Related papers: Krylov Subspace Method for Molecular Dynamics Simu…
Within the realm of early fault-tolerant quantum computing (EFTQC), quantum Krylov subspace diagonalization (QKSD) has emerged as a promising quantum algorithm for the approximate Hamiltonian diagonalization via projection onto the quantum…
Numerical simulations based on electronic structure calculations are finding ever growing applications in many areas of physics. A major limiting factor is however the cubic scaling of the algorithms used. Building on previous work [F. R.…
We propose an algorithm to obtain Green's functions as a continued fraction on quantum computers, which is based on the construction of the Krylov basis using variational quantum algorithms, and included in a Lanczos iterative scheme. This…
A linear scale method for calculating electronic properties of large and complex systems is introduced within a local density approximation. The method is based on the Chebyshev polynomial expansion and the time-dependent method, which is…
Excited state properties play a pivotal role in various chemical and physical phenomena, such as charge separation and light emission. However, the primary focus of most existing quantum algorithms has been the ground state, as seen in…
In this work, we present a method for simulating the large-scale deformation and crumpling of thin, elastoplastic sheets. Motivated by the physical behavior of thin sheets during crumpling, two different formulations of the governing…
One of the goals in the development of large scale electronic structure methods is to perform calculations explicitly for a localised region of a system, while still taking into account the rest of the system outside of this region. An…
We propose a time-exact Krylov-subspace-based method for solving linear ODE (ordinary differential equation) systems of the form $y'=-Ay + g(t)$, where $y(t)$ is the unknown function. The method consists of two stages. The first stage is an…
A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398,…
We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows…
We demonstrate the power of a first principle-based and practicable method that allows for the perturbative computation of reduced density matrix elements of an open quantum system without making use of any master equations. The approach is…
We present a general framework for reconstructing effective Hamiltonians from known gravitational energy density profiles in curved spacetime. Starting from local thermal equilibrium and Liouville dynamics, we establish an inverse procedure…
We present an approach to the calculation of arbitrary spectral, thermal and excited state properties within the full configuration interaction quantum Monte Carlo framework. This is achieved via an unbiased projection of the Hamiltonian…
For many applications involving a sequence of linear systems with slowly changing system matrices, subspace recycling, which exploits relationships among systems and reuses search space information, can achieve huge gains in iterations…
We apply the recently proposed Sample-based Krylov Quantum Diagonalization (SKQD) method to lattice gauge theories, using the Schwinger model with a $\theta$-term as a benchmark. SKQD approximates the ground state of a Hamiltonian,…
Computing the Casimir force and energy between objects is a classical problem of quantum theory going back to the 1940s. Several different approaches have been developed in the literature often based on different physical principles. Most…
Key properties of physical systems can be described by the eigenvalues of matrices that represent the system. Computational algorithms that determine the eigenvalues of these matrices exist, but they generally suffer from a loss of…
An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems. Arguing that any efficient (possibly quantum)…
An exponential interaction is constructed so that one-dimensional atoms and chains of atoms mimic the general behavior of their three-dimensional counterparts. Relative to the more commonly used soft-Coulomb interaction, the exponential…
We investigate the parameter dynamics of eigenvalues of Hamiltonians ('level dynamics') defined on symmetric spaces relevant for condensed matter and particle physics. In particular we: 1) identify appropriate reduced manifold on which the…