Related papers: Eigenvector continuation with subspace learning
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…
In modeling quantum systems or wave phenomena, one is often interested in identifying eigenstates that approximately carry a specified property; scattering states approximately align with incoming and outgoing traveling waves, for instance,…
Traditional computational methods for studying quantum many-body systems are "forward methods," which take quantum models, i.e., Hamiltonians, as input and produce ground states as output. However, such forward methods often limit one's…
Solving for the lowest energy eigenstate of the many-body Schrodinger equation is a cornerstone problem that hinders understanding of a variety of quantum phenomena. The difficulty arises from the exponential nature of the Hilbert space…
Higher-order gravity models have been recently the subject of much attention in the context of cosmic acceleration. These models are derived by adding various curvature invariants to the Einstein-Hilbert action. Several studies showed that…
In order to guarantee the downloading quality requirements of users and improve the stability of data transmission in a BitTorrent-like peer-to-peer file sharing system, this article deals with eigenproblems of addition-min algebras. First,…
Many fields of science and engineering require finding eigenvalues and eigenvectors of large matrices. The solutions can represent oscillatory modes of a bridge, a violin, the disposition of electrons around an atom or molecule, the…
We study the problem of learning the parameters for the Hamiltonian of a quantum many-body system, given limited access to the system. In this work, we build upon recent approaches to Hamiltonian learning via derivative estimation. We…
We introduce an estimation method of covariance matrices in a high-dimensional setting, i.e., when the dimension of the matrix, , is larger than the sample size . Specifically, we propose an orthogonally equivariant estimator. The…
Estimating the eigenvalues of a unitary transformation U by standard phase estimation requires the implementation of controlled-U-gates which are not available if U is only given as a black box. We show that a simple trick allows to measure…
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…
An efficient algorithm for computing eigenvectors of a matrix of integers by exact computation is proposed. The components of calculated eigenvectors are expressed as polynomials in the eigenvalue to which the eigenvector is associated, as…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
Finding a good approximation of the top eigenvector of a given $d\times d$ matrix $A$ is a basic and important computational problem, with many applications. We give two different quantum algorithms that, given query access to the entries…
We describe a midi-superspace quantization scheme for generic single horizon black holes in which only the spatial diffeomorphisms are fixed. The remaining Hamiltonian constraint yields an infinite set of decoupled eigenvalue equations: one…
The Fermi-Hubbard model is a plausible target to be solved by a quantum computer using the variational quantum eigensolver algorithm. However, problem sizes beyond the reach of classical exact diagonalisation are also beyond the reach of…
In this work, we present a quantum neighborhood preserving embedding and a quantum local discriminant embedding for dimensionality reduction and classification. We demonstrate that these two algorithms have an exponential speedup over their…
Characterizing quantum many-body systems is a fundamental problem across physics, chemistry, and materials science. While significant progress has been made, many existing Hamiltonian learning protocols demand digital quantum control over…
Reconstructing a system Hamiltonian through measurements on its eigenstates is an important inverse problem in quantum physics. Recently, it was shown that generic many-body local Hamiltonians can be recovered by local measurements without…
We propose an efficient algorithm for computing a common eigenvector of a finite set of square matrices. As an immediate consequence we obtain an algorithm for determining whether the matrices admit a simultaneous triangulation, and, if so,…