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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Resource-Efficient Chemistry on Quantum Computers with the Variational Quantum Eigensolver and The Double Unitary Coupled-Cluster approach

Applications of quantum simulation algorithms to obtain electronic energies of molecules on noisy intermediate-scale quantum (NISQ) devices require careful consideration of resources describing the complex electron correlation effects. In modeling second-quantized problems, the biggest challenge confronted is that the number of qubits scales linearly with the size of molecular basis. This poses a significant limitation on the size of the basis sets and the number of correlated electrons included in quantum simulations of chemical processes. To address this issue and to enable more realistic simulations on NISQ computers, we employ the double unitary coupled-cluster (DUCC) method to effectively downfold correlation effects into the reduced-size orbital space, commonly referred to as the active space. Using downfolding techniques, we demonstrate that properly constructed effective Hamiltonians can capture the effect of the whole orbital space in small-size active spaces. Combining the downfolding pre-processing technique with the Variational Quantum Eigensolver, we solve for the ground-state energy of H2 and Li2 in the cc-pVTZ basis using the DUCC-reduced active spaces. We compare these results to full configuration-interaction and high-level coupled-cluster reference calculations.

quantum computing, variational quantum solver, cou↗
DOE OSTI2017

Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory

We present two efficient iterative algorithms for solving the linear response eigen- value problem arising from the time dependent density functional theory. Although the matrix to be diagonalized is nonsymmetric, it has a special structure that can be exploited to save both memory and floating point operations. In particular, the nonsymmetric eigenvalue problem can be transformed into a product eigenvalue problem that is self-adjoint with respect to a K-inner product. This product eigenvalue problem can be solved efficiently by a modified Davidson algorithm and a modified locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm that make use of the K-inner product. The solution of the product eigenvalue problem yields one component of the eigenvector associated with the original eigenvalue problem. However, the other component of the eigenvector can be easily recovered in a postprocessing procedure. Therefore, the algorithms we present here are more efficient than existing algorithms that try to approximate both components of the eigenvectors simultaneously. The efficiency of the new algorithms is demonstrated by numerical examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver

We describe a number of recently developed techniques for improving the performance of large-scalenuclear configuration interaction calculations on high performance parallel computers. We show thebenefit of using a preconditioned block iterative method to replace the Lanczos algorithm that hastraditionally been used to perform this type of computation. The rapid convergence of the block iterativemethod is achieved by a proper choice of starting guesses of the eigenvectors and the construction of aneffective preconditioner. These acceleration techniques take advantage of special structure of the nuclearconfiguration interaction problem which we discuss in detail. The use of a block method also allows usto improve the concurrency of the computation, and take advantage of the memory hierarchy of modernmicroprocessors to increase the arithmetic intensity of the computation relative to data movement. Wealso discuss the implementation details that are critical to achieving high performance on massivelyparallel multi-core supercomputers, and demonstrate that the new block iterative solver is two to threetimes faster than the Lanczos based algorithm for problems of moderate sizes on a Cray XC30 system.

Shao, Meiyue↗
DOE OSTI2020

GPU-acceleration of the ELPA2 distributed eigensolver for dense symmetric and hermitian eigenproblems

The solution of eigenproblems is often a key computational bottleneck that limits the tractable system size of numerical algorithms, among them electronic structure theory in chemistry and in condensed matter physics. Large eigenproblems can easily exceed the capacity of a single compute node, thus must be solved on distributed-memory parallel computers. We here present GPU-oriented optimizations of the ELPA two-stage tridiagonalization eigensolver (ELPA2). On top of cuBLAS-based GPU offloading, we add a CUDA kernel to speed up the back-transformation of eigenvectors, which can be the computationally most expensive part of the two-stage tridiagonalization algorithm. Furthermore, we benchmark the performance of this GPU-accelerated eigensolver on two hybrid CPU–GPU architectures, namely a compute cluster based on Intel Xeon Gold CPUs and NVIDIA Volta GPUs, and the Summit supercomputer based on IBM POWER9 CPUs and NVIDIA Volta GPUs. Consistent with previous benchmarks on CPU-only architectures, the GPU-accelerated two-stage solver exhibits a parallel performance superior to the one-stage counterpart. Finally, we demonstrate the performance of the GPU-accelerated eigensolver developed in this work for routine semi-local KS-DFT calculations comprising thousands of atoms.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2003

Eigensolver for a Sparse, Large Hermitian Matrix

A parallel-processing computer program finds a few eigenvalues in a sparse Hermitian matrix that contains as many as 100 million diagonal elements. This program finds the eigenvalues faster, using less memory, than do other, comparable eigensolver programs. This program implements a Lanczos algorithm in the American National Standards Institute/ International Organization for Standardization (ANSI/ISO) C computing language, using the Message Passing Interface (MPI) standard to complement an eigensolver in PARPACK. [PARPACK (Parallel Arnoldi Package) is an extension, to parallel-processing computer architectures, of ARPACK (Arnoldi Package), which is a collection of Fortran 77 subroutines that solve large-scale eigenvalue problems.] The eigensolver runs on Beowulf clusters of computers at the Jet Propulsion Laboratory (JPL).

Tisdale, E. Robert↗
DOE OSTI2018

SIESTA-SIPs: Massively parallel spectrum-slicing eigensolver for an ab initio molecular dynamics package

Integration of Shift-and-Invert Parallel spectral transformation (SIPs) eigensolver (as implemented in the SLEPc library) into an ab initio molecular dynamics package, SIESTA, is described. The effectiveness of the code is demonstrated on applications to polyethylene chains, boron nitride sheets, and bulk water clusters. For problems with the same number of orbitals, the performance of the SLEPc eigensolver depends on the sparsity of the matrices involved, favoring reduced dimensional systems such as polyethylene or boron nitride sheets in comparison to bulk systems like water clusters. For all problems investigated, performance of SIESTA-SIPs exceeds the performance of SIESTA with default solver (ScaLAPACK) at the larger number of cores and the larger number of orbitals. A method that improves the load-balance with each iteration in the self-consistency cycle by exploiting the emerging knowledge of the eigenvalue spectrum is demonstrated

ab initio↗
DOE OSTI2020

A non-orthogonal variational quantum eigensolver

Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the ground state of a system by solving a generalized eigenvalue problem in a subspace spanned by a collection of parametrized quantum states. This allows for the systematic improvement of a logical wavefunction ansatz without a significant increase in circuit complexity. To minimize the circuit complexity of this approach, we propose a strategy for efficiently measuring the Hamiltonian and overlap matrix elements between states parametrized by circuits that commute with the total particle number operator. This strategy doubles the size of the state preparation circuits but not their depth, while adding a small number of additional two-qubit gates relative to standard variational quantum eigensolver. We also propose a classical Monte Carlo scheme to estimate the uncertainty in the ground state energy caused by a finite number of measurements of the matrix elements. We explain how this Monte Carlo procedure can be extended to adaptively schedule the required measurements, reducing the number of circuit executions necessary for a given accuracy. We apply these ideas to two model strongly correlated systems, a square configuration of H4 and the π-system of hexatriene (C6H8).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Enhancing scalability of a matrix-free eigensolver for studying many-body localization

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 exponentially with respect to the number of spins L, and we need to average over different realizations of the random disorder to obtain relevant statistical behavior. For each disorder realization, we need to compute eigenvalues from different regions of the spectrum and their corresponding eigenvectors. In previous work, the interior eigenstates for a single eigenvalue problem are computed via the shift-and-invert Lanczos algorithm. Due to the extremely high memory footprint of the LU factorizations, this technique is not well suited for large L’s. For example, we need thousands of compute nodes on modern high performance computing infrastructures to go beyond L = 24. The matrix-free approach does not suffer from this memory bottleneck, however, its scalability is limited by a computation and communication load imbalance. To reduce this imbalance and to significantly enhance the scalability of the matrix-free eigensolver, we reorder the matrix and leverage the consistent space runtime, CSPACER. We also show its efficiency in managing irregular communication patterns at scale compared to optimized MPI non-blocking two-sided and one-sided RMA implementation variants. This effort enables us to study MBL for spin chains with a larger number of spins. The efficiency and effectiveness of the proposed algorithm is demonstrated by computing eigenstates on a massively parallel many-core high performance computer.

METIS↗
DOE OSTI2023

Improving the Accuracy of Variational Quantum Eigensolvers with Fewer Qubits Using Orbital Optimization

Near-term quantum computers will be limited in the number of qubits on which they can process information as well as the depth of the circuits that they can coherently carry out. To date, experimental demonstrations of algorithms such as the Variational Quantum Eigensolver (VQE) have been limited to small molecules using minimal basis sets for this reason. In this work we propose incorporating an orbital optimization scheme into quantum eigensolvers wherein a parametrized partial unitary transformation is applied to the basis functions set in order to reduce the number of qubits required for a given problem. The optimal transformation is found by minimizing the ground state energy with respect to this partial unitary matrix. Through numerical simulations of small molecules up to 16 spin orbitals, we demonstrate that this method has the ability to greatly extend the capabilities of near-term quantum computers with regard to the electronic structure problem. Finally, we find that VQE paired with orbital optimization consistently achieves lower ground state energies than traditional VQE when using the same number of qubits and even frequently achieves lower ground state energies than VQE methods using more qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Variational quantum state eigensolver

Extracting eigenvalues and eigenvectors of exponentially large matrices will be an important application of near-term quantum computers. The variational quantum eigensolver (VQE) treats the case when the matrix is a Hamiltonian. Here, we address the case when the matrix is a density matrix ρ. We introduce the variational quantum state eigensolver (VQSE), which is analogous to VQE in that it variationally learns the largest eigenvalues of ρ as well as a gate sequence V that prepares the corresponding eigenvectors. VQSE exploits the connection between diagonalization and majorization to define a cost function C=Tr(ρ~H) where H is a non-degenerate Hamiltonian. Due to Schur-concavity, C is minimized when ρ~=VρV† is diagonal in the eigenbasis of H. VQSE only requires a single copy of ρ (only n qubits) per iteration of the VQSE algorithm, making it amenable for near-term implementation. We heuristically demonstrate two applications of VQSE: (1) Principal component analysis, and (2) Error mitigation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A universal variational quantum eigensolver for non-Hermitian systems

Abstract Many quantum algorithms are developed to evaluate eigenvalues for Hermitian matrices. However, few practical approach exists for the eigenanalysis of non-Hermintian ones, such as arising from modern power systems. The main difficulty lies in the fact that, as the eigenvector matrix of a general matrix can be non-unitary, solving a general eigenvalue problem is inherently incompatible with existing unitary-gate-based quantum methods. To fill this gap, this paper introduces a Variational Quantum Universal Eigensolver (VQUE), which is deployable on noisy intermediate scale quantum computers. Our new contributions include: (1) The first universal variational quantum algorithm capable of evaluating the eigenvalues of non-Hermitian matrices—Inspired by Schur’s triangularization theory, VQUE unitarizes the eigenvalue problem to a procedure of searching unitary transformation matrices via quantum devices; (2) A Quantum Process Snapshot technique is devised to make VQUE maintain the potential quantum advantage inherited from the original variational quantum eigensolver—With additional $$O(log_{2}{N})$$ O ( l o g 2 N ) quantum gates, this method efficiently identifies whether a unitary operator is triangular with respect to a given basis; (3) Successful deployment and validation of VQUE on a real noisy quantum computer, which demonstrates the algorithm’s feasibility. We also undertake a comprehensive parametric study to validate VQUE’s scalability, generality, and performance in realistic applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A circuit-generated quantum subspace algorithm for the variational quantum eigensolver

Recent research has shown that wavefunction evolution in real and imaginary time can generate quantum subspaces with significant utility for obtaining accurate ground state energies. Inspired by these methods, we propose combining quantum subspace techniques with the variational quantum eigensolver (VQE). In our approach, the parameterized quantum circuit is divided into a series of smaller subcircuits. The sequential application of these subcircuits to an initial state generates a set of wavefunctions that we use as a quantum subspace to obtain high-accuracy groundstate energies. We call this technique the circuit subspace variational quantum eigensolver (CSVQE) algorithm. By benchmarking CSVQE on a range of quantum chemistry problems, we show that it can achieve significant error reduction in the best case compared to conventional VQE, particularly for poorly optimized circuits, greatly improving convergence rates. Furthermore, we demonstrate that when applied to circuits trapped at local minima, CSVQE can produce energies close to the global minimum of the energy landscape, making it a potentially powerful tool for diagnosing local minima.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Many-fermion simulation from the contracted quantum eigensolver without fermionic encoding of the wave function

Quantum computers potentially have an exponential advantage over classical computers for the quantum simulation of many-fermion quantum systems. Nonetheless, fermions are more expensive to simulate than bosons due to the fermionic encoding—a mapping by which the qubits are encoded with fermion statistics. Here we generalize the contracted quantum eigensolver (CQE) to avoid fermionic encoding of the wave function. In contrast to the variational quantum eigensolver, the CQE solves for a many-fermion stationary state by minimizing the contraction (projection) of the Schrödinger equation onto two fermions. We avoid fermionic encoding of the wave function by contracting the Schrödinger equation onto an unencoded pair of particles. Solution of the resulting contracted equation by a series of unencoded two-body exponential transformations generates an unencoded wave function from which the energy and two-fermion reduced density matrix (2-RDM) can be computed. We apply the unencoded and the encoded CQE algorithms to the hydrogen fluoride molecule, the dissociation of oxygen O 2 , and a series of hydrogen chains. Both algorithms show comparable convergence towards the exact ground-state energies and 2-RDMs, but the unencoded algorithm has computational advantages in terms of state preparation and tomography.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Reducing the cost of energy estimation in the variational quantum eigensolver algorithm with robust amplitude estimation

Quantum chemistry and materials is one of the most promising applications of quantum computing. Yet much work is still to be done in matching industry-relevant problems in these areas with quantum algorithms that can solve them. Most previous efforts have carried out resource estimations for quantum algorithms run on large-scale fault-tolerant architectures, which include the quantum phase estimation algorithm. In contrast, few have assessed the performance of near-term quantum algorithms, which include the variational quantum eigensolver (VQE) algorithm. Recently, a large-scale benchmark study [Gonthier et al. 2020] found evidence that the performance of the variational quantum eigensolver for a set of industry-relevant molecules may be too inefficient to be of practical use. This motivates the need for developing and assessing methods that improve the efficiency of VQE. In this work, we predict the runtime of the energy estimation subroutine of VQE when using robust amplitude estimation (RAE) to estimate Pauli expectation values. Under conservative assumptions, our resource estimation predicts that RAE can reduce the runtime over the standard estimation method in VQE by one to two orders of magnitude. Despite this improvement, we find that the runtimes are still too large to be practical. These findings motivate two complementary efforts towards quantum advantage: 1) the investigation of more efficient near-term methods for ground state energy estimation and 2) the development of problem instances that are of industrial value and classically challenging, but better suited to quantum computation.

Johnson, Peter D.↗
DOE OSTI2024

Crossing The Gap Using Variational Quantum Eigensolver: A Comparative Study

Within the evolving domain of quantum computational chemistry, the Variational Quantum Eigensolver (VQE) has been developed to explore not only the ground state but also the excited states of molecules. In this study, we compare the performance of Variational Quantum Deflation (VQD) and Subspace-Search Variational Quantum Eigensolver (SSVQE) methods in determining the low-lying excited states of $LiH$. Our investigation reveals that while VQD exhibits a slight advantage in accuracy, SSVQE stands out for its efficiency, allowing the determination of all low-lying excited states through a single parameter optimization procedure. We further evaluate the effectiveness of optimizers, including Gradient Descent (GD), Quantum Natural Gradient (QNG), and Adam optimizer, in obtaining $LiH$'s first excited state, with the Adam optimizer demonstrating superior efficiency in requiring the fewest iterations. Moreover, we propose a novel approach combining Folded Spectrum VQE (FS-VQE) with either VQD or SSVQE, enabling the exploration of highly excited states. We test the new approaches for finding all three $H_4$'s excited states. Folded Spectrum SSVQE (FS-SSVQE) can find all three highly excited states near $-1.0$ Ha with only one optimizing procedure, but the procedure converges slowly. In contrast, although Folded spectrum VQD (FS-VQD) gets highly excited states with individual optimizing procedures, the optimizing procedure converges faster.

Chen, I-Chi↗
DOE OSTI2023

Exploring the scaling limitations of the variational quantum eigensolver with the bond dissociation of hydride diatomic molecules

Abstract Materials simulations involving strongly correlated electrons pose fundamental challenges to state‐of‐the‐art electronic structure methods but are hypothesized to be the ideal use case for quantum computing algorithms. To date, no quantum computer has simulated a molecule of a size and complexity relevant to real‐world applications, despite the fact that the variational quantum eigensolver (VQE) algorithm can predict chemically accurate total energies. Nevertheless, because of the many applications of moderately sized, strongly correlated systems, such as molecular catalysts, the successful use of the VQE stands as an important waypoint in the advancement toward useful chemical modeling on near‐term quantum processors. In this paper, we take a significant step in this direction. We lay out the steps, write, and run parallel code for an (emulated) quantum computer to compute the bond dissociation curves of the TiH, LiH, NaH, and KH diatomic hydride molecules using the VQE. TiH was chosen as a relatively simple chemical system that incorporates d orbitals and strong electron correlation. Because current VQE implementations on existing quantum hardware are limited by qubit error rates, the number of qubits available, and the allowable gate depth, recent studies using it have focused on chemical systems involving s and p block elements. Through VQE + UCCSD calculations of TiH, we evaluate the near‐term feasibility of modeling a molecule with d‐orbitals on real quantum hardware. We demonstrate that the inclusion of d‐orbitals and the use of the UCCSD ansatz, which are both necessary to capture the correct TiH physics, dramatically increase the cost of this problem. We estimate the approximate error rates necessary to model TiH on current quantum computing hardware using VQE + UCCSD and show them to likely be prohibitive until significant improvements in hardware and error correction algorithms are available.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Hybrid eigensolvers for nuclear configuration interaction calculations

We examine and compare several iterative methods for solving large-scale eigenvalue problems arising from nuclear structure calculations. In particular, we discuss the possibility of using block Lanczos method, a Chebyshev filtering based subspace iterations and the residual minimization method accelerated by direct inversion of iterative subspace (RMM-DIIS) and describe how these algorithms compare with the standard Lanczos algorithm and the locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm. Although the RMM-DIIS method does not exhibit rapid convergence when the initial approximations to the desired eigenvectors are not sufficiently accurate, it can be effectively combined with either the block Lanczos or the LOBPCG method to yield a hybrid eigensolver that has several desirable properties. We will describe a few practical issues that need to be addressed to make the hybrid solver efficient and robust.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Variational quantum eigensolver with reduced circuit complexity

Abstract The variational quantum eigensolver (VQE) is one of the most promising algorithms to find eigenstates of a given Hamiltonian on noisy intermediate-scale quantum devices (NISQ). The practical realization is limited by the complexity of quantum circuits. Here we present an approach to reduce quantum circuit complexity in VQE for electronic structure calculations. Our ClusterVQE algorithm splits the initial qubit space into clusters which are further distributed on individual (shallower) quantum circuits. The clusters are obtained based on mutual information reflecting maximal entanglement between qubits, whereas inter-cluster correlation is taken into account via a new “dressed” Hamiltonian. ClusterVQE therefore allows exact simulation of the problem by using fewer qubits and shallower circuit depth at the cost of additional classical resources, making it a potential leader for quantum chemistry simulations on NISQ devices. Proof-of-principle demonstrations are presented for several molecular systems based on quantum simulators as well as IBM quantum devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗