Related papers: Automatic differentiation of dominant eigensolver …
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
We show that the quantization of a simple damped system leads to a self-adjoint Hamiltonian with a family of complex generalized eigenvalues. It turns out that they correspond to the poles of energy eigenvectors when continued to the…
The growing size of modern data sets brings many challenges to the existing statistical estimation approaches, which calls for new distributed methodologies. This paper studies distributed estimation for a fundamental statistical machine…
Quantum annealing is a novel type of analog computation that aims to use quantum mechanical fluctuations to search for optimal solutions of Ising problems. Quantum annealing in the transverse field Ising model, implemented on D-Wave…
In the present study, we demonstrate how to perform, using quantum annealing, the singular value decomposition and the principal component analysis. Quantum annealing gives a way to find a ground state of a system, while the singular value…
Automatic differentiation (AD) is conventionally understood as a family of distinct algorithms, rooted in two "modes" -- forward and reverse -- which are typically presented (and implemented) separately. Can there be only one? Following up…
When the eigenvalues of the coefficient matrix for a linear scalar ordinary differential equation are of large magnitude, its solutions exhibit complicated behaviour, such as high-frequency oscillations, rapid growth or rapid decay. The…
Demonstrating the ability of existing quantum platforms to perform certain computational tasks intractable to classical computers represents a cornerstone in quantum computing. Despite the growing number of such proposed "quantum supreme"…
Quantum algorithms exploiting real-time evolution under a target Hamiltonian have demonstrated remarkable efficiency in extracting key spectral information. However, the broader potential of these methods, particularly beyond ground state…
Such problems as computation of spectra of spin chains and vibrational spectra of molecules can be written as high-dimensional eigenvalue problems, i.e., when the eigenvector can be naturally represented as a multidimensional tensor. Tensor…
We aim at computing the derivative of the solution to a parametric optimization problem with respect to the involved parameters. For a class broader than that of strongly convex functions, this can be achieved by automatic differentiation…
We propose a distinct approach to solving linear and nonlinear differential equations (DEs) on quantum computers by encoding the problem into ground states of effective Hamiltonian operators. Our algorithm relies on constructing such…
We introduce a variational quantum computing approach for quantum state reconstruction within a discretized logical framework, using experimental measurement data as input. By mapping the reconstruction cost function onto an Ising model,…
In many dynamical probes of a quantum system, quite often multiple eigenmodes are excited. Therefore, the experimental data can be quite messy due to the mixing of different modes, as well as the background noise, despite that each mode…
This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…
We propose a divide-and-conquer method for the quantum-classical hybrid algorithm to solve larger problems with small-scale quantum computers. Specifically, we concatenate a variational quantum eigensolver (VQE) with a reduction in the…
Quantum algorithms for both differential equation solving and for machine learning potentially offer an exponential speedup over all known classical algorithms. However, there also exist obstacles to obtaining this potential speedup in…
In this paper we develop and analyse domain decomposition methods for linear systems of equations arising from conforming finite element discretisations of positive Maxwell-type equations. Convergence of domain decomposition methods rely…
Principal component analysis is a multivariate statistical method frequently used in science and engineering to reduce the dimension of a problem or extract the most significant features from a dataset. In this paper, using a similar notion…
Efficient quantum circuit optimization schemes are central to quantum simulation of strongly interacting quantum many body systems. Here, we present an optimization algorithm which combines machine learning techniques and tensor network…