24 papers · ranked by Valyu relevance
Ville J. Härkönen, Ivan Gonoskov
A new procedure to diagonalize quadratic Hamiltonians is introduced. We show that one can find a unitary transformation such that the transformed quadratic Hamiltonian is diagonal but still written in terms of the original position and momentum observables. We give a general method to diagonalize an arbitrary quadratic…
Eric Hermes, Khachik Sargsyan, Habib Najm, Judit Zádor
We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, e.g. through the…
Daniel Miller, Laurin E. Fischer, Kyano Levi, Eric J. Kuehnke + 4 more
A central building block of many quantum algorithms is the diagonalization of Pauli operators. Although it is always possible to construct a quantum circuit that simultaneously diagonalizes a given set of commuting Pauli operators, only resource-efficient circuits can be executed reliably on near-term quantum…
Haoze He, Daniel Kressner
We present and analyze a simple numerical method that diagonalizes a complex normal matrix A by diagonalizing the Hermitian matrix obtained from a random linear combination of the Hermitian and skew-Hermitian parts of A.
Manish Kumar
We present two new quantum algorithms for reaction-diffusion equations that employ the truncated Chebyshev polynomial approximation. This method is employed to numerically solve the ordinary differential equation emerging from the linearization of the associated nonlinear differential equation. In the first algorithm…
A. Mandilara
Jacobi diagonalization is a long-established numerical algorithm for the spectral decomposition of Hermitian and, more generally, normal matrices. In this work, we develop a qudit-native quantum realization of the Jacobi diagonalization algorithm for unknown unitary operators. The proposed framework avoids explicit…
Authors not listed
Molecular polaritons are hybrid states formed by the quantum mechanical interaction between light and matter. Recent experiments have shown the ability to drastically modify chemical reactions in both the ground and excited states through the hybridization of the electronic and photonic degrees of freedom. Ab initio…
Erna Begovic, Ana Perkovic
Convergence of this method was studied in [14, 9, 13, 4]. For different pivot strategies, it was shown that the iterations (1.1) converge in the sense that the sequence (B(k) , k ≥ 0) converges to a diagonal matrix, while (A(k) , k ≥ 0) converges to a normal matrix Λ. If all the eigenvalues of A have different real…
Authors not listed
One of the main applications for which quantum computers are hoped to find utility is in simulating ground state energies and other observables of molecular chemical systems. The recently proposed sample-based diagonalization method is a readily implementable method for this task on current-day hardware using short…
Robert A. Baston, Yuji Nakatsukasa
We study the problem of estimating the diagonal of an implicitly given matrix A. For such a matrix we have access to an oracle that allows us to evaluate the matrix vector product Av. For random variable v drawn from an appropriate distribution, this may be used to return an estimate of the diagonal of the matrix A.…
Marine De Clerck, Oleg Evnin
Gérard and Grellier proposed, under the name of the cubic Szegő equation, a remarkable classical field theory on a circle with a quartic Hamiltonian. The Lax integrability structure that emerges from their definition is so constraining that it allows for writing down an explicit general solution for prescribed initial…
Benjamin Lieser, Georgy Belousov, Johannes Söding
Background Most popular tools for reconstructing phylogenetic trees from multiple sequence alignments use a model of molecular evolution in which a single substitution matrix or a small set of fixed matrices are shared between all columns. Models with column-specific rate matrices can in principle be fit by automatic…
Zongyuan Han, Wenhao Li, Shengxin Zhu
In this paper, we investigate diagonal estimation for large or implicit matrices, aiming to develop a novel and efficient stochastic algorithm that incorporates adaptive parameter selection. We explore the influence of different eigenvalue distributions on diagonal estimation and analyze the necessity of introducing…
AMIRHOSSEIN NAZERIAN, KSHITIJ BHATTA, FRANCESCO SORRENTINO
In this paper, we consider optimal control problems (OCPs) applied to large-scale linear dynamical systems with a large number of states and inputs. We attempt to reduce such problems into a set of independent OCPs of lower dimensions. Our decomposition is ‘exact’ in the sense that it preserves all the information…
Davoud Mirzaei
These lecture notes focus on some numerical linear algebra algorithms in scientific computing. We assume that students are familiar with elementary linear algebra concepts such as vector spaces, systems of equations, matrices, norms, eigenvalues, and eigenvectors. In the numerical part, we do not pursue Gaussian…
Serena Castellotti, Elvio Blini, Maria Del Viva, Qasim Zaidi
Artists and photographers use diagonals to convey dynamism, tension and instability in naturalistic and abstract images. However, the oblique effect in visual perception refers to a reduced sensitivity to oblique compared to cardinal (vertical/horizontal) orientations, linked to anisotropy in the distribution of…
Abd‐Krim Seghouane, Yousef Saad
Given a set of p symmetric (real) matrices, the Orthogonal Joint Diagonalization (OJD) problem consists of finding an orthonormal basis in which the representation of each of these p matrices is as close as possible to a diagonal matrix. We argue that when the matrices are of large dimension, then the natural…
Authors not listed
We present a comprehensive theoretical analysis of quantum subspace diagonalization methods for molecular electronic structure calculations, establishing rigorous complexity bounds and convergence guarantees. Building on recent developments in adaptive quantum algorithms for chemical systems, we formulate a general…
Authors not listed
Ongoing research involving electronic spin-dependent dynamics, such as chiral- induced spin selectivity, is providing impetus to revise our understanding of nuclear en- tanglement with electronic spatial and spin degrees of freedom. In a spin-independent setting, non-adiabatic couplings are well-known mediators of…
Authors not listed
The SCF part of the HF-SCF method is responsible for finding the ground state as the global minimum of the one-determinant approximation of the electronic energy, which is a 4th order multivariable polynomial of the LCAO coefficients and Lagrange multipliers. In this work we replace this SCF part with algebraic…
Evan D. Gorman, Manuel E. Lladser
Ultrametric matrices have a rich structure that is not apparent from their definition. Notably, the subclass of strictly ultrametric matrices are covariance matrices of certain weighted rooted binary trees. In applications, these matrices can be large and dense, making them difficult to store and handle. In this…
Authors not listed
This article is the second in a two-part tutorial review on electronic spin-dependent dynamics. In Part I, we presented the fundamental theory within the adiabatic Born– Huang framework that describes the interaction between nuclear motion and the elec- tronic (spin and spatial) degrees of freedom. In particular, we…
Amir Akbari, Zachary B. Haiman, Bernhard O. Palsson
Understanding the dynamics of biological systems in evolving environments is a challenge due to their scale and complexity. Here, we present a computational framework for timescale decomposition of biochemical reaction networks to distill essential patterns from their intricate dynamics. This approach identifies…
Rafael G. Viegas, Ingrid B. S. Martins, Murilo N. Sanches, Antonio B. Oliveira + 3 more
Molecular dynamics (MD) simulations provide a powerful means to explore the dynamic behavior of biomolecular systems at the atomic level. However, analyzing the vast datasets generated by MD simulations poses significant challenges. This manuscript discusses the Energy Landscape Visualization Method (ELViM), a…