Related papers: Contour Integral-based Quantum Algorithm for Estim…
The procedure for simulating the nuclear magnetic resonance spectrum linked to the spin system of a molecule for a certain nucleus entails diagonalizing the associated Hamiltonian matrix. As the dimensions of said matrix grow exponentially…
We propose a quantum algorithm for solving the following problem: given the Hamiltonian of a physical system and one of its eigenvalues, how to obtain the corresponding eigenstate? The algorithm is based on the resonance phenomena. For a…
We study fast algorithms for computing fundamental properties of a positive semidefinite kernel matrix $K \in \mathbb{R}^{n \times n}$ corresponding to $n$ points $x_1,\ldots,x_n \in \mathbb{R}^d$. In particular, we consider estimating the…
We propose an adaptive random quantum algorithm to obtain an optimized eigensolver. Specifically, we introduce a general method to parametrize and optimize the probability density function of a random number generator, which is the core of…
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…
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…
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the dimension of the problem space grows exponentially, finding the eigenvalues of certain…
We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal,…
The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the…
This paper presents a hybrid classical-quantum program for density estimation and supervised classification. The program is implemented as a quantum circuit in a high-dimensional quantum computer simulator. We show that the proposed quantum…
Impressive progress has been made in the past decade in the study of technological applications of varied types of quantum systems. With industry giants like IBM laying down their roadmap for scalable quantum devices with more than…
Estimating the eigenstate properties of quantum systems is a long-standing, challenging problem for both classical and quantum computing. Existing universal quantum algorithms typically rely on ideal and efficient query models (e.g. time…
This chapter concerns with the recent development of a new DFT methodology for accurate, reliable prediction of many-electron systems. Background, need for such a scheme, major difficulties encountered, as well as their potential remedies…
Solving large-scale Generalized Eigenvalue Problems (GEPs) is a fundamental yet computationally prohibitive task in science and engineering. As a promising direction, contour integral (CI) methods, such as the CIRR algorithm, offer an…
The autoencoder is one of machine learning algorithms used for feature extraction by dimension reduction of input data, denoising of images, and prior learning of neural networks. At the same time, autoencoders using quantum computers are…
Quantum computers open up new avenues for modelling the physical properties of materials and molecules. Density Functional Theory (DFT) is the gold standard classical algorithm for predicting these properties, but relies on approximations…
Density matrix electronic structure theory is used in many quantum chemistry methods to "alleviate" the computational cost that arises from directly using wave functions. Although density matrix based methods are computationally more…
In this work, we propose a machine learning-based approach to address a specific aspect of the Quantum Marginal Problem: reconstructing a global density matrix compatible with a given set of quantum marginals. Our method integrates a…
Quantum Process Tomography (QPT) methods aim at identifying, i.e. estimating, a quantum process. QPT is a major quantum information processing tool, since it especially allows one to experimentally characterize the actual behavior of…
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…