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In this report we detail the development and application of an efficient quantum molecular dynamics computational algorithm and its application to the nanotube-tip assisted reactions on silicon and diamond surfaces. The calculations shed interesting insights into the microscopic picture of tip surface interactions.
Helium (He) plays a critical role in numerous areas ranging from the study of celestial objects like brown dwarfs and gas giants to modern-day technologies like nuclear energy and rocket propulsion. For many of these applications, it is essential to have a reliable equation of state (EOS) for He that yields an accurate representation of its thermodynamic behavior. To help constrain and develop such EOS models, we have performed a series of shock-compression experiments on cryogenic liquid He to pressures exceeding 100 GPa using a magnetically accelerated flyer plate on Sandia National Laboratories' Z-machine. We have also performed quantum molecular dynamics simulations that are consistent with our shock measurements. None of the previously available EOSs agree with our experimental and simulation results, motivating the development of a fluid-phase He EOS that we present in this study. Here, we show that our EOS yields good agreement with published data that span temperatures and pressures encountered across a diverse array of applications.
Magnetic diffusion plays an important role in inertial confinement fusion with strong magnetic fields. In this paper, we improve a previous analysis of the generation and diffusion of the magnetic field [Morita et al., Phys. Plasmas 25, 094505 (2018)]. For the generation process, we calculate the temporal evolution of the coil current using a self-consistent circuit model. The results show that the peak of the calculated magnetic field is delayed by 1.2 ns compared with that of the incident laser pulse. For the diffusion process, we evaluate the electrical conductivity of warm dense gold over a wide temperature range (300 K–100 eV) by combining the Kubo–Greenwood formula based on a quantum molecular dynamics simulation with the modified Spitzer model. Our simulation shows that the maximum magnetic field (530 T) that penetrates the cone is delayed by 2.5 ns compared with the laser peak. This result is consistent with experiments [Sakata et al., Nat. Commun. 9, 3937 (2018)] that showed that applying a strong magnetic field improved the heating efficiency of fusion fuel.
In this work, we present simulations of nonequilibrium dynamics of quantum field theories on digital quantum computers. As a representative example, we consider the Schwinger model, a (1+1)-dimensional U(1) gauge theory, coupled through a Yukawa-type interaction to a thermal environment described by a scalar field theory. We use the Hamiltonian formulation of the Schwinger model discretized on a spatial lattice. With the thermal scalar fields traced out, the Schwinger model can be treated as an open quantum system and its real-time dynamics are governed by a Lindblad equation in the Markovian limit. The interaction with the environment ultimately drives the system to thermal equilibrium. In the quantum Brownian motion limit, the Lindblad equation is related to a field theoretical Caldeira-Leggett equation. By using the Stinespring dilation theorem with ancillary qubits, we perform studies of both the nonequilibrium dynamics and the preparation of a thermal state in the Schwinger model using IBM's simulator and quantum devices. The real-time dynamics of field theories as open quantum systems and the thermal state preparation studied here are relevant for a variety of applications in nuclear and particle physics, quantum information and cosmology.
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.
Here, we explore how the fundamental problems in quantum molecular dynamics can be modeled using classical simulators (emulators) of quantum computers and the actual quantum hardware available to us today. The list of problems we tackle includes propagation of a free wave packet, vibration of a harmonic oscillator, and tunneling through a barrier. Each of these problems starts with the initial wave packet setup. Although Qiskit provides a general method for initializing wave functions, in most cases it generates deep quantum circuits. While these circuits perform well on noiseless simulators, they suffer from excessive noise on quantum hardware. To overcome this issue, we designed a shallower quantum circuit for preparing a Gaussian-like initial wave packet, which improves the performance of real hardware. Next, quantum circuits are implemented to apply the kinetic and potential energy operators for the evolution of a wave function over time. The results of our modeling on classical emulators of quantum hardware agree perfectly with the results obtained using the traditional (classical) methods. This serves as a benchmark and demonstrates that the quantum algorithms and Qiskit codes we developed are accurate. However, the results obtained on the actual quantum hardware available today, such as IBM’s superconducting qubits and IonQ’s trapped ions, indicate large discrepancies due to hardware limitations. This work highlights both the potential and challenges of using quantum computers to solve fundamental quantum molecular dynamics problems.
Understanding carbonate speciation and how it may be modulated is essential for the advancement of carbon dioxide (CO 2 ) capture and storage technologies, which often rely on the transformation of CO 2 into carbonate, e.g. via the formation of carbonate minerals. To date, few atomic-level, quantum-mechanics-based simulations have been carried out to characterize how carbonic acid (H 2 CO 3 ) and bicarbonate ($HCO^{-}_{3}$) form in aqueous solution, and how pH affects this process. Recently, Martirez and Carter utilized rare-event sampling density functional theory molecular dynamics simulations in combination with multi-level embedded correlated wavefunction theory, thus accounting for both solvent dynamics and electron correlation accurately, to elucidate the mechanism of H 2 CO 3 formation in neutral solution (J. Am. Chem. Soc., 145, 12561, 2023). Here, we perform a complementary simulation using the same method to map out the energetics of $HCO^{-}_{3}$ formation from dissolved CO 2 in basic solution. We find that, as in H 2 CO 3 formation, including water dynamics is important to obtain an accurate prediction of the energetics for the aforementioned reaction. Furthermore, only with MD did we identify the correct pathway for the reaction, in which water – not hydroxide – acts as the initial nucleophile and only at the transition state does it lose a proton.
An external drive can improve the coherence of a quantum many-body system by averaging out noise sources. It can also be used to realize models that are inaccessible in the static limit, through Floquet Hamiltonian engineering. The full possibilities for combining these tools remain unexplored. We develop the requirements needed for a pulse sequence to decouple a quantum many-body system from an external field without altering the intended dynamics. Demonstrating this technique experimentally in an ion-trap platform, we show that it can provide a large improvement to coherence in real-world applications. Finally, we engineer an approximate quantum simulation of the Haldane-Shastry model, an exactly solvable paradigm for long-range interacting spins. Our results expand and unify the quantum simulation toolbox.
Herein we propose to simulate dynamical phases of a BCS superconductor using an ensemble of cold atoms trapped in an optical cavity. Effective Cooper pairs are encoded via the internal states of the atoms, and attractive interactions are realized via the exchange of virtual photons between atoms coupled to a common cavity mode. Control of the interaction strength combined with a tunable dispersion relation of the effective Cooper pairs allows exploration of the full dynamical phase diagram of the BCS model as a function of system parameters and the prepared initial state. Our proposal paves the way for the study of the nonequilibrium features of quantum magnetism and superconductivity by harnessing atom-light interactions in cold atomic gases.
Recent advances in (scanning) transmission electron microscopy have enabled a routine generation of large volumes of high-veracity structural data on 2D and 3D materials, naturally offering the challenge of using these as starting inputs for atomistic simulations. In this fashion, the theory will address experimentally emerging structures, as opposed to the full range of theoretically possible atomic configurations. However, this challenge is highly nontrivial due to the extreme disparity between intrinsic timescales accessible to modern simulations and microscopy, as well as latencies of microscopy and simulations per se. Addressing this issue requires as a first step bridging the instrumental data flow and physics-based simulation environment, to enable the selection of regions of interest and exploring them using physical simulations. Here we report the development of the machine learning workflow that directly bridges the instrument data stream into Python-based molecular dynamics and density functional theory environments using pre-trained neural networks to convert imaging data to physical descriptors. Additionally, the pathways to ensure structural stability and compensate for the observational biases universally present in the data are identified in the workflow. This approach is used for a graphene system to reconstruct optimized geometry and simulate temperature-dependent dynamics including adsorption of Cr as an ad-atom and graphene healing effects. However, it is universal and can be used for other material systems.
Here, solutions and minerals containing sulfate (SO 4 2- ), and Ca 2+ and Mg 2+ cations, are ubiquitous throughout the lithosphere and are significant components of seawater, thus presenting a prototypical system for the study of strong electrolytes and crystal nucleation mechanisms. However, despite their relative abundance, key questions remain unanswered about the most fundamental atomic-level steps of their mineralization pathways and aqueous dynamics. Here, we carry out enhanced sampling multi-level molecular dynamics (MD) embedded correlated wavefunction theory simulations to elucidate ion-pairing mechanisms for Mg–SO 4 and Ca–SO 4 in concentrated aqueous solution, accurately capturing effects arising from both structural dynamics and electron exchange–correlation. We predict contact-ion-pair formation to be barrierless and highly exoergic for Ca–SO 4 , in agreement with its minimal solubility, whereas for Mg–SO 4 , solvent-shared and contact ion pairs have similar free energies, qualitatively consistent with its higher solubility. Finally, we demonstrate that brief high-temperature pre-equilibration may be utilized to accelerate convergence of free energies in blue-moon-ensemble enhanced-sampling MD.
The dehydration of aqueous calcium and magnesium cations is the most fundamental process controlling their reactivity in chemical and biological phenomena, such as the formation of ionic solids or passing through ion channels. It holds particular relevance in light of recent advancements in the development of carbon capture techniques that rely on mineralization for long-term carbon storage. Specifically, dehydration of Ca 2+ and Mg 2+ is a key step in proposed carbon capture processes aiming to exploit the relatively high concentration of dissolved carbon dioxide in seawater via the formation of carbonate minerals from solvated Ca 2+ and Mg 2+ cations for sequestration and storage. Nevertheless, atomic-scale understanding of the dehydration of aqueous Ca 2+ and Mg 2+ cations remains limited. Here, we utilize rare event sampling via density functional theory molecular dynamics and embedded wavefunction theory calculations to elucidate the dehydration dynamics of aqueous Ca 2+ and Mg 2+ . Emphasis is placed on the investigation of the effect pH has on the stability of the different coordination environments. Here, our results reveal significant differences in the dehydration dynamics of the two cations and provide insight into how they may be modulated by pH changes.
In this work Δ learning is used to map orbital-free density functional theory (OF-DFT) ionic forces to the corresponding Kohn-Sham (KS) DFT ionic forces. The development of the approximate force difference in terms of the ion positions is constructed and serves as a stand in for the ground truth force difference. Descriptor vectors for ion configurations are constructed using all distance between ions in conjunction with an indexing based on a nearest neighbor ranking. It is demonstrated that such a scheme of descriptors can uniquely describe an ionic configuration up to a rotation and reflection when no ambiguity in the nearest neighbor ranking exists. How to handle the case when an ambiguity exists in the nearest neighbor ranking is discussed. As a proof of principle, the model is trained and tested on warm dense hydrogen at temperatures between 1 and 15 eV. Once tested, the model was used to perform molecular dynamic simulations of warm dense hydrogen. Furthermore, the resulting energies and pressures are within 1% and 2% of their respective target KS values.
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Quantum subspace diagonalization (QSD) algorithms have emerged as a competitive family of algorithms that avoid many of the optimization pitfalls associated with parameterized quantum circuit algorithms. While the vast majority of the QSD algorithms have focused on solving the eigenpair problem for ground, excited-state, and thermal observable estimation, there has been a lot less work in considering QSD algorithms for the problem of quantum dynamical simulation. In this work, we propose several quantum Krylov fast-forwarding (QKFF) algorithms capable of predicting long-time dynamics well beyond the coherence time of current quantum hardware. Our algorithms use real-time evolved Krylov basis states prepared on the quantum computer and a multi-reference subspace method to ensure convergence towards high-fidelity, long-time dynamics. In particular, we show that the proposed multi-reference methodology provides a systematic way of trading off circuit depth with classical post-processing complexity. Further, we also demonstrate the efficacy of our approach through numerical implementations for several quantum chemistry problems including the calculation of the auto-correlation and dipole moment correlation functions.
In this paper, we present a superpolynomial improvement in the precision scaling of quantum simulations for coupled quantum-classical systems. Such systems are found in, e.g., molecular-dynamics simulations within the Born-Oppenheimer approximation. By employing a framework based on the Koopman–von Neumann formulation of classical mechanics, we express the Liouville equation of motion as unitary dynamics and utilize phase kickback from a dynamical quantum simulation to calculate the quantum forces acting on classical particles. This approach allows us to simulate the dynamics of these classical particles without the overheads associated with measuring gradients and solving the equations of motion on a classical computer, resulting in a superpolynomial advantage at the price of increased space complexity. We demonstrate that these simulations can be performed in both microcanonical and canonical ensembles, enabling the estimation of thermodynamic properties from the prepared probability density. Published by the American Physical Society 2024
Functional layered material (LM) architectures will dominate nanomaterials science in this century. We have developed theory, modeling, simulation, and software and data tools that enhance understanding and AI guide synthesis, enable characterization of complex structures, and improve capabilities in the predictive design and growth of LMs. Research at the Center has focused on: Computational synthesis and characterization: AI guided synthesis and experimental synthesis of stacked LMs with tailored properties via optimized chemical vapor deposition (CVD) growth and liquid-phase exfoliation; study defects, edges, grain boundaries, wrinkling of atomic layers and their effects on chemical, mechanical, electrical, and optical properties. Far-from-equilibrium processes: Joint experimental and simulation based probe of electronic processes with NAQMD and ultrafast X-ray free-electron laser (XFEL) and ultrafast electron diffraction (UED) facilities at Stanford. Experimentally validate NAQMD by ultrafast electron diffraction and X-ray spectroscopy studies of structural and excited state dynamics, shape fluctuations, and phonon dynamics. Scalable software: Simulation engines for desktop-to-exascale platforms using low-overhead, linear-scaling QMD algorithms; divide-conquer-recombine NAQMD with electronic excitations; extended-Lagrangian reactive molecular dynamics (RMD), machine learning (ML) based neural-network quantum molecular dynamics (NNQMD), and super-state accelerated molecular dynamics (AMD) and kinetic Monte Carlo codes; thermal and electrical transport software; and design 3D architectures of LMs with desired functionality using scalable software. Distribution of software and data, and training: Software and simulation-experimental data generated within the Center are distributed to the materials science community via Berkeley Materials Project (MP) framework. We have also organized three workshops for software distribution and training at USC (Nov. 2017, Mar. 2018) and Gaithersburg, MD (Nov. 2018) to train researchers, with the last one in focused on underrepresented groups, in collaboration with Howard University which is one of the largest HBCUs. The Center supported a total of 46 personnel and 6 undergraduate students. These include 14 faculty, 11 postdoctoral research associates, 20 graduate research assistants, and mentored 6 undergraduate students. This resulted in the publications of 63 research papers that include 46 publications on Reactive and Quantum Dynamics Simulations, 13 publications on Machine Learning for Quantum Materials, and 4 publications on Quantum Computing.
Simulating quantum dynamics on classical computers is challenging for large systems due to the significant memory requirements. Simulation on quantum computers is a promising alternative, but fully optimizing quantum circuits to minimize limited quantum resources remains an open problem. In this study, we tackle this problem by presenting a constructive algorithm, based on Cartan decomposition of the Lie algebra generated by the Hamiltonian, which generates quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one-dimensional transverse field $\mathrm{XY}$ model, where $\mathscr{O}$(n 2 )-gate circuits naturally emerge. Compared to product formulas with significantly larger gate counts, our algorithm drastically improves simulation precision. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.