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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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DOE OSTI2024

Report for the ASCR Workshop on Basic Research Needs in Quantum Computing and Networking - 2023

Employing quantum mechanical resources in computing and networking opens the door to new computation and communication models and potential disruptive advantages over classical counterparts. However, quantifying and realizing such advantages face extensive scientific and engineering challenges. Investments by the Department of Energy (DOE) have driven progress toward addressing such challenges. Quantum algorithms have been recently developed, in some cases offering asymptotic exponential advantages in speed or accuracy, for fundamental scientific problems such as simulating physical systems, solving systems of linear equations, or solving differential equations. Empirical demonstrations on nascent quantum hardware suggest better performance than classical analogs on specialized computational tasks favorable to the quantum computing systems. However, demonstration of an end-to-end, substantial and rigorously quantifiable quantum performance advantage over classical analogs remains a grand challenge, especially for problems of practical value. The definition of requirements for quantum technologies to exhibit scalable, rigorous, and transformative performance advantages for practical applications also remains an outstanding open question, namely, what will be required to ultimately demonstrate practical quantum advantage?

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Benchmarking Optimizers for Qumode State Preparation with Variational Quantum Algorithms

Quantum state preparation involves preparing a target state from an initial system, a process integral to applications such as quantum machine learning and solving systems of linear equations. Recently, there has been a growing interest in qumodes due to advancements in the field and their potential applications. However there is a notable gap in the literature specifically addressing this area. This paper aims to bridge this gap by providing performance benchmarks of various optimizers used in state preparation with Variational Quantum Algorithms. We conducted extensive testing across multiple scenarios, including different target states, both ideal and sampling simulations, and varying numbers of basis gate layers. Our evaluations offer insights into the complexity of learning each type of target state and demonstrate that some optimizers perform better than others in this context. Notably, the Powell optimizer was found to be exceptionally robust against sampling errors, making it a preferred choice in scenarios prone to such inaccuracies. Additionally, the Simultaneous Perturbation Stochastic Approximation optimizer was distinguished for its efficiency and ability to handle increased parameter dimensionality effectively.

Kan, Shuwen [Fordham University]↗
DOE OSTI2024

HHL algorithm with mapping function and enhanced sampling for model predictive control in microgrids

Here, this paper presents a refined quantum Harrow Hassidim Lloyd (HHL) algorithm for microgrid control. The first novelty of the developed method is that a mapping shift function enables the original HHL algorithm to handle general linear equations with non-singular and indefinite matrix. Second, a method of Matrix Extension for Amplifying Sampling Probabilities of Intended Solution (ME-ASPI) is proposed to design the reformulated linear algebraic equations, allowing for improved sampling efficiency of the quantum tomography in the refined HHL algorithm. Then, we applied the method to solve the model predictive control (MPC) problem in nonlinear dynamical microgrids. Specifically, with the ME-ASPI method, the refined HHL algorithm can effectively obtain the intended partial optimal control inputs for MPC. The optimization of quadratic programming problem in each time step of MPC is transformed into a linear system problem, which is addressed by the proposed quantum solver through using only partial information, with the time complexity improved from $\mathscr{O}(\mathscr{N}^{2.37286})$ classically to $\mathscr{O}(\mathscr{N}^{2} log \mathscr{N}$ x $p$ log $p)$ in quantum. Numerical examples have validated the effectiveness of the refined HHL algorithm with the proposed mapping function and the ME-ASPI method. By leveraging quantum properties, the proposed method provides a hybrid quantum–classical framework for microgrid control. This generic method can also potentially tackle many other challenges in analyzing and controlling general complex engineered systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Co-designing Spectral Transformation Oracles with Hybrid Oscillator-Qubit Quantum Processors: From Algorithms to Compilation

We co-design a family of quantum eigenvalue transformation oracles that can be efficiently implemented on hybrid discrete- or continuous-variable (qubit or qumode) hardware. To illustrate the oracle’s representation-theoretic power and near-term experimental accessibility, we encode a Gaussian imaginary time-evolution spectral filter. As a result, we define a continuous linear combination of unitaries block encoding. Due to the ancillary qumode’s infinite-dimensional nature, continuous-variable qumodes constitute a powerful compilation tool for encoding continuous spectral functions without discretization errors while minimizing resource requirements. We then focus on the ubiquitous task of preparing eigenstates in quantum spin models. For completeness, we provide an end-to-end compilation which expresses high-level oracles in terms of an experimentally realizable instruction set architecture in both 1D and 2D. Finally, we examine the leading-order effects of physical errors and highlight open research directions. Our algorithms scale linearly with the spatial extent of the target system and are applicable to both near-term and large-scale quantum processors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Solving differential‐algebraic equations in power system dynamic analysis with quantum computing

Abstract Power system dynamics are generally modeled by high dimensional non‐linear differential‐algebraic equations (DAEs) given a large number of components forming the network. These DAEs' complexity can grow exponentially due to the increasing penetration of distributed energy resources, whereas their computation time becomes sensitive due to the increasing interconnection of the power grid with other energy systems. This paper demonstrates the use of quantum computing algorithms to solve DAEs for power system dynamic analysis. We leverage a symbolic programming framework to equivalently convert the power system's DAEs into ordinary differential equations (ODEs) using index reduction methods and then encode their data into qubits using amplitude encoding. The system non‐linearity is captured by Hamiltonian simulation with truncated Taylor expansion so that state variables can be updated by a quantum linear equation solver. Our results show that quantum computing can solve the power system's DAEs accurately with a computational complexity polynomial in the logarithm of the system dimension. We also illustrate the use of recent advanced tools in scientific machine learning for implementing complex computing concepts, that is, Taylor expansion, DAEs/ODEs transformation, and quantum computing solver with abstract representation for power engineering applications.

computational complexity↗
DOE OSTI2025

Block encoding bosons by signal processing

Block Encoding (BE) is a crucial subroutine in many modern quantum algorithms, including those with near-optimal scaling for simulating quantum many-body systems, which often rely on Quantum Signal Processing (QSP). Currently, the primary methods for constructing BEs are the Linear Combination of Unitaries (LCU) and the sparse oracle approach. In this work, we demonstrate that QSP-based techniques, such as Quantum Singular Value Transformation (QSVT) and Quantum Eigenvalue Transformation for Unitary Matrices (QETU), can themselves be efficiently utilized for BE implementation. Specifically, we present several examples of using QSVT and QETU algorithms, along with their combinations, to block encode Hamiltonians for lattice bosons, an essential ingredient in simulations of high-energy physics. We also introduce a straightforward approach to BE based on the exact implementation of Linear Operators Via Exponentiation and LCU (LOVE-LCU). We find that, while using QSVT for BE results in the best asymptotic gate count scaling with the number of qubits per site, LOVE-LCU outperforms all other methods for operators acting on up to qubits, highlighting the importance of concrete circuit constructions over mere comparisons of asymptotic scalings. Using LOVE-LCU to implement the BE, we simulate the time evolution of single-site and two-site systems in the lattice theory using the Generalized QSP algorithm and compare the gate counts to those required for Trotter simulation.

Kane, Christopher F↗
DOE OSTI2022

Advanced Quantum Poisson Solver in the NISQ era

The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far, either suffer from lack of accuracy and/or are limited to very small sizes of the problem, and thus have no practical usage. Here we present an advanced quantum algorithm for solving the Poisson equation with high accuracy and dynamically tunable problem size. After converting the Poisson equation to the linear systems through the finite difference method, we adopt the Harrow-Hassidim-Lloyd (HHL) algorithm as the basic framework. Particularly, in this work we present an advanced circuit that ensures the accuracy of the solution by implementing non-truncated eigenvalues through eigenvalue amplification as well as by increasing the accuracy of the controlled rotation angular coefficients, which are the critical factors in the HHL algorithm. We show that our algorithm not only increases the accuracy of the solutions, but also composes more practical and scalable circuits by dynamically controlling problem size in the NISQ devices. We present both simulated and experimental results, and discuss the sources of errors. Finally, we conclude that overall results on the quantum hardware are dominated by the error in the CNOT gates.

Robson, Walter↗
DOE OSTI2021

Efficient numerical method for evaluating normal and anomalous time-domain equilibrium Green's functions in inhomogeneous systems

In this work we develop EPOCH (equilibrium propagator by orthogonal polynomial chain), a computationally efficient method to calculate the time-dependent equilibrium Green's functions, including the anomalous Green's functions of superconductors, to capture the time evolution in large inhomogeneous systems. The EPOCH method generalizes the Chebyshev wave-packet propagation method from quantum chemistry and efficiently incorporates the Fermi-Dirac statistics that is needed for equilibrium quantum condensed matter systems. The computational cost of EPOCH scales only linearly in the system degrees of freedom, generating an extremely efficient algorithm also for very large systems. We demonstrate the power of the EPOCH method by calculating the time evolution of an excitation near a superconductor–normal metal interface in two and three dimensions, capturing transmission as well as normal and Andreev reflections.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Noisy-Intermediate-Scale Quantum Electromagnetic Transients Program

Quantum-empowered electromagnetic transients program (QEMTP) is a promising paradigm for tackling EMTP's computational burdens. Nevertheless, no existing studies truly achieve a practical and scalable QEMTP operable on today's noisy-intermediate-scale quantum (NISQ) computers. The strong reliance on noise-free and fault-tolerant quantum devices--which appears to be decades away--hinder practical applications of current QEMTP methods. Here, we devise a NISQ-QEMTP methodology which for the first time transitions the QEMTP operations from ideal, noise-free quantum simulators to real, noisy quantum computers. The main contributions lie in: (1) a shallow-depth QEMTP quantum circuit for mitigating noises on NISQ quantum devices; (2) practical QEMTP linear solvers incorporating executable quantum state preparation and measurements for nodal voltage computations; (3) a noise-resilient QEMTP algorithm leveraging quantum resources logarithmically scaled with power system dimension; (4) a quantum shifted frequency analysis (QSFA) for accelerating QEMTP by exploiting dynamic phasor simulations with larger time steps; (5) a systematical analysis on QEMTPs performance under various noisy quantum environments. Extensive experiments systematically verify the accuracy, efficacy, universality and noise-resilience of QEMTP on both noise-free simulators and IBM real quantum computers.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2025

Bridging paradigms: Designing for HPC-Quantum convergence

Here, this paper presents a comprehensive software stack architecture for integrating quantum computing (QC) capabilities with High-Performance Computing (HPC) environments. While quantum computers show promise as specialized accelerators for scientific computing, their effective integration with classical HPC systems presents significant technical challenges. We propose a hardware-agnostic software framework that supports both current noisy intermediate-scale quantum devices and future fault-tolerant quantum computers, while maintaining compatibility with existing HPC workflows. The architecture includes a quantum gateway interface, standardized APIs for resource management, and robust scheduling mechanisms to handle both simultaneous and interleaved quantum–classical workloads. Key innovations include: (1) a unified resource management system that efficiently coordinates quantum and classical resources, (2) a flexible quantum programming interface that abstracts hardware-specific details, (3) A Quantum Platform Manager API that simplifies the integration of various quantum hardware systems, and (4) a comprehensive tool chain for quantum circuit optimization and execution. We demonstrate our architecture through implementation of quantum–classical algorithms, including the variational quantum linear solver, showcasing the framework’s ability to handle complex hybrid workflows while maximizing resource utilization. This work provides a foundational blueprint for integrating QC capabilities into existing HPC infrastructures, addressing critical challenges in resource management, job scheduling, and efficient data movement between classical and quantum resources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Simulation of Linear Non-Hermitian Boundary-Value Problems with Quantum Singular-Value Transformation

Herein we propose a quantum algorithm for simulating dissipative waves in inhomogeneous linear media as a boundary-value problem. Using the so-called quantum singular value transformation (QSVT), we construct a quantum circuit that models the propagation of electromagnetic waves in a one-dimensional system with outgoing boundary conditions. The corresponding measurement procedure is also discussed. Limitations of the QSVT algorithm are identified in connection with the large condition numbers that the dispersion matrices exhibit at weak dissipation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Quantum Simulation of Open Quantum Systems Using a Unitary Decomposition of Operators

Electron transport in realistic physical and chemical systems often involves the nontrivial exchange of energy with a large environment, requiring the definition and treatment of open quantum systems. Because the time evolution of an open quantum system employs a nonunitary operator, the simulation of open quantum systems presents a challenge for universal quantum computers constructed from only unitary operators or gates. Here, we present a general algorithm for implementing the action of any nonunitary operator on an arbitrary state on a quantum device. We show that any quantum operator can be exactly decomposed as a linear combination of at most four unitary operators. We demonstrate this method on a two-level system in both zero and finite temperature amplitude damping channels. Furthermore, the results are in agreement with classical calculations, showing promise in simulating nonunitary operations on intermediate-term and future quantum devices.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Provably accurate simulation of gauge theories and bosonic systems

Quantum many-body systems involving bosonic modes or gauge fields have infinite-dimensional local Hilbert spaces which must be truncated to perform simulations of real-time dynamics on classical or quantum computers. To analyze the truncation error, we develop methods for bounding the rate of growth of local quantum numbers such as the occupation number of a mode at a lattice site, or the electric field at a lattice link. Our approach applies to various models of bosons interacting with spins or fermions, and also to both abelian and non-abelian gauge theories. We show that if states in these models are truncated by imposing an upper limit Λ on each local quantum number, and if the initial state has low local quantum numbers, then an error at most ϵ can be achieved by choosing Λ to scale polylogarithmically with ϵ − 1 , an exponential improvement over previous bounds based on energy conservation. For the Hubbard-Holstein model, we numerically compute a bound on Λ that achieves accuracy ϵ , obtaining significantly improved estimates in various parameter regimes. We also establish a criterion for truncating the Hamiltonian with a provable guarantee on the accuracy of time evolution. Building on that result, we formulate quantum algorithms for dynamical simulation of lattice gauge theories and of models with bosonic modes; the gate complexity depends almost linearly on spacetime volume in the former case, and almost quadratically on time in the latter case. We establish a lower bound showing that there are systems involving bosons for which this quadratic scaling with time cannot be improved. By applying our result on the truncation error in time evolution, we also prove that spectrally isolated energy eigenstates can be approximated with accuracy ϵ by truncating local quantum numbers at Λ = polylog ( ϵ − 1 ) .

Tong, Yu↗
DOE OSTI2025

Accelerating resonant spectroscopy simulations using multishifted biconjugate gradient

Resonant spectroscopies, which involve intermediate states with finite lifetimes, provide important insights into collective excitations in quantum materials that are otherwise inaccessible. However, theoretical understanding in this area is often limited by the numerical challenges of solving Kramers-Heisenberg-type response functions for large-scale systems. To address this, we introduce a multishifted biconjugate gradient algorithm that exploits the shared structure of Krylov subspaces across spectra with varying incident energies, effectively reducing the computational complexity to that of linear spectroscopies. Both mathematical proofs and numerical benchmarks confirm that this algorithm substantially accelerates spectral simulations, achieving constant complexity independent of the number of incident energies, while ensuring accuracy and stability. This development provides a scalable, versatile framework for simulating advanced spectroscopies in quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Universal framework for simultaneous tomography of quantum states and SPAM noise

We present a general denoising algorithm for performing simultaneous tomography of quantum states and measurement noise. This algorithm allows us to fully characterize state preparation and measurement (SPAM) errors present in any quantum system. Our method is based on the analysis of the properties of the linear operator space induced by unitary operations. Given any quantum system with a noisy measurement apparatus, our method can output the quantum state and the noise matrix of the detector up to a single gauge degree of freedom. We show that this gauge freedom is unavoidable in the general case, but this degeneracy can be generally broken using prior knowledge on the state or noise properties, thus fixing the gauge for several types of state-noise combinations with no assumptions about noise strength. Such combinations include pure quantum states with arbitrarily correlated errors, and arbitrary states with block independent errors. This framework can further use available prior information about the setting to systematically reduce the number of observations and measurements required for state and noise detection. Our method effectively generalizes existing approaches to the problem, and includes as special cases common settings considered in the literature requiring an uncorrelated or invertible noise matrix, or specific probe states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

A Tensor Network-Based Quantum Algorithm for the Nonlinear 1D Burgers' Equation

In this work, we implement a tensor network-based quantum algorithm to solve unsteady, nonlinear partial differential equations (PDEs). The challenge lies in how to effectively represent, encode, process, and evolve the nonlinear system of PDEs on quantum computers. We will discuss the new techniques using the compressible 1-dimensional (1D) Burgers' equation as an example, because it represents the fundamental nonlinear feature and yet removes certain complexity in physics, allowing us to focus on the design of quantum algorithms. Previous attempts to solve nonlinear PDEs in quantum computation have often involved storing multiple copies of solutions or employing linearizations. Neither is practical due to exponential scaling with evolution time or insufficient solution accuracy. Our framework is based on matrix product states (MPSs) and matrix product operators (MPOs). For example, the velocity field is represented by MPS, whereas the linear and nonlinear spatial differential terms of the velocity field are processed by MPOs. Our primary focus herein is to verify and validate the various tensor network components of the algorithm using solutions obtained by the classical algorithms on high performance computing (HPC) architectures. We use a classical time marching method to demonstrate the functionality of the tensor network operations to model the PDE and their robustness with the time evolution of the system. Our classical simulation results demonstrate the utility of tensor network-based operations in modeling nonlinear PDEs and highlight the necessity as well as potential advantages of using quantum simulations for these techniques.

Gopalakrishnan Meena, Murali [ORNL] (ORCID:0000000↗
DOE OSTI2023

ADoSPSiQS (Automated Detection of Symmetry-Protected Subspaces in Quantum Simulations ) [SWR-23-55]

Symmetry-protected subspaces in quantum systems are subspaces demarcated by a conserved quantity of that quantum system. We introduce two classical algorithms, which efficiently compute and elucidate features of these subspaces. The first algorithm explores the entire symmetry-protected subspace of an initial state in time complexity linear to the size of the subspace by closing local basis state-to-basis state transitions. The second algorithm determines, with bounded error, if a given measurement outcome of a dynamically-generated state is within the symmetry-protected subspace of the state in which the dynamical system is initialized. This software is paired with the paper of the same name at https://arxiv.org/pdf/2302.08586.pdf.

Rotello, Caleb↗
DOE OSTI2023

Adaptive variational quantum minimally entangled typical thermal states for finite temperature simulations

Scalable quantum algorithms for the simulation of quantum many-body systems in thermal equilibrium are important for predicting properties of quantum matter at finite temperatures. Here we describe and benchmark a quantum computing version of the minimally entangled typical thermal states (METTS) algorithm for which we adopt an adaptive variational approach to perform the required quantum imaginary time evolution. The algorithm, which we name AVQMETTS, dynamically generates compact and problem-specific quantum circuits, which are suitable for noisy intermediate-scale quantum (NISQ) hardware. We benchmark AVQMETTS on statevector simulators and perform thermal energy calculations of integrable and nonintegrable quantum spin models in one and two dimensions and demonstrate an approximately linear system-size scaling of the circuit complexity. We further map out the finite-temperature phase transition line of the two-dimensional transverse field Ising model. Finally, we study the impact of noise on AVQMETTS calculations using a phenomenological noise model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗