Related papers: Molecular Properties from Quantum Krylov Subspace …
Quantum-chemical simulations are essential for predicting energies of chemical reactions. Accurately solving the many-body Schr\"odinger equation for reagent and product states of most relevant chemical process is, however, unfeasible.…
Quantum annealing is a heuristic optimization algorithm that exploits quantum evolution to approximately find lowest energy states. Quantum annealers have scaled up in recent years to tackle increasingly larger and more highly connected…
We introduce a multireference selected quantum Krylov (MRSQK) algorithm suitable for quantum simulation of many-body problems. MRSQK is a low-cost alternative to the quantum phase estimation algorithm that generates a target state as a…
Computing ground-state properties of molecules is a promising application for quantum computers operating in concert with classical high-performance computing resources. Quantum embedding methods are a family of algorithms particularly…
Thanks to its great potential in reducing both computational cost and memory requirements, combining sketching and Krylov subspace techniques has attracted a lot of attention in the recent literature on projection methods for linear…
Bivariate matrix functions provide a unified framework for various tasks in numerical linear algebra, including the solution of linear matrix equations and the application of the Fr\'echet derivative. In this work, we propose a novel…
Based on recently introduced efficient quantum state tomography schemes, we propose a scalable method for the tomography of unitary processes and the reconstruction of one-dimensional local Hamiltonians. As opposed to the exponential…
We report quantum chemistry calculations performed on superconducting quantum processors for a molecule exhibiting the half-M\"obius electronic topology originally introduced by Ron\v{c}evi\'c et al. Using SqDRIFT, a randomized sample-based…
We consider the discretization and subsequent model reduction of a system of partial differential-algebraic equations describing the propagation of pressure waves in a pipeline network. Important properties like conservation of mass,…
Randomized Krylov subspace methods that employ the sketch-and-solve paradigm to substantially reduce orthogonalization cost have recently shown great promise in speeding up computations for many core linear algebra tasks (e.g., solving…
In the distributed nucleus approximation we represent the singular nucleus as smeared over a smallportion of a Cartesian grid. Delocalizing the nucleus allows us to solve the Poisson equation for theoverall electrostatic potential using a…
Quantifying complexity in quantum systems has witnessed a surge of interest in recent years, with Krylov-based measures such as Krylov complexity ($C_K$) and Spread complexity ($C_S$) gaining prominence. In this study, we investigate their…
We propose a new numerical method to solve linear ordinary differential equations of the type $\frac{\partial u}{\partial t}(t,\varepsilon) = A(\varepsilon) \, u(t,\varepsilon)$, where $A:\mathbb{C}\rightarrow\mathbb{C}^{n\times n}$ is a…
For linear inverse problems with a large number of unknown parameters, uncertainty quantification remains a challenging task. In this work, we use Krylov subspace methods to approximate the posterior covariance matrix and describe efficient…
The control and manipulation of quantum-entangled non-local states is a crucial step for the development of quantum information processing. A promising route to achieve such states on a wide scale is to couple solid-state quantum emitters…
Motivated by recent quantum gas microscope experiments for fermions in optical lattices, we present proof of principle calculations showing that it is possible to obtain the complete information about the quantum state on a small subsystem…
Low-rank Krylov methods are one of the few options available in the literature to address the numerical solution of large-scale general linear matrix equations. These routines amount to well-known Krylov schemes that have been equipped with…
Randomized sketching is currently introduced into every area of numerical linear algebra. In Krylov subspace methods, it allows runtime savings at the cost of small accuracy reductions. This work offers a different view on sketching in…
The partial scaling transform of the density matrix for multiqubit states is introduced to detect entanglement of quantum states. The transform contains partial transposition as a special case. The scaling transform corresponds to partial…
Studies of entanglement in many-particle systems suggest that most quantum critical ground states have infinitely more entanglement than non-critical states. Standard algorithms for one-dimensional many-particle systems construct model…