Related papers: Eigenvector Continuation and Projection-Based Emul…
Eigenvector continuation is a computational method that finds the extremal eigenvalues and eigenvectors of a Hamiltonian matrix with one or more control parameters. It does this by projection onto a subspace of eigenvectors corresponding to…
A common challenge faced in quantum physics is finding the extremal eigenvalues and eigenvectors of a Hamiltonian matrix in a vector space so large that linear algebra operations on general vectors are not possible. There are numerous…
We develop an extension of eigenvector continuation (EC) that makes it possible to extrapolate simulations of quantum systems in finite periodic boxes across large ranges of box sizes. The formal justification for this approach, which we…
A typical task for classical and quantum computing in chemistry is finding a potential energy surface (PES) along a reaction coordinate, which involves solving the quantum chemistry problem for many points along the reaction path.…
Emulators that can bypass computationally expensive scientific calculations with high accuracy and speed can enable new studies of fundamental science as well as more potential applications. In this work we discuss solving a system of…
The study of open quantum systems (OQSs), i.e., systems interacting with an environment, impacts our understanding of exotic nuclei in low-energy nuclear physics, hadrons, cold-atom systems, or even noisy intermediate-scale quantum…
Quantum subspace diagonalization (QSD) methods are quantum-classical hybrid methods, commonly used to find ground and excited state energies by projecting the Hamiltonian to a smaller subspace. In applying these, the choice of subspace…
In this article, we study eigenvalue problems associated to self-adjoint operators and their approximation obtained by subspace projection, as used in the reduced basis method for instance. We provide error bounds between the exact…
Shell-model calculations play a key role in elucidating various properties of nuclei. In general, those studies require a huge number of calculations to be repeated for parameter calibration and quantifying uncertainties. To reduce the…
We present a new numerical technique to solve large-scale eigenvalue problems. It is based on the projection technique, used in strongly correlated quantum many-body systems, where first an effective approximate model of smaller complexity…
Subspace methods are powerful, noise-resilient methods that can effectively prepare ground states on quantum computers. The challenge is to get a subspace with a small condition number that spans the states of interest using minimal quantum…
We present the reduced basis method as a tool for developing emulators for equations with tunable parameters within the context of the nuclear many-body problem. The method uses a basis expansion informed by a set of solutions for a few…
The development of emulators for the evaluation of many-body observables has gained increasing attention over the last years. In particular the framework of eigenvector continuation (EC) has been identified as a powerful tool when the…
The method of computing eigenvectors from eigenvalues of submatrices can be shown as equivalent to a method of computing the constraint which achieves specified stationary values of a quadratic optimization. Similarly, we show computation…
Quantum many-body theory has witnessed tremendous progress in various fields, ranging from atomic and solid-state physics to quantum chemistry and nuclear structure. Due to the inherent computational burden linked to the ab initio treatment…
Recently, a new eigenvalue problem, called the transmission eigenvalue problem, has attracted many researchers. The problem arose in inverse scattering theory for inhomogeneous media and has important applications in a variety of inverse…
Eigensolvers involving complex moments can determine all the eigenvalues in a given region in the complex plane and the corresponding eigenvectors of a regular linear matrix pencil. The complex moment acts as a filter for extracting…
The problem of construction of projection operators on eigen-subspaces of symmetry operators is considered. This problem arises in many approximate methods for solving time-independent and time-dependent quantum problems, and its solution…
We develop a class of emulators for solving quantum three-body scattering problems. They are based on combining the variational method for scattering observables and the recently proposed eigenvector continuation concept. The emulators are…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…