Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “quantum computing algorithms”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,531 records · Page 85
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Predicting solid state material platforms for quantum technologies

Semiconductor materials provide a compelling platform for quantum technologies (QT). However, identifying promising material hosts among the plethora of candidates is a major challenge. Therefore, we have developed a framework for the automated discovery of semiconductor platforms for QT using material informatics and machine learning methods. Different approaches were implemented to label data for training the supervised machine learning (ML) algorithms logistic regression, decision trees, random forests and gradient boosting. We find that an empirical approach relying exclusively on findings from the literature yields a clear separation between predicted suitable and unsuitable candidates. In contrast to expectations from the literature focusing on band gap and ionic character as important properties for QT compatibility, the ML methods highlight features related to symmetry and crystal structure, including bond length, orientation and radial distribution, as influential when predicting a material as suitable for QT.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Mixed stochastic-deterministic density functional theoretic decomposition of Kubo–Greenwood conductivities in the projector augmented wave formalism

Pairing the accuracy of the Kohn–Sham density-functional framework with the efficiency of a stochastic algorithmic approach, mixed stochastic-deterministic density functional theory (mDFT) achieves a favorable computational scaling with system sizes and electronic temperatures. We employ the recently developed mDFT formalism to investigate the dynamic charge-transport properties of systems in the warm dense matter regime. The optical conductivity spectra are computed for single- and multi- component mixtures of carbon, hydrogen, and beryllium using two complementary approaches: Kubo–Greenwood in the mDFT picture and real-time time-dependent mDFT. We further devise a decomposition of the Onsager coefficients leading up to the Kubo–Greenwood spectra to exhibit contributions from the deterministic, stochastic, and mixed electronic state transitions at different incident photon energies.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Synthesis of single-qutrit circuits from Clifford+𝑅 gates

Here, we present two deterministic compilation algorithms for single-qutrit unitaries with O ( log 1 / ɛ ) gate depth. Each algorithm selects a nearby approximation to the target unitary and then exactly synthesizes the approximation over the Clifford + R basis. The first algorithm exhaustively searches over the group; while the second algorithm searches only for Householder reflections. The exhaustive search algorithm yields an average R count of 2.193 ( 11 ) + 8.621 ( 7 ) log 10 ( 1 / ɛ ) , albeit with a time complexity of O ( ɛ − 4.4 ) . The Householder search algorithm results in a larger average R count of 3.20 ( 13 ) + 10.77 ( 3 ) log 10 ( 1 / ɛ ) at a reduced time complexity of O ( ɛ − 0.42 ) , greatly extending the reach in ɛ . These costs correspond asymptotically to 35% and 69% more non-Clifford gates compared with synthesizing the same unitary with two qubits. Such initial results are encouraging for using the R gate as the nontransversal gate for qutrit-based computation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Modeling Mesoscale Processes of Scalable Synthesis (Final Report)

The main objective of the center is to develop tools that can help for the understanding of equilibrium and non-equilibrium properties of nanoparticles in aqueous electrolytes. To achieve this goal, we need to develop new computational methodologies that can integrate molecular level description such as the electronic structure analysis to mesoscale description such as generalized hydrodynamics. The challenge is to develop systematic coarse graining techniques that can adaptively choose the level of description needed for the particular task. For example, if bonding breaking is involved, then one should use appropriate models from quantum mechanics to accurately model the time scale and molecular mechanism for the breaking process. However, to model transport process or the process of self-assembly, much less detailed models can be used. There are two main components to this task. One is to develop accurate models that bridge different levels of description. The classical example is the QM/MM model that bridges quantum mechanics and molecular mechanics for studying chemical reactions of large molecules. This work was awarded the Nobel prize this year. For our purpose, we also need to develop methods that bridge molecular and continuum levels of description. Another main task is to develop systematic coarse-graining methods that can give rise to accurate mesoscale and macroscale models, starting from more detailed models at the atomic or molecular scale. None of these ideas are new. By now they have been fashionable topics for quite some time. But neither problem is satisfactorily resolved. The main problem is that uncontrolled approximations are used. As a result, we have very little idea about the validity and accuracy of these models. The main purpose of the center is to exploit the Mori-Zwanzig formalism to achieve the goals stated above. The Mori-Zwanzig formalism is a general tool for eliminating degrees of freedom from existing models. What is attractive about this formalism is its generality. The flip side is that it is also somewhat of a tautology. In order to make it a practical tool, one has to make approximations and this is where the trouble comes. Instead of focusing on Mori-Zwanzig formalism, the PI proposes to study the closely related renormalization group formalism (RG). Like Mori-Zwanzig, RG is a general strategy for eliminating small scale degrees of freedom in a model. Unlike Mori-Zwanzig, RG has the advantage that at least for some problems, one can write a PDE (partial differential equation) type of model for the exact RG flow, without any approximation. This gives us a solid starting point for discussing and analyzing approximations. The PI studied approximate RG flows for turbulent diffusion and related problems. However, extending it to more practical problems proved to be hard. The second line that the PI has pursued is to develop special numerical algorithms for studying particularly important events for dynamics processes in meso-scale systems. The PI succeeded in doing so for the problem of understanding phase transition in metallic systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications

This work is concerned with the Fourier spectral approximation of various integral differential equations associated with some linear nonlocal diffusion and peridynamic operators under periodic boundary conditions. For radially symmetric kernels, the nonlocal operators under consideration are diagonalizable in the Fourier space so that the main computational challenge is on the accurate and fast evaluation of their eigenvalues or Fourier symbols consisting of possibly singular and highly oscillatory integrals. For a large class of fractional power-like kernels, we propose a new approach based on reformulating the Fourier symbols both as coefficients of a series expansion and solutions of some simple ODE models. We then propose a hybrid algorithm that utilizes both truncated series expansions and high order Runge–Kutta ODE solvers to provide fast evaluation of Fourier symbols in both one and higher dimensional spaces. It is shown that this hybrid algorithm is robust, efficient and accurate. As applications, we combine this hybrid spectral discretization in the spatial variables and the fourth-order exponential time differencing Runge–Kutta for temporal discretization to offer high order approximations of some nonlocal gradient dynamics including nonlocal Allen–Cahn equations, nonlocal Cahn–Hilliard equations, and nonlocal phase-field crystal models. Numerical results show the accuracy and effectiveness of the fully discrete scheme and illustrate some interesting phenomena associated with the nonlocal models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Quantum error mitigation by Pauli check sandwiching

Abstract We describe and analyze an error mitigation technique that uses multiple pairs of parity checks to detect the presence of errors. Each pair of checks uses one ancilla qubit to detect a component of the error operator and represents one layer of the technique. We build on the results on extended flag gadgets and put it on a firm theoretical foundation. We prove that this technique can recover the noiseless state under the assumption of noise not affecting the checks. The method does not incur any encoding overhead and instead chooses the checks based on the input circuit. We provide an algorithm for obtaining such checks for an arbitrary target circuit. Since the method applies to any circuit and input state, it can be easily combined with other error mitigation techniques. We evaluate the performance of the proposed methods using extensive numerical simulations on 1850 random input circuits composed of Clifford gates and non-Clifford single-qubit rotations, a class of circuits encompassing most commonly considered variational algorithm circuits. We observe average improvements in fidelity of 34 percentage points with six layers of checks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Coarse grained simulation of convectively driven turbulent mixing, transition, and turbulence decay

Accurate predictions with quantifiable uncertainties are essential to many practical turbulent flow applications exhibiting extreme geometrical complexity and broad ranges of length and time scales. Under-resolved computer simulations are typically unavoidable in such applications, and implicit large-eddy simulation (ILES) often becomes the effective strategy. In this work, we focus on assessing ILES initialized with well-characterized 25 6 3 homogeneous isotropic turbulence datasets generated with direct numerical simulation (DNS). ILES solutions based on the LANL xRAGE code are studied as function of resolution for 6 4 3 , 12 8 3 , 25 6 3 , and 51 2 3 grids. ILES performance of new directionally-unsplit high-order numerical hydrodynamics algorithms in xRAGE is examined in this context. Compared to the initial 25 6 3 DNS, we find longer inertial subranges and higher turbulence Reynolds number (Re) for 25 6 3 and 51 2 3 xRAGE — attributed to having linked DNS (Navier–Stokes based) solutions to nominally inviscid (higher Re) Euler based ILES solutions. For fixed 25 6 3 resolution, we find that significantly larger simulated turbulence Re can be achieved with the higher-order unsplit (vs. split) discretizations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Filtered Rayleigh-Ritz is all you need

Recent work has shown that the (block) Lanczos algorithm can be used to extract approximate energy spectra and matrix elements from (matrices of) correlation functions in quantum field theory, and identified exact coincidences between Lanczos analysis methods and others. In this work, we note another coincidence: the Lanczos algorithm is equivalent to the well-known Rayleigh-Ritz method applied to Krylov subspaces. Rayleigh-Ritz provides optimal eigenvalue approximations within subspaces; we find that spurious-state filtering allows these optimality guarantees to be retained in the presence of statistical noise. We explore the relation between Lanczos and Prony's method, their block generalizations, generalized pencil of functions (GPOF), and methods based on the generalized eigenvalue problem (GEVP), and find they all fall into a larger "Prony-Ritz equivalence class", identified as all methods which solve a finite-dimensional spectrum exactly given sufficient correlation function (matrix) data. This equivalence allows simpler and more numerically stable implementations of (block) Lanczos analyses.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Quantum algorithms from fluctuation theorems: Thermal-state preparation

Fluctuation theorems provide a correspondence between properties of quantum systems in thermal equilibrium and a work distribution arising in a non-equilibrium process that connects two quantum systems with Hamiltonians H 0 and H 1 = H 0 + V. Building upon these theorems, we present a quantum algorithm to prepare a purification of the thermal state of H 1 at inverse temperature β ≥ 0 starting from a purification of the thermal state of H 0 . The complexity of the quantum algorithm, given by the number of uses of certain unitaries, is $\mathcal{O}$ (e β(ΔA - w l )/2 ), where ΔA is the free-energy difference between H 1 and H 0 , and w l is a work cutoff that depends on the properties of the work distribution and the approximation error ϵ > 0. If the non-equilibrium process is trivial, this complexity is exponential i β∥V∥, where ∥V∥ is the spectral norm of V. This represents a significant improvement of prior quantum algorithms that have complexity exponential in β∥H 1 ∥ in the regime where ∥V∥$\ll$ ∥H 1 ∥. The dependence of the complexity in ϵ varies according to the structure of the quantum systems. It can be exponential in 1/ϵ in general, but we show it to be sublinear in 1/ϵ if H 0 and H 1 commute, or polynomial in 1/ϵ if H 0 and H 1 are local spin systems. The possibility of applying a unitary that drives the system out of equilibrium allows one to increase the value of w l and improve the complexity even further. To this end, we analyze the complexity for preparing the thermal state of the transverse field Ising model using different non-equilibrium unitary processes and see significant complexity improvements.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Freedom of the mixer rotation axis improves performance in the quantum approximate optimization algorithm

Variational quantum algorithms such as the quantum approximate optimization algorithm (QAOA) are particularly attractive candidates for implementation on near-term quantum processors. As hardware realities such as error and qubit connectivity will constrain achievable circuit depth in the near future, new ways to achieve high performance at low depth are of great interest. In this work, we present a modification to QAOA that adds additional variational parameters in the form of freedom of the rotation axis in the XY plane of the mixer Hamiltonian. Here, via numerical simulation, we show that this leads to a drastic performance improvement over standard QAOA at finding solutions to the MaxCut problem on graphs of up to seven qubits. Furthermore, we explore the Z-phase error mitigation properties of our modified Ansatz, its performance under a realistic error model for a neutral atom quantum processor, and the class of problems it can solve in a single round.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Reinforcement Learning Configuration Interaction

Selected configuration interaction (sCI) methods exploit the sparsity of the full configuration interaction (FCI) wave function, yielding significant computational savings and wave function compression without sacrificing the accuracy. Despite recent advances in sCI methods, the selection of important determinants remains an open problem. Furthermore, we explore the possibility of utilizing reinforcement learning approaches to solve the sCI problem. By mapping the configuration interaction problem onto a sequential decision-making process, the agent learns on-the-fly which determinants to include and which to ignore, yielding a compressed wave function at near-FCI accuracy. This method, which we call reinforcement-learned configuration interaction, adds another weapon to the sCI arsenal and highlights how reinforcement learning approaches can potentially help solve challenging problems in electronic structure theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Thermal Weight Determination and Interstate Coupling in State-Averaged ADAPT-VQE

Characterizing electronic thermal states at low temperatures is an important but challenging task in quantum chemistry and condensed matter physics, making it a prime candidate for a useful application in quantum computing. One of the most successful methods for state preparation on quantum computers is the Adaptive, Problem-Tailored (ADAPT) Variational Quantum Eigensolver (VQE), which has recently been generalized to treat excited states within a state-averaged framework as well as Gibbs states. In this work, we introduce Helmholtz-Optimized Thermal (HOT) ADAPT-VQE, an ancilla-free strategy for preparing Gibbs states that directly minimizes the Helmholtz free energy by targeting the dominant eigenstates of the thermal ensemble. We demonstrate the usefulness of HOT-ADAPT-VQE by predicting the free energy of two model systems with strongly correlated ground states: (1) the Fe 2+ cation in a magnetic field and (2) a [Cu 2 O 7 ] 10– fragment of the Mott insulator La 2 CuO 4 . Our results demonstrate that HOT-ADAPT-VQE significantly improves upon Gibbs-state estimates from multistate variants of ADAPT-VQE, often with substantially shallower quantum circuits, making it a promising candidate for thermal-state calculations.

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

One and Two Dimensional Quantum Lattice Algorithms for Maxwell Equations in Inhomogeneous Scalar Dielectric Media. II: Simulations

Long time quantum lattice algorithm (QLA) simulations are performed for the mul- tiple reflection-transmission of an initial electromagnetic pulse propagating normally to a boundary layer region joining two media of different refractive index. For these one dimensional (1D) sim- ulations, there is excellent agreement between x-, y- and z- representations, as well as very good agreement with nearly all the standard plane wave boundary condition results for reflection and transmission off a dielectric discontinuity. In the QLA simulation, no boundary conditions are im- posed at the continuous, but sharply increasing, dielectic boundary layers. Two dimensional (2D) QLA scattering simulations in the x-z plane are performed for an electromagnetic pulse interacting with a conical dielectric obstacle for the 8-16 qubit model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Mixed quantum-classical methods for polaron spectral functions

In this work, using two distinct semiclassical approaches—namely, the mean-field Ehrenfest method and the mapping approach to surface hopping—we investigate the spectral function of a single charge interacting with phonons on a lattice. This quantity is relevant for the description of angle-resolved photoemission experiments. Focusing on the one-dimensional Holstein model, we compare the performance of these approaches across a range of coupling strengths and lattice sizes, exposing the relative strengths and weaknesses of each. We demonstrate that these approaches can be efficiently applied with reasonable accuracy to ab initio polaron models. Furthermore, our work provides a route to the calculation of spectral properties in realistic electron–phonon-coupled systems in a computationally inexpensive manner with encouraging accuracy.

Atomic and molecular spectra↗
DOE OSTI2018

Removal of Stationary Sinusoidal Noise from Random Vibration Signals

In random vibration environments, sinusoidal line noise may appear in the vibration signal and can affect analysis of the resulting data. We studied two methods which remove stationary sine tones from random noise: a matrix inversion algorithm and a chirp-z transform algorithm. In addition, we developed new methods to determine the frequency of the tonal noise. The results show that both of the removal methods can eliminate sine tones in prefabricated random vibration data when the sine-to-random ratio is at least 0.25. For smaller ratios down to 0.02 only the matrix inversion technique can remove the tones, but the metrics to evaluate its effectiveness also degrade. We also found that using fast Fourier transforms best identified the tonal noise, and determined that band-pass-filtering the signals prior to the process improved sine removal. When applied to actual vibration test data, the methods were not as effective at removing harmonic tones, which we believe to be a result of mixed-phase sinusoidal noise.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

On the closedness and geometry of tensor network state sets

Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse of dimensionality is addressed by parametrizing the many-body state in terms of a network of partially contracted tensors. These tensors form a substantially reduced set of effective degrees of freedom. In practical algorithms, functionals like energy expectation values or overlaps are optimized over certain sets of TNS. Concerning algorithmic stability, it is important whether the considered sets are closed because, otherwise, the algorithms may approach a boundary point that is outside the TNS set and tensor elements diverge. Here we discuss the closedness and geometries of TNS sets, and we propose regularizations for optimization problems on non-closed TNS sets. We show that sets of matrix product states (MPS) with open boundary conditions, tree tensor network states, and the multiscale entanglement renormalization ansatz are always closed, whereas sets of translation-invariant MPS with periodic boundary conditions (PBC), heterogeneous MPS with PBC, and projected entangled pair states are generally not closed. The latter is done using explicit examples like the W state, states that we call two-domain states, and fine-grained versions thereof.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Distribution of centrality measures on undirected random networks via the cavity method

The Katz centrality of a node in a complex network is a measure of the node’s importance as far as the flow of information across the network is concerned. For ensembles of locally tree-like undirected random graphs, this observable is a random variable. Its full probability distribution is of interest but difficult to handle analytically because of its “global” character and its definition in terms of a matrix inverse. Leveraging a fast Gaussian Belief Propagation-Cavity algorithm to solve linear systems on tree-like structures, we show that i) the Katz centrality of a single instance can be computed recursively in a very fast way, and ii) the probability P ( K ) that a random node in the ensemble of undirected random graphs has centrality K satisfies a set of recursive distributional equations, which can be analytically characterized and efficiently solved using a population dynamics algorithm. We test our solution on ensembles of Erdős-Rényi and Scale Free networks in the locally tree-like regime, with excellent agreement. The analytical distribution of centrality for the configuration model conditioned on the degree of each node can be employed as a benchmark to identify nodes of empirical networks with over- and underexpressed centrality relative to a null baseline. We also provide an approximate formula based on a rank- 1 projection that works well if the network is not too sparse, and we argue that an extension of our method could be efficiently extended to tackle analytical distributions of other centrality measures such as PageRank for directed networks in a transparent and user-friendly way.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Context-dependent piano music transcription with convolutional sparse coding

The present disclosure presents a novel approach to automatic transcription of piano music in a context-dependent setting. Embodiments described herein may employ an efficient algorithm for convolutional sparse coding to approximate a music waveform as a summation of piano note waveforms convolved with associated temporal activations. The piano note waveforms may be pre-recorded for a particular piano that is to be transcribed and may optionally be pre-recorded in the specific environment where the piano performance is to be performed. During transcription, the note waveforms may be fixed and associated temporal activations may be estimated and post-processed to obtain the pitch and onset transcription. Experiments have shown that embodiments of the disclosure significantly outperform state-of-the-art music transcription methods trained in the same context-dependent setting, in both transcription accuracy and time precision, in various scenarios including synthetic, anechoic, noisy, and reverberant environments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗