# Roel Van BeeumenLawrence Berkeley National Laboratory | LBL · Computational Research Division (CRD)

Roel Van Beeumen

PhD in Engineering Science: Computer Science

## About

45

Publications

3,487

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493

Citations

Citations since 2017

Introduction

**Skills and Expertise**

Additional affiliations

June 2019 - present

September 2016 - May 2019

April 2015 - August 2016

## Publications

Publications (45)

We present an efficient and reliable algorithm for solving a class of nonlinear eigenvalue problems arising from the modeling of particle accelerator cavities. The eigenvalue nonlinearity in these problems results from the use of waveguides to couple external power sources or to allow certain excited electromagnetic modes to exit the cavity. We use...

The ab initio description of the spectral interior of the absorption spectrum poses both a theoretical and computational challenge for modern electronic structure theory. Due to the often spectrally dense character of this domain in the quantum propagator's eigenspectrum for medium-to-large sized systems, traditional approaches based on the partial...

We propose a new uniform framework of compact rational Krylov (CORK) methods for solving large-scale nonlinear eigenvalue problems $A(\lambda) x = 0$. For many years, linearizations were used for solving polynomial and rational eigenvalue problems. On the other hand, for the general nonlinear case, $A(\lambda)$ can first be approximated by a (ratio...

This paper considers interpolating matrix polynomials P(λ) in Lagrange and Hermite bases. A classical approach to investigating the polynomial eigenvalue problem P(λ) x = 0 is linearization, by which the polynomial is converted into a larger matrix pencil with the same eigenvalues. Since the
current linearizations of degree n Lagrange polynomials c...

This paper proposes a new rational Krylov method for solving the nonlinear eigenvalue problem: A(λ)x = 0. The method approximates A(λ) by Hermite interpolation where the degree of the interpolating polynomial and the interpolation points are not fixed in advance. It uses a companion-type reformulation to obtain a linear generalized eigenvalue probl...

Recently we developed a local and constructive algorithm based on Lie algebraic methods for compressing Trotterized evolution under Hamiltonians that can be mapped to free fermions. The compression algorithm yields a circuit which scales linearly in the number of qubits, is fixed depth for for arbitrarily long evolution times and is applicable to t...

We introduce qclab++, a light-weight, fully-templated C++ package for GPU-accelerated quantum circuit simulations. The code offers a high degree of portability as it has no external dependencies and the GPU kernels are generated through OpenMP offloading. qclab++ is designed for performance and numerical stability through highly optimized gate simu...

Compact quantum data representations are essential to the emerging field of quantum algorithms for data analysis. We introduce two new data encoding schemes, QCrank and QBArt, which have a high degree of quantum parallelism through uniformly controlled rotation gates. QCrank encodes a sequence of real-valued data as rotations of the data qubits, al...

The physics of dirty bosons highlights the intriguing interplay of disorder and interactions in quantum systems, playing a central role in describing, for instance, ultracold gases in a random potential, doped quantum magnets, and amorphous superconductors. Here, we demonstrate how quantum computers can be used to elucidate the physics of dirty bos...

We introduce a novel and uniform framework for quantum pixel representations that overarches many of the most popular representations proposed in the recent literature, such as (I)FRQI, (I)NEQR, MCRQI, and (I)NCQI. The proposed QPIXL framework results in more efficient circuit implementations and significantly reduces the gate complexity for all co...

Block-encodings of matrices have become an essential element of quantum algorithms derived from the quantum singular value transformation. This includes a variety of algorithms ranging from the quantum linear systems problem to quantum walk, Hamiltonian simulation, and quantum machine learning. Many of these algorithms achieve optimal complexity in...

We propose several techniques to enhance the parallel scalability of a matrix-free eigensolver designed for studying many-body localization (MBL) of quantum spin chain models with nearest-neighbor interactions and on-site disorder. This type of problem is computationally challenging because the dimension of the associated Hamiltonian matrix grows e...

Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encoding and quantum eigenvalue / singular value transformations. Block encoding embeds a properly scaled matrix of interest $A$ in a larger unitary transformation $U$ that can be decomposed...

Unitary evolution under a time-dependent Hamiltonian is a key component of simulation on quantum hardware. Synthesizing the corresponding quantum circuit is typically done by breaking the evolution into small time steps, also known as Trotterization, which leads to circuits the depth of which scales with the number of steps. When the circuit elemen...

Dynamic simulation of materials is a promising application for near-term quantum computers. Current algorithms for Hamiltonian simulation, however, produce circuits that grow in depth with increasing simulation time, limiting feasible simulations to short-time dynamics. Here, we present a method for generating circuits that are constant in depth wi...

We introduce a novel and uniform framework for quantum pixel representations that overarches many of the most popular representations proposed in the recent literature, such as (I)FRQI, (I)NEQR, MCRQI, and (I)NCQI. The proposed QPIXL framework results in more efficient circuit implementations and significantly reduces the gate complexity for all co...

Quantum computing is a promising technology that harnesses the peculiarities of quantum mechanics to deliver computational speedups for some problems that are intractable to solve on a classical computer. Current generation noisy intermediate-scale quantum (NISQ) computers are severely limited in terms of chip size and error rates. Shallow quantum...

Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. Synthesizing the corresponding quantum circuit is typically done by breaking the evolution into small time steps, also known as Trotterization, which leads to circuits whose depth scales with the number of steps. When the circuit elements are...

Dynamic simulation of materials is a promising application for noisy intermediate-scale quantum (NISQ) computers. The difficulty in carrying out such simulations is that a quantum circuit must be executed for each time-step, and in general, these circuits grow in size with the number of time-steps simulated. NISQ computers can only produce high-fid...

We propose a flexible power method for computing the leftmost, i.e., algebraically smallest, eigenvalue of an infinite dimensional tensor eigenvalue problem, $H x = \lambda x$, where the infinite dimensional symmetric matrix $H$ exhibits a translational invariant structure. We assume the smallest eigenvalue of $H$ is simple and apply a power iterat...

In [Van Beeumen, et. al, HPC Asia 2020, https://www.doi.org/10.1145/3368474.3368497] a scalable and matrix-free eigensolver was proposed for studying the many-body localization (MBL) transition of two-level quantum spin chain models with nearest-neighbor $XX+YY$ interactions plus $Z$ terms. This type of problem is computationally challenging becaus...

One of the challenges in quantum computing is the synthesis of unitary operators into quantum circuits with polylogarithmic gate complexity. Exact synthesis of generic unitaries requires an exponential number of gates in general. We propose a novel approximate quantum circuit synthesis technique by relaxing the unitary constraints and interchanging...

We present a greedy algorithm for computing selected eigenpairs of a large sparse matrix H that can exploit localization features of the eigenvector. When the eigenvector to be computed is localized, meaning only a small number of its components have large magnitudes, the proposed algorithm identifies the location of these components in a greedy ma...

The fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a particular matrix decomposition of the discrete Fourier transform (DFT) matrix. In this paper, we show that the...

Simulating chemical systems on quantum computers has been limited to a few electrons in a minimal basis. We demonstrate experimentally that the virtual quantum subspace expansion (Takeshita, T.; Phys. Rev. X 2020, 10, 011004, 10.1103/PhysRevX.10.011004) can achieve full basis accuracy for hydrogen and lithium dimers, comparable to simulations requi...

One of the challenges in quantum computing is the synthesis of unitary operators into quantum circuits with polylogarithmic gate complexity. Exact synthesis of generic unitaries requires an exponential number of gates in general. We propose a novel approximate quantum circuit synthesis technique by relaxing the unitary constraints and interchanging...

The fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a particular matrix decomposition of the discrete Fourier transform (DFT) matrix. In this paper, we show that the...

Several novel methods for performing calculations relevant to quantum chemistry on quantum computers have been proposed but not yet explored experimentally. Virtual quantum subspace expansion [T. Takeshita et al., Phys. Rev. X 10, 011004 (2020)] is one such algorithm developed for modeling complex molecules using their full orbital space and withou...

We present a scalable and matrix-free eigensolver for studying two-level quantum spin chain models with nearest-neighbor XX +YY interactions plus Z terms. In particular, we focus on the Heisenberg interaction plus random on-site fields, a model that is commonly used to study the many-body localization (MBL) transition. This type of problem is compu...

We present a greedy algorithm for computing selected eigenpairs of a large sparse matrix $H$ that can exploit localization features of the eigenvector. When the eigenvector to be computed is localized, meaning only a small number of its components have large magnitudes, the proposed algorithm identifies the location of these components in a greedy...

The Green’s function coupled cluster (GFCC) method, originally proposed in the early 1990s, is a powerful many-body tool for computing and analyzing the electronic structure of molecular and periodic systems, especially when electrons of the system are strongly correlated. However, in order for the GFCC to become a method that may be routinely used...

The Green's function coupled cluster (GFCC) method is a powerful many-body tool for computing the electronic structure of molecular and periodic systems, especially when electrons of the system are strongly correlated. However, for the GFCC to be routinely used in the electronic structure calculations, robust numerical techniques and approximations...

The modal characteristics of structures are usually computed disregarding any interaction with the soil. This paper presents a finite element-perfectly matched layers model to compute the modal characteristics of 2D and 3D coupled soil-structure systems while taking fully into account dynamic soil-structure interaction. The methodology can facilita...

Modal analysis of structures is usually performed based on finite element models where the structures are considered undamped and fixed at their base, disregarding any interaction with the soil. In some cases though, these modeling assumptions may lead to erroneous estimates. This paper presents a finite element-perfectly matched layers model which...

We present an algorithm to compute the pseudospectral abscissa for a nonlinear eigenvalue problem. The algorithm relies on global under-estimator and over-estimator functions for the eigenvalue and singular value functions involved. These global models follow from eigenvalue perturbation theory. The algorithm has three particular features. First, i...

We consider the nonlinear eigenvalue problem M(λ)x = 0, where M(λ) is a large parameter-dependent matrix. In several applications, M(λ) has a structure where the higher-order terms of its Taylor expansion have a particular low-rank structure. We propose a new Arnoldi-based algorithm that can exploit this structure. More precisely, the proposed algo...

A new rational Krylov method for the efficient solution of nonlinear eigenvalue problems, $A(backslash lambda)x = 0$, is proposed. This iterative method, called fully rational Krylov method for nonlinear eigenvalue problems (abbreviated as NLEIGS), is based on linear rational interpolation and generalizes the Newton rational Krylov method proposed...

We present a nonlinear eigenvalue solver enabling the calculation of bound solutions of the Schrödinger equation in a system with contacts. We discuss how the imposition of contacts leads to a nonlinear eigenvalue problem and discuss the numerics for a one- and two-dimensional potential. We reformulate the problem so that the eigenvalue problem can...

A continuous dynamical system is stable if all eigenvalues lie strictly in the left half of the complex plane. However, this is not a robust measure because stability is no longer guaranteed when the system parameters are slightly perturbed. Therefore, the pseudospectrum of a matrix and its pseudospectral abscissa are studied. Mostly, one is often...

Finite element models for structures and vibrations often lead to second order dynamical systems with large sparse matrices. For large‐scale finite element models, the computation of the frequency response function and the structural response to dynamic loads may present a considerable computational cost. Padé via Krylov methods are widely used and...

Balanced truncation is a widely used and appreciated projection‐based model reduction technique for linear systems. This technique has the following two important properties: approximations by balanced truncation preserve the stability and the
H
∞
‐norm (the maximum of the frequency response) of the error system is bounded above by twice the su...