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DOE OSTI2025

SympGNNs: Symplectic Graph Neural Networks for identifying high-dimensional Hamiltonian systems and node classification

Existing neural network models to learn Hamiltonian systems, such as SympNets, although accurate in low-dimensions, struggle to learn the correct dynamics for high-dimensional many-body systems. Herein, we introduce Symplectic Graph Neural Networks (SympGNNs) that can effectively handle system identification in high-dimensional Hamiltonian systems, as well as node classification. SympGNNs combine symplectic maps with permutation equivariance, a property of graph neural networks. Specifically, we propose two variants of SympGNNs: (i) G-SympGNN and (ii) LA-SympGNN, arising from different parameterizations of the kinetic and potential energy. We demonstrate the capabilities of SympGNN on two physical examples: a 40-particle coupled Harmonic oscillator, and a 2000-particle molecular dynamics simulation in a two-dimensional Lennard-Jones potential. Furthermore, we demonstrate the performance of SympGNN in the node classification task, achieving accuracy comparable to the state-of-the-art. Finally, we also empirically show that SympGNN can overcome the oversmoothing and heterophily problems, two key challenges in the field of graph neural networks.

Deep learning↗

DOE OSTI2025

Systematic many-fermion Hamiltonian input scheme and spectral calculations on quantum computers

We present a novel input scheme for general second-quantized Hamiltonians of relativistic or non-relativistic many-fermion systems. This input scheme incorporates the fermionic anticommutation relations, particle number variations, and respects the symmetries of the Hamiltonian. Based on our input scheme, we propose a hybrid quantum-classical framework for spectral calculations on future quantum hardwares. We provide explicit circuit designs and the associated gate cost. We demonstrate our hybrid framework by solving the low-lying spectra of 42 Ca and 46 Ca. Our input scheme provides new pathways to solving the spectra and dynamics of the relativistic and nonrelativistic many-fermion systems via first-principles approaches.

Hybrid spectral calculation framework↗

DOE OSTI2025

More about the lattice Hamiltonian for Adjoint QCD 2

In our earlier work [1], we introduced a lattice Hamiltonian for Adjoint QCD 2 using staggered Majorana fermions. We found the gauge invariant space of states explicitly for the gauge group SU(2) and used them for numerical calculations of observables, such as the spectrum and the expectation value of the fermion bilinear. In this paper, we carry out a more in-depth study of our lattice model, extending it to any compact and simply-connected gauge group G. We show how to find the gauge invariant space of states and use it to study various observables. We also use the lattice model to calculate the mixed ’t Hooft anomalies of Adjoint QCD 2 for arbitrary G. We show that the matrix elements of the lattice Hamiltonian can be expressed in terms of the Wigner 6j-symbols of G. For G = SU(3), we perform exact diagonalization for lattices of up to six sites and study the low-lying spectrum, the fermion bilinear condensate, and the string tension. We also show how to write the lattice strong coupling expansion for ground state energies and operator expectation values in terms of the Wigner 6j-symbols. For SU(3) we carry this out explicitly and find good agreement with the exact diagonalizations, and for SU(4) we give expansions that can be compared with future numerical studies.

confinement↗

DOE OSTI2024

Security of quantum position-verification limits Hamiltonian simulation via holography

We investigate the link between quantum position-verification (QPV) and holography established in [1] using holographic quantum error correcting codes as toy models. By inserting the “temporal” scaling of the AdS metric by hand via the bulk Hamiltonian interaction strength, we recover a toy model with consistent causality structure. This leads to an interesting implication between two topics in quantum information: if position-based verification is secure against attacks with small entanglement then there are new fundamental lower bounds for resources required for one Hamiltonian to simulate another.

AdS-CFT Correspondence↗

DOE OSTI2024

Generalized boost transformations in finite volumes and application to Hamiltonian methods

The investigation of hadron interactions within lattice QCD has been facilitated by the well-known quantisation condition, linking scattering phase shifts to finite-volume energies. Additionally, the ability to utilise systems at finite total boosts has been pivotal in smoothly charting the energy-dependent behaviour of these phase shifts. The existing implementations of the quantization condition at finite boosts rely on momentum transformations between rest and moving frames, defined directly in terms of the energy eigenvalues. This energy dependence is unsuitable in the formulation of a Hamiltonian. In this work, we introduce a novel approach to generalise the three-momentum boost prescription, enabling the incorporation of energy-independent finite-volume Hamiltonians within moving frames. We demonstrate the application of our method through numerical comparisons, employing a phenomenological ππ scattering example.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Hamiltonian switching control of noisy bipartite qubit systems

Abstract We develop a Hamiltonian switching ansatz for bipartite control that is inspired by the quantum approximate optimization algorithm, to mitigate environmental noise on qubits. We demonstrate the control for a central spin coupled to bath spins via isotropic Heisenberg interactions, and then make physical applications to the protection of quantum gates performed on superconducting transmon qubits coupling to environmental two-level-systems (TLSs) through dipole-dipole interactions, as well as on such qubits coupled to both TLSs and a Lindblad bath. The control field is classical and acts only on the system qubits. We use reinforcement learning with policy gradient to optimize the Hamiltonian switching control protocols, using a fidelity objective for specific target quantum gates. We use this approach to demonstrate effective suppression of both coherent and dissipative noise, with numerical studies achieving target gate implementations with fidelities over 0.9999 (four nines) in the majority of our test cases and showing improvement beyond this to values of 0.999 999 999 (nine nines) upon a subsequent optimization by GRadient Ascent Pulse Engineering (GRAPE). We analyze how the control depth, total evolution time, number of environmental TLS, and choice of optimization method affect the fidelity achieved by the optimal protocols and reveal some critical behaviors of bipartite control of quantum gates.

Physics↗

DOE OSTI2025

Topological triviality of flat Hamiltonians

Landau levels play a key role in theoretical models of the quantum Hall effect. Each Landau level is degenerate, flat, and topologically nontrivial. Motivated by Landau levels, we study tight-binding Hamiltonians whose energy levels are all flat. Here, we demonstrate that in two dimensions, for such Hamiltonians, the flat bands must be topologically trivial. To that end, we show that the projector onto each flat band is necessarily strictly local. Our conclusions do not need the assumption of lattice translational invariance.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Neutrino many-body flavor evolution: The full Hamiltonian

We study neutrino flavor evolution in the quantum many-body approach using the full neutrino-neutrino Hamiltonian, including the usually neglected terms that mediate nonforward scattering processes. Working in the occupation number representation with plane waves as single-particle states, we explore the time evolution of simple initial states with up to N = 10 neutrinos. We discuss the time evolution of the Loschmidt echo, one body flavor and kinetic observables, and the one-body entanglement entropy. For the small systems considered, we observe “thermalization” of both flavor and momentum degrees of freedom on comparable time scales, with results converging towards expectation values computed within a microcanonical ensemble. We also observe that the inclusion of nonforward processes generates a faster flavor evolution compared to the one induced by the truncated (forward) Hamiltonian. Published by the American Physical Society 2024

Cirigliano, Vincenzo (ORCID:000000029056754X)↗

DOE OSTI2025

Fully gauge-fixed SU(2) Hamiltonian for quantum simulations

Here, we demonstrate how to construct a fully gauge-fixed lattice Hamiltonian for a pure SU(2) gauge theory. Our work extends upon previous work, where a formulation of an SU(2) lattice gauge theory was developed that is efficient to simulate at all values of the gauge coupling. That formulation utilized maximal-tree gauge, where all local gauge symmetries are fixed and a residual global gauge symmetry remains. By using the geometric picture of an SU(2) lattice gauge theory as a system of rotating rods, we demonstrate how to fix the remaining global gauge symmetry. In particular, the quantum numbers associated with total charge can be isolated by rotating between the lab and body frames using the three Euler angles. The Hilbert space in this new “sequestered” basis partitions cleanly into sectors with differing total angular momentum, which makes gauge-fixing to a particular total charge sector trivial, particularly for the charge-zero sector. In addition to this sequestered basis inheriting the property of being efficient at all values of the coupling, we show that, despite the global nature of the final gauge-fixing procedure, this Hamiltonian can be simulated using quantum resources scaling only polynomially with the lattice volume.

Lattice gauge theory↗

DOE OSTI2025

First-principles effective Hamiltonian for finite-temperature modeling of nonperovskite ferroelectrics

First-principles-based effective Hamiltonian techniques have been widely employed for over three decades to investigate ferroelectricity and related phenomena in perovskite materials. These techniques offer high accuracy, transferability, compatibility with various finite-temperature algorithms, computational efficiency, and ease in incorporating interactions with external fields. They have been adapted to study diverse phenomena, ranging from topological dipole patterns in ferroelectric nanostructures to multicaloric effects. In this work, we develop an effective Hamiltonian for the nonperovskite ferroelectric HfO 2 (hafnia). Applying this methodology to explore the finite-temperature and finite-electric-field properties of ferroelectric hafnia revealed (1) exceptionally large intrinsic coercive fields, an order of magnitude higher than those observed in perovskite ferroelectrics; (2) their atomistic origin; and (3) the existence of a regime where the relationship between the coercive field and the energy barrier for polarization reversal is counterintuitive. Here, these developments could accelerate progress both in methodological advancements for simulating ferroics and in the atomistic understanding of a broad range of ferroelectrics.

Electric polarization↗

DOE OSTI2025

Hamiltonian parameter inference from resonant inelastic x-ray scattering with active learning

Identifying model Hamiltonians is a vital step toward creating predictive models of materials. Here, in this study, we combine Bayesian optimization with the EDRIXS numerical package to infer Hamiltonian parameters from resonant inelastic x-ray scattering (RIXS) spectra within the single atom approximation. To evaluate the efficacy of our method, we test it on experimental RIXS spectra of NiPS 3 , NiCl 2 , Ca 3 ⁢LiOsO 6 , and Fe 2⁢ O 3 , and demonstrate that it can reproduce results obtained from hand-fitted parameters to a precision similar to expert human analysis while providing a more systematic mapping of parameter space. Our work provides a key first step toward solving the inverse scattering problem to extract effective multi-orbital models from information-dense RIXS measurements, which can be applied to a host of quantum materials. We also propose atomic model parameter sets for two materials, Ca 3⁢ LiOsO 6 and Fe 2⁢ O 3 , that were previously missing from the literature.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Sharp Page transitions in generic Hamiltonian dynamics

Here, we consider the entanglement dynamics of a subsystem initialized in a pure state at high energy density (corresponding to negative temperature) and coupled to a cold bath. The subsystem's Rényi entropies 𝑆 𝛼 first rise as the subsystem gets entangled with the bath and then fall as the subsystem cools. We find that the peak of the min-entropy, lim 𝛼→∞ ⁡𝑆 𝛼 , sharpens to a cusp in the thermodynamic limit at a well-defined time we call the Page time. We construct a hydrodynamic ansatz for the evolution of the entanglement Hamiltonian, which accounts for the sharp Page transition as well as the intricate dynamics of the entanglement spectrum before the Page time. Our results hold both when the bath has the same Hamiltonian as the system and when the bath is taken to be Markovian. Our ansatz suggests conditions under which the Page transition should remain sharp even for Rényi entropies of finite index 𝛼.

dynamical phase transitions↗

DOE OSTI2024

HamLib: A library of Hamiltonians for benchmarking quantum algorithms and hardware

In order to characterize and benchmark computational hardware, software, and algorithms, it is essential to have many problem instances on-hand. This is no less true for quantum computation, where a large collection of real-world problem instances would allow for benchmarking studies that in turn help to improve both algorithms and hardware designs. To this end, here we present a large dataset of qubit-based quantum Hamiltonians. The dataset, called HamLib (for Hamiltonian Library), is freely available online and contains problem sizes ranging from 2 to 1000 qubits. HamLib includes problem instances of the Heisenberg model, Fermi-Hubbard model, Bose-Hubbard model, molecular electronic structure, molecular vibrational structure, MaxCut, Max- k -SAT, Max- k -Cut, QMaxCut, and the traveling salesperson problem. The goals of this effort are (a) to save researchers time by eliminating the need to prepare problem instances and map them to qubit representations, (b) to allow for more thorough tests of new algorithms and hardware, and (c) to allow for reproducibility and standardization across research studies.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Neutrinoless Double-Beta Decay Investigations of 82Se Using Three Shell Model Hamiltonians

Neutrinoless double-beta decay is considered one of the most promising processes that would help clarify some of the symmetry-breaking problems in our understanding of the observable universe. Recent studies of neutrinoless double-beta decay matrix elements have employed statistical approaches based on modified shell model effective Hamiltonians for 48Ca (Phys. Rev. C 106, 054302 (2022)) and 136Xe (Phys. Rev. C 107, 045501 (2023)). The analyses rely on inducing perturbations in the starting effective Hamiltonians to observe the behavior of a wide range of observables, besides the 0νββ) NME, that are compared with experimental data. Following a Bayesian model averaging approach, the range of probable values for the neutrinoless double-beta decay matrix elements is presented. In this paper, we present a similar study for 82Se, which is described in the same model space as 76Ge that is under experimental observation. Due to its faster calculation time compared to 76Ge, 82Se can be used as an appropriate substitute in our complex statistical study. Using the calculations performed for the statistical analysis of the neutrinoless double-beta decay matrix elements, we also search for the correlations between the observables that we can compare to experimental data.

Science & Technology - Other Topics↗

NASA NTRS1971

Hamiltonian formulation of guiding center motion

The nonrelativistic guiding center motion of a charged particle in a static magnetic field is derived using the Hamiltonian formalism. By repeated application of first-order canonical perturbation theory, the first two adiabatic invariants and their averaged Hamiltonians are obtained, including the first-order correction terms. Other features of guiding center theory are also given, including lowest order drifts and the flux invariant.

Stern, D. P.↗

NASA NTRS1978

Numerical integration of nearly-Hamiltonian systems

The reported investigation is concerned with the solution of systems of differential equations which are derived from a Hamiltonian function in the extended phase space. The problem selected involves a one-dimensional perturbed harmonic oscillator. The van der Pol equation considered has an exact asymptotic value for its amplitude. Comparisons are made between a numerical solution and a known analytical solution. In addition to the van der Pol problem, known solutions regarding the restricted problem of three bodies are used as examples for perturbed Keplerian motion. The extended phase space Hamiltonian discussed by Stiefel and Scheifele (1971) is considered. A description is presented of two canonical formulations of the perturbed harmonic oscillator.

Bond, V. R.↗

NASA NTRS1988

A study to evaluate STS heads-up ascent trajectory performance employing a minimum-Hamiltonian optimization strategy

A study was conducted to evaluate the performance implications of a heads-up ascent flight design for the Space Transportation System, as compared to the current heads-down flight mode. The procedure involved the use of the Minimum Hamiltonian Ascent Shuttle Trajectory Evaluation Program, which is a three-degree-of-freedom moment balance simulation of shuttle ascent. A minimum-Hamiltonian optimization strategy was employed to maximize injection weight as a function of maximum dynamic pressure constraint and Solid Rocket Motor burnrate. Performance Reference Mission Four trajectory groundrules were used for consistency. The major conclusions are that for heads-up ascent and a mission nominal design maximum dynamic pressure value of 680 psf, the optimum solid motor burnrate is 0.394 ips, which produces a performance enhancement of 4293 lbm relative to the baseline heads-down ascent, with 0.368 ips burnrate solid motors and a 680 psf dynamic pressure constraint. However, no performance advantage exists for heads-up flight if the current Solid Rocket Motor target burnrate of 0.368 ips is used. The advantage of heads-up ascent flight employing the current burnrate is that Space Shuttle Main Engine throttling for dynamic pressure control is not necessary.

Sinha, Sujit↗

NASA NTRS1990

Boson Hamiltonians and stochasticity for the vorticity equation

The evolution of the vorticity in time for two-dimensional inviscid flow and in Lagrangian time for three-dimensional viscous flow is written in Hamiltonian form by introducing Bose operators. The addition of the viscous and convective terms, respectively, leads to an interpretation of the Hamiltonian contribution to the evolution as Langevin noise.

Shen, Hubert H.↗