Related papers: Automatic grid construction for few-body quantum m…
Quantum theory has been remarkably successful in providing an understanding of physical systems at foundational scales. Solving the Schr\"odinger equation provides full knowledge of all dynamical quantities of the physical system. However…
Random many-body states are both a useful tool to model certain physical systems and an important asset for quantum computation. Realising them, however, generally requires an exponential (in system size) amount of resources. Recent…
Two non-equidistant grid implementations of infinite range exterior complex scaling are introduced that allow for perfect absorption in the time dependent Schr\"odinger equation. Finite element discrete variables grid discretizations…
Many problems in computational science and engineering involve partial differential equations and thus require the numerical solution of large, sparse (non)linear systems of equations. Multigrid is known to be one of the most efficient…
Building on recent results for adiabatic gauge potentials, we propose a variational approach for computing the generator of Schrieffer-Wolff transformations. These transformations consist of block diagonalizing a Hamiltonian through a…
In the field of complex networks and graph theory, new results are typically tested on graphs generated by a variety of algorithms such as the Erd\H{o}s-R\'{e}nyi model or the Barab\'{a}si-Albert model. Unfortunately, most graph generating…
A multigrid method is proposed for solving nonlinear eigenvalue problems by the finite element method. With this new scheme, solving nonlinear eigenvalue problem is decomposed to a series of solutions of linear boundary value problems on…
We consider the two-body problem in a periodic potential, and study the bound-state dispersion of a spin-$\uparrow$ fermion that is interacting with a spin-$\downarrow$ fermion through a short-range attractive interaction. Based on a…
The energy-based stochastic extension of the Schrodinger equation is a rather special nonlinear stochastic differential equation on Hilbert space, involving a single free parameter, that has been shown to be very useful for modelling the…
We introduce a geometric multigrid method for solving linear systems arising from variational problems on surfaces in geometry processing, Gravo MG. Our scheme uses point clouds as a reduced representation of the levels of the multigrid…
Many-body quantum-mechanical scattering problem is solved asymptotically when the size of the scatterers (inhomogeneities) tends to zero and their number tends to infinity. A method is given for calculation of the number of small…
Optimal implementation of quantum gates is crucial for designing a quantum computer. We consider the matrix representation of an arbitrary multiqubit gate. By ordering the basis vectors using the Gray code, we construct the quantum circuit…
Visually sorted grid layouts provide an efficient method for organizing high-dimensional vectors in two-dimensional space by aligning spatial proximity with similarity relationships. This approach facilitates the effective sorting of…
Full information about a many-body quantum system is usually out-of-reach due to the exponential growth -- with the size of the system -- of the number of parameters needed to encode its state. Nonetheless, in order to understand the…
The Gridding algorithm has shown great utility for reconstructing images from non-uniformly spaced samples in the Fourier domain in several imaging modalities. Due to the non-uniform spacing, some correction for the variable density of the…
Due to the presence of strong correlations, theoretical or experimental investigations of quantum many-body systems belong to the most challenging tasks in modern physics. Stimulated by tensor networks, we propose a scheme of constructing…
Topological quantum computing is an alternative framework for avoiding the quantum decoherence problem in quantum computation. The problem of executing a gate in this framework can be posed as the problem of braiding quasiparticles. Because…
We construct quantum circuits for solving one-dimensional Schr\"odinger equations. Simulations of three typical examples, i.e., harmonic oscillator, square-well and Coulomb potential, show that reasonable results can be obtained with eight…
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum…
Introducing low-energy effective Hamiltonians is usual to grasp most correlations in quantum many-body problems. For instance, such effective Hamiltonians can be treated at the mean-field level to reproduce some physical properties of…