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DOE OSTI2025

Parallel-in-time quantum simulation via Page and Wootters quantum time

In the past few decades, researchers have created a veritable zoo of quantum algorithms by drawing inspiration from classical computing, information theory, and even from physical phenomena. Here, we present quantum algorithms for parallel-in-time simulations that are inspired by the Page and Wootters formalism. In this framework, and thus in our algorithms, the classical time variable of quantum mechanics is promoted to the quantum realm by introducing a Hilbert space of “clock” qubits that are then entangled with the “system” qubits. We show that our algorithms can compute temporal properties over 𝑁 different times of many-body systems by only using log⁡(𝑁) clock qubits. As such, we achieve an exponential trade-off between time and spatial complexities. In addition, we rigorously prove that the entanglement created between the system qubits and the clock qubits has operational meaning, as it encodes valuable information about the system’s dynamics. We also provide a circuit depth estimation of all the protocols, showing a running time advantage in computation times over traditional sequential-in-time algorithms. In particular, for the case when the dynamics are determined by the Aubry-Andre model, we present a hybrid method for which our algorithms have a depth that only scales as 𝒪⁡(log⁡(𝑁)⁢𝑛). As a by-product, we can relate the previous schemes to the problem of equilibration of an isolated quantum system, thus indicating that our framework enables a new dimension for studying dynamical properties of many-body systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Tensor Network Quantum Virtual Machine for Simulating Quantum Circuits at Exascale

The numerical simulation of quantum circuits is an indispensable tool for development, verification, and validation of hybrid quantum-classical algorithms intended for near-term quantum co-processors. The emergence of exascale high-performance computing (HPC) platforms presents new opportunities for pushing the boundaries of quantum circuit simulation. Here, we present a modernized version of the Tensor Network Quantum Virtual Machine (TNQVM) that serves as the quantum circuit simulation backend in the eXtreme-scale ACCelerator (XACC) framework. The new version is based on the scalable tensor network processing library ExaTN (Exascale Tensor Networks). It provides multiple configurable quantum circuit simulators that perform either an exact quantum circuit simulation via the full tensor network contraction or an approximate simulation via a suitably chosen tensor factorization scheme. Upon necessity, stochastic noise modeling from real quantum processors is incorporated into the simulations by modeling quantum channels with Kraus tensors. By combining the portable XACC quantum programming frontend and the scalable ExaTN numerical processing backend, we introduce an end-to-end virtual quantum development environment that can scale from laptops to future exascale platforms. We report initial benchmarks of our framework, which include a demonstration of the distributed execution, incorporation of quantum decoherence models, and simulation of the random quantum circuits used for the certification of quantum supremacy on Google’s Sycamore superconducting architecture.

Nguyen, Thien↗

DOE OSTI2024

Localization in Energy Materials (Final Project Report)

The last year of this award we have continued our research on using quantum machine learning to identify phase transitions. By combining quantum machine learning with quantum computing, we extended a hybrid classical-quantum algorithm to capture the metal-insulator quantum phase transition of the Hubbard model. We have also continued our studies of non-equilibrium dynamics of interacting disordered systems. In particular, we studied the non-equilibrium transient dynamics of a system described by the Anderson-Hubbard model following an interaction and disorder quench, and the effect of disorder on the out-of-time-order correlator on the Hubbard model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Variational Quantum Fidelity Estimation

Computing quantum state fidelity will be important to verify and characterize states prepared on a quantum computer. In this work, we propose novel lower and upper bounds for the fidelity F ( ρ , σ ) based on the ``truncated fidelity'' F ( ρ m , σ ) , which is evaluated for a state ρ m obtained by projecting ρ onto its m -largest eigenvalues. Our bounds can be refined, i.e., they tighten monotonically with m . To compute our bounds, we introduce a hybrid quantum-classical algorithm, called Variational Quantum Fidelity Estimation, that involves three steps: (1) variationally diagonalize ρ , (2) compute matrix elements of σ in the eigenbasis of ρ , and (3) combine these matrix elements to compute our bounds. Our algorithm is aimed at the case where σ is arbitrary and ρ is low rank, which we call low-rank fidelity estimation, and we prove that no classical algorithm can efficiently solve this problem under reasonable assumptions. Finally, we demonstrate that our bounds can detect quantum phase transitions and are often tighter than previously known computable bounds for realistic situations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Quantum Machine Learning with SQUID

In this work we present the Scaled QUantum IDentifier (SQUID), an open-source framework for exploring hybrid Quantum-Classical algorithms for classification problems. The classical infrastructure is based on PyTorch and we provide a standardized design to implement a variety of quantum models with the capability of back-propagation for efficient training. We present the structure of our framework and provide examples of using SQUID in a standard binary classification problem from the popular MNIST dataset. In particular, we highlight the implications for scalability for gradient-based optimization of quantum models on the choice of output for variational quantum models.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Hybrid Quantum-Classical Eigensolver without Variation or Parametric Gates

The use of near-term quantum devices that lack quantum error correction, for addressing quantum chemistry and physics problems, requires hybrid quantum-classical algorithms and techniques. Here, we present a process for obtaining the eigenenergy spectrum of electronic quantum systems. This is achieved by projecting the Hamiltonian of a quantum system onto a limited effective Hilbert space specified by a set of computational bases. From this projection, an effective Hamiltonian is obtained. Furthermore, a process for preparing short depth quantum circuits to measure the corresponding diagonal and off-diagonal terms of the effective Hamiltonian is given, whereby quantum entanglement and ancilla qubits are used. The effective Hamiltonian is then diagonalized on a classical computer using numerical algorithms to obtain the eigenvalues. The use case of this approach is demonstrated for ground state and excited states of BeH2 and LiH molecules, and the density of states, which agrees well with exact solutions. Additionally, hardware demonstration is presented using IBM quantum devices for H2 molecule.

Jouzdani, Pejman (ORCID:0000000256470381)↗

NASA NTRS1975

Weight minimization of structures for fixed flutter speed via an optimality criterion

A rigorous optimality criterion is derived and a hybrid weight-reduction algorithm developed for the weight minimization of lifting surfaces with a constraint on flutter speed. The weight-reduction algorithm incorporates a simple recursion formula derived from the optimality criterion. Monotonic weight reduction is accomplished by dynamically adjusting a parameter in the recursion formula so as to achieve a predetermined weight decrease. The algorithm thus combines the simplicity of optimality-criterion methods with the convergence characteristics of mathematical-programming methods. The imposition of the flutter constraint is simplified by forcing to zero the imaginary part of the flutter eigenvalue, with the airspeed fixed. Four examples are discussed. The results suggest that significant improvements in efficiency are possible, in comparison with techniques based purely on mathematical programming.

Segenreich, S. A.↗

NASA NTRS1983

Inelastic stress analyses at finite deformation through complementary energy approaches

A new hybrid-stress finite element algorithm, suitable for analyses of large, quasistatic, inelastic deformations, is presented. The algorithm is based upon a generalization of de Veubeke's (1972) complementary energy principle. The principal variables in the formulation are the nominal stress rate and spin, and the resulting finite element equations are discrete versions of the equations of compatibility and angular momentum balance. The algorithm produces true rates, time derivatives, as opposed to 'increments'. There results a boundary value problem (for stress rate and velocity) and an initial value problem (for total stress and deformation). A discussion of the numerical treatment of the boundary value problem is followed by a detailed examination of the numerical treatment of the initial value problem, covering the topics of efficiency, stability, and objectivity. The paper is closed with a set of examples, finite homogeneous deformation problems, which serve to bring out important aspects of the algorithm.

Atluri, S. N.↗

NASA NTRS1984

Hybrid stress finite elements for large deformations of inelastic solids

A new hybrid stress finite element algorithm, based on a generalization of Fraeijs de Veubeke's complementary energy principle is presented. Analyses of large quasistatic deformation of inelastic solids (hypoelastic, plastic, viscoplastic) are within its capability. Principle variables in the formulation are the nominal stress rate and spin. A brief account is given of the boundary value problem in these variables, and the 'equivalent' variational principle. The finite element equation, along with initial positions and stresses, comprise an initial value problem. Factors affecting the choice of time integration schemes are discussed. Results found by application of the new algorithm are compared to those obtained by a velocity based finite element algorithm.

Reed, K. W.↗

NASA NTRS1987

Numerical simulations of magnetospheric plasmas - Review and quadrennial report to the IUGG

This article provides a broad survey of U.S. progress during the quadrennium 1983-1986 in the category 'numerical simulations of magnetospheric plasmas'. There has been a substantial increase of activity in this area during this period. Simulations have been instrumental in providing valuable insights into large scale dynamic phenomena, nonlinear effects, and complex kinetic phenomena in a wide variety of subject areas, including shocks and double layers, ionosphere-magnetosphere coupling phenomena, and important microphysical processes such as broadband electrostatic noise. The methodology of computer simulation has also been advanced during this quadrennium. Vlasov algorithms have been improved; hybrid codes in 2 and 3D have been developed and applied to magnetospheric problems; and complex problems have been subjected with increasing frequency to a multipronged attack in which several types of simulation models, each designed to accurately model phenomena within a particular range of temporal or spatial scales, are employed synergistically.

Palmadesso, Peter J.↗

NASA NTRS1992

Grid generation research at OSU

In the last two years, effort was concentrated on: (1) surface modeling; (2) surface grid generation; and (3) 3-D flow space grid generation. The surface modeling shares the same objectives as the surface modeling in computer aided design (CAD), so software available in CAD can in principle be used for solid modeling. Unfortunately, however, the CAD software cannot be easily used in practice for grid generation purposes, because they are not designed to provide appropriate data base for grid generation. Therefore, we started developing a generalized surface modeling software from scratch, that provides the data base for the surface grid generation. Generating surface grid is an important step in generating a 3-D space for flow space. To generate a surface grid on a given surface representation, we developed a unique algorithm that works on any non-smooth surfaces. Once the surface grid is generated, a 3-D space can be generated. For this purpose, we also developed a new algorithm, which is a hybrid of the hyperbolic and the elliptic grid generation methods. With this hybrid method, orthogonality of the grid near the solid boundary can be easily achieved without introducing empirical fudge factors. Work to develop 2-D and 3-D grids for turbomachinery blade geometries was performed, and as an extension of this research we are planning to develop an adaptive grid procedure with an interactive grid environment.

Nakamura, S.↗

NASA NTRS1992

Analysis of Large Quasistatic Deformations of Inelastic Solids by a New Stress Based Finite Element Method

A new hybrid stress finite element algorithm suitable for analyses of large quasistatic deformation of inelastic solids is presented. Principal variables in the formulation are the nominal stress rate and spin. The finite element equations which result are discrete versions of the equations of compatibility and angular momentum balance. Consistent reformulation of the constitutive equation and accurate and stable time integration of the stress are discussed at length. Examples which bring out the feasibility and performance of the algorithm conclude the work.

Reed, Kenneth W.↗

NASA NTRS1996

CI Controls for Energy and Environment

Computational intelligence (CI) is a rapidly evolving field that utilizes life imitating metaphors for guiding model building including, but not limited to neural networks, fuzzy logic, genetic algorithms, artificial life, and hybrid CI paradigms. Although the boundaries between artificial intelligence (AI) and CI are not distinct, their research communities are separate and distinct. CI researchers tend to focus on processing numerical data from sensors, while the AI community generally relies on symbolic computing to capture human knowledge. In both areas, there is a great deal of interest and activity in hybrid systems that can offset the limitations of individual methods, extend their capabilities, and create new capabilities. Examples of the benefits that can accrue from hybrid systems are contained.

Biondo, Samuel J.↗

NASA NTRS2002

NASA Smart Surgical Probe Project

Information Technologies being developed by NASA to assist astronaut-physician in responding to medical emergencies during long space flights are being employed for the improvement of women's health in the form of "smart surgical probe". This technology, initially developed for neurosurgery applications, not only has enormous potential for the diagnosis and treatment of breast cancer, but broad applicability to a wide range of medical challenges. For the breast cancer application, the smart surgical probe is being designed to "see" a suspicious lump, determine by its features if it is cancerous, and ultimately predict how the disease may progress. A revolutionary early breast cancer detection tool based on this technology has been developed by a commercial company and is being tested in human clinical trials at the University of California at Davis, School of Medicine. The smart surgical probe technology makes use of adaptive intelligent software (hybrid neural networks/fuzzy logic algorithms) with the most advanced physiologic sensors to provide real-time in vivo tissue characterization for the detection, diagnosis and treatment of tumors, including determination of tumor microenvironment and evaluation of tumor margins. The software solutions and tools from these medical applications will lead to the development of better real-time minimally-invasive smart surgical probes for emergency medical care and treatment of astronauts on long space flights.

Mah, Robert W.↗

NASA NTRS2008

Aircraft Engine On-Line Diagnostics Through Dual-Channel Sensor Measurements: Development of an Enhanced System

In this paper, an enhanced on-line diagnostic system which utilizes dual-channel sensor measurements is developed for the aircraft engine application. The enhanced system is composed of a nonlinear on-board engine model (NOBEM), the hybrid Kalman filter (HKF) algorithm, and fault detection and isolation (FDI) logic. The NOBEM provides the analytical third channel against which the dual-channel measurements are compared. The NOBEM is further utilized as part of the HKF algorithm which estimates measured engine parameters. Engine parameters obtained from the dual-channel measurements, the NOBEM, and the HKF are compared against each other. When the discrepancy among the signals exceeds a tolerance level, the FDI logic determines the cause of discrepancy. Through this approach, the enhanced system achieves the following objectives: 1) anomaly detection, 2) component fault detection, and 3) sensor fault detection and isolation. The performance of the enhanced system is evaluated in a simulation environment using faults in sensors and components, and it is compared to an existing baseline system.

Kobayashi, Takahisa↗

NASA NTRS2012

Follow on Researches for X-56A Aircraft at NASA Dryden Flight Research Center (Progress Report)

A lot of composite materials are used for the modern aircraft to reduce its weight. Aircraft aeroservoelastic models are typically characterized by significant levels of model parameter uncertainty due to composite manufacturing process. Small modeling errors in the finite element model will eventually induce errors in the structural flexibility and mass, thus propagating into unpredictable errors in the unsteady aerodynamics and the control law design. One of the primary objectives of X-56A aircraft is the flight demonstration of active flutter suppression, and therefore in this study, the identification of the primary and secondary modes is based on the flutter analysis of X-56A aircraft. It should be noted that for all three Mach number cases rigid body modes and mode numbers seven and nine are participated 89.1 92.4 % of the first flutter mode. Modal participation of the rigid body mode and mode numbers seven and nine for the second flutter mode are 94.6 96.4%. Rigid body mode and the first two anti-symmetric modes, eighth and tenth modes, are participated 93.2 94.6% of the third flutter mode. Therefore, rigid body modes and the first four flexible modes of X-56A aircraft are the primary modes during the model tuning procedure. The ground vibration test-validated structural dynamic finite element model of the X-56A aircraft is to obtain in this study. The structural dynamics finite element model of X-56A aircraft is improved using the parallelized big-bang big-crunch algorithm together with a hybrid optimization technique.

Structural Dynamic Model Tuning↗

NASA NTRSDate not supplied

Hyperspectral Sounder Spectral Fingerprinting: Using Machine Learning Techniques to Enhance Model-Based Physical Inversion

Different retrieval algorithms have been developed to process top-of-atmosphere (TOA) spectral radiance data provided by hyperspectral infrared sounder missions. Those algorithms are either optimal estimation method (OEM) based schemes with radiative transfer calculation involved in the retrieval process, or machine learning based methods that allow ultra-efficient data procession but lack of radiometric consistency validation based on the directly measured information. Combining both approaches leverages their respective technical advantages, leading to more accurate results. This study introduces a hyperspectral sounder fingerprinting algorithm to explore this hybrid approach. This approach involves the use of a spectral information-based classification method to identify an reference geophysical state and the corresponding radiative kernel. This enables the efficient retrieval of geophysical variables of interest through a radiative kernel-based linear inversion procedure. The fingerprinting method has been applied to analyze a decade-long hyperspectral sounder data record.

Wan Wu↗

DOE OSTI2024

Integrating machine learning interatomic potentials with hybrid reverse Monte Carlo structure refinements in RMCProfile

Structure refinement with reverse Monte Carlo (RMC) is a powerful tool for interpreting experimental diffraction data. To ensure that the under-constrained RMC algorithm yields reasonable results, the hybrid RMC approach applies interatomic potentials to obtain solutions that are both physically sensible and in agreement with experiment. To expand the range of materials that can be studied with hybrid RMC, we have implemented a new interatomic potential constraint in RMCProfile that grants flexibility to apply potentials supported by the Large-scale Atomic/Molecular Massively Parallel Simulator ( LAMMPS ) molecular dynamics code. This includes machine learning interatomic potentials, which provide a pathway to applying hybrid RMC to materials without currently available interatomic potentials. To this end, we present a methodology to use RMC to train machine learning interatomic potentials for hybrid RMC applications.

Cuillier, Paul↗