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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Collective neutrino oscillations on a quantum computer with hybrid quantum-classical algorithm

We simulate the time evolution of collective neutrino oscillations in two-flavor settings on a quantum computer. We explore the generalization of Trotter-Suzuki approximation to time-dependent Hamiltonian dynamics. The trotterization steps are further optimized using the Cartan decomposition of two-qubit unitary gates U ϵ SU(4) in the minimum number of controlled-NOT (CNOT) gates making the algorithm more resilient to the hardware noise. As a result, a more efficient hybrid quantum-classical algorithm is also explored to solve the problem on noisy intermediate-scale quantum devices.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity

We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by (i) the temporal trajectory of a quantum state under unitary evolution or (ii) the quantum states of small subsystems obtained by partial, local projective measurements performed on their complements. These cases, respectively, exemplify the phenomena of “Hilbert-space ergodicity” and “deep thermalization.” In both cases, the resultant ensembles are defined by a simple principle: The distributions of pure states have maximum entropy, subject to constraints such as energy conservation, and effective constraints imposed by thermalization. We present and numerically verify quantifiable signatures of this principle by deriving explicit formulas for all statistical moments of the ensembles, proving the necessary and sufficient conditions for such universality under widely accepted assumptions, and describing their measurable consequences in experiments. We further discuss information-theoretic implications of the universality: Our ensembles have maximal information content while being maximally difficult to interrogate, establishing that generic quantum state ensembles that occur in nature hide (scramble) information as strongly as possible. Our results generalize the notions of Hilbert-space ergodicity to time-independent Hamiltonian dynamics and deep thermalization from infinite to finite effective temperature. Our work presents new perspectives to characterize and understand universal behaviors of quantum dynamics using statistical and information-theoretic tools.

Eigenstate thermalization↗
DOE OSTI2025

Optimizers for stabilizing likelihood-free inference

A growing number of applications in particle physics and beyond use neural networks as unbinned likelihood ratio estimators applied to real or simulated data. Precision requirements on the inference tasks demand a high-level of stability from these networks, which are affected by the stochastic nature of training. We show how physics concepts can be used to stabilize network training through a physics-inspired optimizer. In particular, the energy conserving descent (ECD) optimization framework uses classical Hamiltonian dynamics on the space of network parameters to reduce the dependence on the initial conditions while also stabilizing the result near the minimum of the loss function. We develop a version of this optimizer known as , which has few free hyperparameters with limited ranges guided by physical reasoning. We apply to representative likelihood-ratio estimation tasks in particle physics and find on average that it out-performs the widely used Adam optimizer. We expect that ECD will be a useful tool for wide array of data-limited problems, where it is computationally expensive to exhaustively optimize hyperparameters and mitigate fluctuations with ensembling.

Monte Carlo methods↗
DOE OSTI2025

Construction of approximate invariants for non-integrable Hamiltonian systems

We present a method to construct high-order polynomial approximate invariants (AI) for non integrable Hamiltonian dynamical systems, and apply it to a modern ring-based particle accelerator. Taking advantage of a special property of one-turn transformation maps in the form of a square matrix, AIs can be constructed order-by-order iteratively. Evaluating AI with simulation data, we observe that AI’s fluctuation is actually a measure of chaos. Through minimizing the fluctuations, the stable region of long-term motions, i.e., the dynamic aperture of the accelerator, could be enlarged.

43 PARTICLE ACCELERATORS↗
DOE OSTI2026

Quantum-Inspired Bayesian Sampling for Uncertainty Quantification and Machine Learning (Final Technical Report)

With increasing simulation and measurement data, machine learning and artificial intelligence have been widely used in computational decision-making of complex engineering systems. The resulting tools, such as uncertainty quantification solvers, reinforcement learning, and physics-informed machine learning, have achieved great success in critical DOE tasks such as material discovery and design, energy system modeling and control, and numerical weather and climate prediction. A core topic in scientific machine learning and artificial intelligence is Bayesian inference: given an observed data set, people want to estimate the posterior distribution of a (possibly large) number of hidden parameters. Due to the flexibility and weak assumptions, Bayesian sampling has been the mainstream Bayesian inference solvers despite the rapid progress of approximate Bayesian inference. Classical Bayesian sampling methods such as Markov-chain Monte Carlo suffer from a low-acceptance rate due to the random walk nature, therefore state-of-the-art techniques use Hamiltonian Monte Carlo and its variants to efficiently draw posterior samples in a high dimension. The key idea of Hamiltonian Monte Carlo and its variants is to simulate the Hamiltonian dynamics of a classical particle with a fixed mass, and their performance significantly degrades when the posterior distribution is highly spiky or has multiple modes. Leveraging the idea of quantum physics, this project has investigated new theory, algorithms and applications of Bayesian inference (especially Bayesian sampling). The main results include: (1) novel quantum-inspired Bayesian sampling methods that can lead to better accuracy for challenging multi-modal or spiky distributions, (2) more scalable machine learning framework leveraging tensor-compressed Bayesian inference, and (3) Bayesian and sampling approaches for verifying the robustness of continuous and binary neural networks.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

Invariant two-dimensional structures of vorticity field in nonviscous fluid

It is shown that a fluid flow which are invariant under translations along their vorticity field directions can be described in terms of a formally 2D system. Its nonviscous behavior of the scalar vorticity is governed by Hamiltonian dynamics, similar to the 2D line vortex case. Applying a statistical mechanical method, the equilibrium distribution of the vorticity field for such a general 2D system is shown to obey a nonlinear partial differential equation that is a generalization of the sinh-Poisson equation derived by Montgomery and Joyce (1973, 1974). Thus, if the domain containing the fluid is finite, similar negative temperature states may occur and the distribution of the vorticity intensity may become localized in space. The results are believed to have applications in studying large-scale partial and temporal properties of flows having small but nonzero viscosity. The analysis can probably be extended to other fluid systems with curved magnetic field lines.

Chen, Hudong↗
NASA NTRS1994

Fourfold Clusters of Rovibrational Energies in H2Te Studied With an Ab Initio Potential Energy Function

We report an ab initio investigation of the cluster effect (i.e., the formation of nearly degenerate, four member groups of rotation-vibration energy levels at higher J and K(sub a). values) in the H2Te molecule. The potential energy function has been calculated ab initio at a total of 334 molecular geometries by means of the CCSD(T) method where the (1s-4f) core electrons of Te were described by an effective core potential. The values of the potential energy function obtained cover the region up to around 10,000/cm above the equilibrium energy. On the basis of the ab initio potential, the rotation-vibration energy spectra of H2Te-130 and its deuterated isotopomers have been calculated with the MORBID (Morse Oscillator Rigid Bender Internal Dynamics) Hamiltonian and computer program. In particular, we have calculated the rotational energy manifolds for J less than or = 40 in the vibrational ground state, the upsilon(sub 2) state, the "first triad" (the upsilon(sub l)/upsilon(sub 3)/2upsilon(sub 2) interacting vibrational states), and the "second triad" (the upsilon(sub 1) + upsilon(sub 2/upsilon(sub 2) + upsilon(sub 3)/3upsilon(sub 2) states) of H2Te-130. We find that the cluster formation in H2Te is very similar to those of of H2Se and H2S, which we have studied previously. However, contrary to semiclassical predictions, we do not determine any significant displacement of the clusters towards lower J values relative to H2Se. Hence the experimental observation of the cluster states in H2Te will be at least as difficult as in H2Se.

Jensen, Per↗
DOE OSTI2024

Light-induced electron dynamics of molecules in cavities: comparison of model Hamiltonians

The rapidly expanding field of polaritonic chemistry requires accurate theoretical simulations to understand new phenomena at the atomic scale. Computing the optoelectronic properties of molecules using established electronic structure methods is a careful balance of accuracy and computational expense, and expanding these methods to quantum electrodynamics to describe coupled cavity-molecule systems is an active topic of development. Key to these methods are the Hamiltonian operators representing the photon cavity modes. The recently introduced quantum electrodynamics time-dependent configuration interaction (QED-TDCI) method allows for the combination of electron dynamics simulations with quantum electrodynamics, enabling the simulation of time-dependent optoelectronic properties of cavity-molecule systems. Using this method, a comparison of two many-state QED Hamiltonians—the Pauli-Fierz and quantum Rabi model Hamiltonians—is presented, with a particular focus on time-dependent properties in applied electric fields.

Peyton, Benjamin G. (ORCID:0000000163190751)↗
DOE OSTI2020

Machine learning a molecular Hamiltonian for predicting electron dynamics

We develop a computational method to learn a molecular Hamiltonian matrix from matrix-valued time series of the electron density. As we demonstrate for three small molecules, the resulting Hamiltonians can be used for electron density evolution, producing highly accurate results even when propagating 1,000 time steps beyond the training data. As a more rigorous test, we use the learned Hamiltonians to simulate electron dynamics in the presence of an applied electric field, extrapolating to a problem that is beyond the field-free training data. We find that the resulting electron dynamics predicted by our learned Hamiltonian are in close quantitative agreement with the ground truth. Our method relies on combining a reduced-dimensional, linear statistical model of the Hamiltonian with a time-discretization of the quantum Liouville equation within time-dependent Hartree Fock theory. In conclusion, we train the model using a least-squares solver, avoiding numerous, CPU-intensive optimization steps. For both field-free and field-on problems, we quantify training and propagation errors, highlighting areas for future development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Partial dynamical symmetry versus quasi dynamical symmetry examination within a quantum chaos analyses of spectral data for even–even nuclei

Statistical analyses of the spectral distributions of rotational bands in 51 deformed prolate even–even nuclei in the 152 ≤ A ≤ 250 mass region $R_{{4_{1}^{ + } /2_{1}^{ + } }} \ge 3.00$ are examined in terms of nearest neighbor spacing distributions. Specifically, the focus is on data for 0 + , 2 + , and 4 + energy levels of the ground, gamma, and beta bands. The chaotic behavior of the gamma band, especially the position of the $2_{\gamma }^{ + }$ band-head compared to other levels and bands, is clear. The levels are analyzed within the framework of two models, namely, a SU(3)-partial dynamical symmetry Hamiltonian and a SU(3) two-coupled quasi-dynamical symmetry Hamiltonian, with results that are further analyzed using random matrix theory. The partial and quasi dynamics both yield outcomes that are in reasonable agreement with the known experimental results. However, due to the degeneracy of the beta and gamma bands within the simplest SU(3) picture, the theory cannot be used to describe the fluctuation properties of excited bands. By changing relative weights of the different terms in the partial and quasi dynamical Hamiltonians, results are obtained that show more GOE-like statistics in the partial dynamical formalism as the strength of the pairing term is increased. Also, in the quasi-dynamical symmetry limit, more correlations are found because of the stronger couplings.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

The Gauge Picture of Quantum Dynamics

Although local Hamiltonians exhibit local time dynamics, this locality is not explicit in the Schrödinger picture in the sense that the wavefunction amplitudes do not obey a local equation of motion. We show that geometric locality can be achieved explicitly in the equations of motion by "gauging" the global unitary invariance of quantum mechanics into a local gauge invariance. That is, expectation values $\langle \psi|A|\psi \rangle$ are invariant under a global unitary transformation acting on the wavefunction $|\psi\rangle \to U |\psi\rangle$ and operators $A \to U A U^\dagger$, and we show that it is possible to gauge this global invariance into a local gauge invariance. To do this, we replace the wavefunction with a collection of local wavefunctions $|\psi_J\rangle$, one for each patch of space $J$. The collection of spatial patches is chosen to cover the space; e.g. we could choose the patches to be single qubits or nearest-neighbor sites on a lattice. Local wavefunctions associated with neighboring pairs of spatial patches $I$ and $J$ are related to each other by dynamical unitary transformations $U_{IJ}$. The local wavefunctions are local in the sense that their dynamics are local. That is, the equations of motion for the local wavefunctions $|\psi_J\rangle$ and connections $U_{IJ}$ are explicitly local in space and only depend on nearby Hamiltonian terms. (The local wavefunctions are many-body wavefunctions and have the same Hilbert space dimension as the usual wavefunction.) We call this picture of quantum dynamics the gauge picture since it exhibits a local gauge invariance. The local dynamics of a single spatial patch is related to the interaction picture, where the interaction Hamiltonian consists of only nearby Hamiltonian terms. We can also generalize the explicit locality to include locality in local charge and energy densities.

Physics↗
DOE OSTI2024

Practical Hamiltonian learning with unitary dynamics and Gibbs states

We study the problem of learning the parameters for the Hamiltonian of a quantum many-body system, given limited access to the system. In this work, we build upon recent approaches to Hamiltonian learning via derivative estimation. We propose a protocol that improves the scaling dependence of prior works, particularly with respect to parameters relating to the structure of the Hamiltonian (e.g., its locality k). Furthermore, by deriving exact bounds on the performance of our protocol, we are able to provide a precise numerical prescription for theoretically optimal settings of hyperparameters in our learning protocol, such as the maximum evolution time (when learning with unitary dynamics) or minimum temperature (when learning with Gibbs states). Thanks to these improvements, our protocol has practical scaling for large problems: we demonstrate this with a numerical simulation of our protocol on an 80-qubit system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Hamiltonian structure of 2D fluid dynamics with broken parity

Isotropic fluids in two spatial dimensions can break parity symmetry and sustain transverse stresses which do not lead to dissipation. Corresponding transport coefficients include odd viscosity, odd torque, and odd pressure. We consider an isotropic Galilean invariant fluid dynamics in the adiabatic regime with momentum and particle density conservation. We find conditions on transport coefficients that correspond to dissipationless and separately to Hamiltonian fluid dynamics. The restriction on the transport coefficients will help identify what kind of hydrodynamics can be obtained by coarse-graining a microscopic Hamiltonian system. Interestingly, not all parity-breaking transport coefficients lead to energy conservation and, generally, the fluid dynamics is energy conserving but not Hamiltonian. We show how this dynamics can be realized by imposing a nonholonomic constraint on the Hamiltonian system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Koopman–von Neumann approach to quantum simulation of nonlinear classical dynamics

Quantum computers can be used to simulate nonlinear non-Hamiltonian classical dynamics on phase space by using the generalized Koopman–von Neumann formulation of classical mechanics. The Koopman–von Neumann formulation implies that the conservation of the probability distribution function on phase space, as expressed by the Liouville equation, can be recast as an equivalent Schrödinger equation on Hilbert space with a Hermitian Hamiltonian operator and a unitary propagator. This Schrödinger equation is linear in the momenta because it derives from a constrained Hamiltonian system with twice the classical phase-space dimension. A quantum computer with finite resources can be used to simulate a finite-dimensional approximation of this unitary evolution operator. Quantum simulation of classical dynamics is exponentially more efficient than a deterministic Eulerian discretization of the Liouville equation if the Koopman–von Neumann Hamiltonian is sparse. Utilizing quantum walk techniques for state preparation and amplitude estimation for the calculation of observables leads to a quadratic improvement over classical probabilistic Monte Carlo algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Heisenberg-limited Hamiltonian learning for interacting bosons

We develop a protocol for learning a class of interacting bosonic Hamiltonians from dynamics with Heisenberg-limited scaling. For Hamiltonians with an underlying bounded-degree graph structure, we can learn all parameters with root mean square error ϵ using ${\mathcal{O}}(1/\epsilon )$ total evolution time, which is independent of the system size, in a way that is robust against state-preparation and measurement error. In the protocol, we only use bosonic coherent states, beam splitters, phase shifters, and homodyne measurements, which are easy to implement on many experimental platforms. A key technique we develop is to apply random unitaries to enforce symmetry in the effective Hamiltonian, which may be of independent interest.

computer science↗