molecular electronics [1,2], where molecules have been investigated as switches [3-5], diodes [6], and electronic mixers [7]. In much of the previous work a Scanning Tunnelling…
Determining properties of ground states of spin Hamiltonians remains a topic of central relevance connecting disciplines of mathematical, theoretical and applied physics. In the last few decades, ground state properties of physical systems…
Quantum and classical physics can be used for mathematical computations that are hard to tackle by conventional electronics. Very recently, optical Ising machines have been demonstrated for computing the minima of spin Hamiltonians, paving…
Physics-inspired molecular representations are the cornerstone of similarity-based learning applied to solve chemical problems. Despite their conceptual and mathematical diversity, this class of descriptors shares a common underlying…
The fundamental problem faced in quantum chemistry is the calculation of molecular properties, which are of practical importance in fields ranging from materials science to biochemistry. Within chemical precision, the total energy of a…
Recent conjectures on the complexity of black holes suggest that their evolution manifests in the structural properties of Einstein-Rosen bridges, like the length and volume. The complexity of black holes relates to the computational…
Quantum annealing aims at solving optimization problems efficiently by preparing the ground state of an Ising spin-Hamiltonian quantum mechanically. A prerequisite of building a quantum annealer is the implementation of programmable…
Multi-configurational electronic structure theory delivers the most versatile approximations to many-electron wavefunctions, flexible enough to deal with all sorts of transformations, ranging from electronic excitations, to open-shell…
We have provided a concise introduction to the Ising model as one of the most important models in statistical mechanics and in studying the phenomenon of phase transition. The required theoretical background and derivation of the…
Quantum computers have the potential for an exponential speedup of classical molecular computations. However, existing algorithms have limitations; quantum phase estimation (QPE) algorithms are intractable on current hardware while…
Quantum computers have the potential to advance material design and drug discovery by performing costly electronic structure calculations. A critical aspect of this application requires optimizing the limited resources of the quantum…
The reduced-density-matrix method is an promising candidate for the next generation electronic structure calculation method; it is equivalent to solve the Schr\"odinger equation for the ground state. The number of variables is the same as a…
The past decade has seen the emergence of Ising machines targeting hard combinatorial optimization problems by minimizing the Ising Hamiltonian with spins represented by continuous dynamical variables. However, capabilities of these…