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Integration of machine learning with neutron scattering for the Hamiltonian tuning of spin ice under pressure
Quantum materials research requires co-design of theory with experiments and involves demanding simulations and the analysis of vast quantities of data, usually including pattern recognition and clustering. Artificial intelligence is a natural route to optimise these processes and bring theory and experiments together. Here, we propose a scheme that integrates machine learning with high-performance simulations and scattering measurements, covering the pipeline of typical neutron experiments. Our approach uses nonlinear autoencoders trained on realistic simulations along with a fast surrogate for the calculation of scattering in the form of a generative model. We demonstrate this approach in a highly frustrated magnet, Dy 2 Ti 2 O 7 , using machine learning predictions to guide the neutron scattering experiment under hydrostatic pressure, extract material parameters and construct a phase diagram. Our scheme provides a comprehensive set of capabilities that allows direct integration of theory along with automated data processing and provides on a rapid timescale direct insight into a challenging condensed matter system.
Nuclear studies with FSU Hamiltonian
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Machine learning Frenkel Hamiltonian parameters to accelerate simulations of exciton dynamics
In this manuscript, we develop multiple machine learning (ML) models to accelerate a scheme for parameterizing site-based models of exciton dynamics from all-atom configurations of condensed phase sexithiophene systems. This scheme encodes the details of a system’s specific molecular morphology in the correlated distributions of model parameters through the analysis of many single-molecule excited-state electronic-structure calculations. These calculations yield excitation energies for each molecule in the system and the network of pair-wise intermolecular electronic couplings. In this work, we demonstrate that the excitation energies can be accurately predicted using a kernel ridge regression (KRR) model with Coulomb matrix featurization. We present two ML models for predicting intermolecular couplings. The first one utilizes a deep neural network and bi-molecular featurization to predict the coupling directly, which we find to perform poorly. The second one utilizes a KRR model to predict unimolecular transition densities, which can subsequently be analyzed to compute the coupling. We find that the latter approach performs excellently, indicating that an effective, generalizable strategy for predicting simple bimolecular properties is through the indirect application of ML to predict higher-order unimolecular properties. Such an approach necessitates a much smaller feature space and can incorporate the insight of well-established molecular physics.
Degradation of performance in ICF implosions due to Rayleigh–Taylor instabilities: A Hamiltonian perspective
The Rayleigh–Taylor instability (RTI) is an ubiquitous phenomenon that occurs in inertial-confinement-fusion (ICF) implosions and is recognized as an important limiting factor of ICF performance. To analytically understand the RTI dynamics and its impact on ICF capsule implosions, we develop a first-principle variational theory that describes an imploding spherical shell undergoing RTI. The model is based on a thin-shell approximation and includes the dynamical coupling between the imploding spherical shell and an adiabatically compressed fluid within its interior. Using a quasilinear analysis, we study the degradation trends of key ICF performance metrics (e.g., stagnation pressure, residual kinetic energy, and areal density) as functions of initial RTI parameters (e.g., the initial amplitude and Legendre mode), as well as the 1D implosion characteristics (e.g., the convergence ratio). We compare analytical results from the theory against nonlinear results obtained by numerically integrating the governing equations of this reduced model. Our findings emphasize the need to incorporate polar flows in the calculation of residual kinetic energy and demonstrate that higher convergence ratios in ICF implosions lead to significantly greater degradation of key performance metrics.
Symmetry breaking as predicted by a phase space Hamiltonian with a spin Coriolis potential
Here, we perform electronic structure calculations for a set of molecules with degenerate spin-dependent ground states ( 3 CH 2 , 2 CH$^{•}_{3}$, 3 O 2 ) going beyond the Born–Oppenheimer approximation and accounting for nuclear motion. According to a phase space approach that parameterizes electronic states (|Φ⟩) and electronic energies (E) by nuclear position and momentum [i.e., |Φ(R, P)⟩ and E(R, P)], we find that the presence of degenerate spin degrees of freedom leads to broken symmetry ground states. More precisely, rather than a single degenerate minimum at (R, P) = (R min , 0), the ground state energy has two minima at (R,P)=(R' min ,±P min ) (where R' min is close to R min ), dramatically contradicting the notion that the total energy of the system can be written in separable form as E = $\frac{P^2}{2M}$ + V el . Although we find that the broken symmetry solutions have small barriers between them for the small molecules, we hypothesize that the barriers should be macroscopically large for metallic solids, thus offering up a new phase-space potential energy surface for simulating the Einstein–de Haas effect.
Bayesian Federated Learning with Hamiltonian Monte Carlo: Algorithm and Theory
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Qutrit circuits and algebraic relations: A pathway to efficient spin-1 Hamiltonian simulation
Quantum information processing has witnessed significant advancements through the application of qubit-based techniques within universal gate sets. Recently, exploration beyond the qubit paradigm to d -dimensional quantum units or qudits has opened new avenues for improving computational efficiency. This paper delves into the qudit-based approach, particularly addressing the challenges presented in the high-fidelity implementation of qudit-based circuits due to increased complexity. As an innovative approach towards enhancing qudit circuit fidelity, we explore algebraic relations, such as the Yang-Baxter-like turnover equation, which may enable circuit compression and optimization. The paper introduces the turnover relation for the three-qutrit time propagator and its potential use in reducing circuit depth. We further investigate whether this relation can be generalized for higher-dimensional quantum circuits, including a focused study on the one-dimensional spin-1 Heisenberg model. Our paper outlines both rigorous and numerically efficient approaches to potentially achieve this generalization, providing a foundation for further explorations in the field of qudit-based quantum computing.
Isometric tensor network optimization for extensive Hamiltonians is free of barren plateaus
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Doubling the efficiency of Hamiltonian simulation via generalized quantum signal processing
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Bifurcation analysis of nonlinear Hamiltonian dynamics in the Fermilab Integrable Optics Test Accelerator
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Entanglement and its relation to energy variance for local one-dimensional Hamiltonians
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Quantum Hamiltonian for the surface charge density on a ring torus and radiative decay of plasmons
Photon scattering and the ensuing excitation of surface plasmons in single rings, single composite rings, and many-ring systems was recently shown to provide dispersion and field distributions [K. V. Garapati et al., J. Phys. Commun. 2, 015031 (2018)] of potential for specific applications in particle and molecular trapping [R. Alaee et al., Appl. Phys. Lett. 109, 141102 (2016); M. Salhi et al., Phys. Rev. A 92, 033416 (2015)], in addition to metamaterials and sensing. Furthermore, following photon or electron interactions with metallic nanorings, both radiative and nonradiative decay channels are important in the consideration of the nanoparticle as a photon or phonon source, and in related applications. In this work, we quantize the electronic normal modes of the ring torus and obtain the radiative decay of plasmons. Due to a geometry-related complexity, we employ a perturbation approach to obtain analytical expressions for the radiative decay channel for a vacuum bounded single solid nanoring. In quantizing the fields, the frequency spectrum of the charge density normal modes of the nanoring is obtained and shown to agree with the exact quasistatic plasmon dispersion relations. Higher-order corrections beyond the presented zero- and first-order calculations may be obtained following the presented results. The results are of potential interest in quantum sensing such as entangling photons and plasmons, or plasmons and trapped molecules.
Mana and thermalization: Probing the feasibility of near-Clifford Hamiltonian simulation
Quantum hydrodynamics is the emergent classical dynamics governing transport of conserved quantities in generic strongly interacting quantum systems. Here, recent matrix product operator methods [1,2] have made simulations of quantum hydrodynamics in 1+1D tractable, but they do not naturally generalize to 2+1D or higher, and they offer limited guidance as to the difficulty of simulations on quantum computers. Near-Clifford simulation algorithms are not limited to one dimension, and future error-corrected quantum computers will likely be bottlenecked by non-Clifford operations. We therefore investigate the non-Clifford resource requirements for simulation of quantum hydrodynamics using mana, a resource theory of non-Clifford operations. For infinite-temperature starting states, we find that the mana of subsystems quickly approaches zero, while for starting states with energy above some threshold the mana approaches a nonzero value. Surprisingly, in each case the finite-time mana is governed by the subsystem entropy, not the thermal state mana; we argue that this is because mana is a sensitive diagnostic of finite-time deviations from canonical typicality.
Wannier orbital theory and angle-resolved photoemission spectroscopy for the quasi-one-dimensional conductor LiMo 6 O 17 . I. Six-band t 2 g Hamiltonian
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FeGe as a building block for the kagome 1:1, 1:6:6, and 1:3:5 families: Hidden d -orbital decoupling of flat band sectors, effective models, and interaction Hamiltonians
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Ab initio benchmarks of neutrinoless double- β decay in light nuclei with a chiral Hamiltonian
Here, we report ab initio benchmark calculations of nuclear matrix elements (NMEs) for neutrinoless double-β (0νββ) decays in light nuclei with mass numbers ranging from A = 6 to A = 22. We use the transition operator derived from light-Majorana neutrino exchange and evaluate the NME with three different methods: two variants of in-medium similarity renormalization group (IMSRG) and importance-truncated no-core shell model (IT-NCSM). The same two plus three nucleon interaction from chiral effective field theory is employed, and both isospin-conserving (ΔT = 0) and isospin-changing (ΔT = 2) transitions are studied. We compare our resulting ground-state energies and NMEs to those of recent ab initio no-core shell model and coupled-cluster calculations, also with the same inputs. We show that the NMEs of ΔT = 0 transitions are in good agreement among all calculations, at the level of 10%. For ΔT = 2, relative deviations are more significant in some nuclei. The comparison with the exact IT-NCSM result allows us to analyze these cases in detail, and indicates the next steps toward improving the IMSRG-based approaches. The present study clearly demonstrates the power of consistent cross checks that are made possible by ab initio methodology. This capability is crucial for providing meaningful many-body uncertainties in the NMEs for the 0νββ decays in heavier candidate nuclei, where quasiexact benchmarks are not available.