Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Hamiltonian”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4

Deep learning of dynamically responsive chemical Hamiltonians with semiempirical quantum mechanics

Conventional machine-learning (ML) models in computational chemistry learn to directly predict molecular properties using quantum chemistry only for reference data. While these heuristic ML methods show quantum-level accuracy with speeds several orders of magnitude faster than traditional quantum chemistry methods, they suffer from poor extensibility and transferability; i.e., their accuracy degrades on large or new chemical systems. Incorporating quantum chemistry frameworks into the ML models directly solves this problem. Here we take the structure of semiempirical quantum mechanics (SEQM) methods to construct dynamically responsive Hamiltonians. SEQM methods use empirical parameters fitted to experimental properties to construct reduced-order Hamiltonians, facilitating much faster calculations than ab initio methods but with compromised accuracy. By replacing these static parameters with machine-learned dynamic values inferred from the local environment, we greatly improve the accuracy of the SEQM methods. Trained on molecular energies and atomic forces, these dynamically generated Hamiltonian parameters show a strong correlation with atomic hybridization and bonding. Trained with only about 60,000 small organic molecular conformers, the resulting model retains interpretability, extensibility, and transferability when testing on much larger chemical systems and predicting various molecular properties. Overall, this work demonstrates the virtues of incorporating physics-based descriptions with ML to develop models that are simultaneously accurate, transferable, and interpretable.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Hamiltonian simulation in Zeno subspaces

Here, we investigate the quantum Zeno effect as a framework for designing and analyzing quantum algorithms for Hamiltonian simulation. We show that frequent projective measurements of an ancilla qubit register can be used to simulate quantum dynamics on a target qubit register with a circuit complexity similar to randomized approaches. The classical sampling overhead in the latter approaches is traded for ancilla qubit overhead in Zeno-based approaches. A second-order Zeno sequence is developed to improve scaling and implementations through unitary kicks are discussed. We derive rigorous error bounds that allow for identifying the associated circuit complexities for the first- and second-order Zeno sequences. We show that the circuits over the combined register can be identified as a subroutine commonly used in post-Trotter Hamiltonian simulation methods. We build on this observation to reveal connections between different Hamiltonian simulation algorithms.

Hamiltonian simulation↗

Bayesian Inference with Latent Hamiltonian Neural Networks (L-HNNs)

When sampling for Bayesian inference, one popular approach is to use Hamiltonian Monte Carlo (HMC) and the No-U-Turn Sampler (NUTS). However, HMC and NUTS can require numerous numerical gradients of the target density and can prove slow in practice. We propose Hamiltonian neural networks (HNNs) with HMC and NUTS for solving Bayesian inference problems [1, 2]. Once trained, HNNs do not require gradients of the target density while sampling. Moreover, they satisfy important properties such as perfect time reversibility and Hamiltonian conservation, making them well suited for use within HMC and NUTS because stationarity can be shown. We also propose an HNN extension called latent HNNs (L-HNNs), which predict latent variable outputs. Compared to HNNs, L-HNNs offer improved expressivity and a reduction in integration errors. Finally, we propose employing L-HNNs in NUTS with an online error monitoring scheme to prevent degeneracy of the sampling in regions of low probability density. We demonstrate L-HNNs in NUTS with online error monitoring by using several example cases involving complex, heavy-tailed, and high local curvature probability densities. Overall, L-HNNs in NUTS with online error monitoring satisfactorily inferred these probability densities. Compared to traditional NUTS, L-HNNs in NUTS with online error monitoring improved the effective sample size (ESS) per gradient by an order of magnitude.

97 MATHEMATICS AND COMPUTING↗

Spin Waves and Magnetic Exchange Hamiltonian in CrSBr

Abstract CrSBr is an air‐stable two‐dimensional (2D) van der Waals semiconducting magnet with great technological promise, but its atomic‐scale magnetic interactions—crucial information for high‐frequency switching—are poorly understood. An experimental study is presented to determine the CrSBr magnetic exchange Hamiltonian and bulk magnon spectrum. The A ‐type antiferromagnetic order using single crystal neutron diffraction is confirmed here. The magnon dispersions are also measured using inelastic neutron scattering and rigorously fit the excitation modes to a spin wave model. The magnon spectrum is well described by an intra‐plane ferromagnetic Heisenberg exchange model with seven nearest in‐plane exchanges. This fitted exchange Hamiltonian enables theoretical predictions of CrSBr behavior: as one example, the fitted Hamiltonian is used to predict the presence of chiral magnon edge modes with a spin‐orbit enhanced CrSBr heterostructure.

2D materials↗

Discrete Superconvergence Analysis for Quantum Magnus Algorithms of Unbounded Hamiltonian Simulation

Motivated by various applications, unbounded Hamiltonian simulation has recently garnered great attention. Quantum Magnus algorithms, designed to achieve commutator scaling for time-dependent Hamiltonian simulation, have been found to be particularly efficient for such applications. When applied to unbounded Hamiltonian simulation in the interaction picture, they exhibit an unexpected superconvergence phenomenon. However, existing proofs are limited to the spatially continuous setting and do not extend to discrete spatial discretizations. Here, in this work, we provide the first superconvergence estimate in the fully discrete setting with a finite number of spatial discretization points N, and show that it holds with an error constant uniform in N. The proof is based on the two-parameter symbol class, which, to our knowledge, is applied for the first time in algorithm analysis. The key idea is to establish a semiclassical framework by identifying two parameters through the discretization number and the time step size rescaled by the operator norm, such that the semiclassical uniformity guarantees the uniformity of both. This approach may have broader applications in numerical analysis beyond the specific context of this work.

Borns-Weil, Yonah [University of California, Berke↗

Hamiltonian reduction of Vlasov–Maxwell to a dark slow manifold

In this work, we show that non-relativistic scaling of the collisionless Vlasov–Maxwell system implies the existence of a formal invariant slow manifold in the infinite-dimensional Vlasov–Maxwell phase space. Vlasov–Maxwell dynamics restricted to the slow manifold recovers the Vlasov–Poisson and Vlasov–Darwin models as low-order approximations, and provides higher-order corrections to the Vlasov–Darwin model more generally. The slow manifold may be interpreted to all orders in perturbation theory as a collection of formal Vlasov–Maxwell solutions that do not excite light waves, and are therefore ‘dark’. We provide a heuristic lower bound for the time interval over which Vlasov–Maxwell solutions initialized optimally near the slow manifold remain dark. We also show how the dynamics on the slow manifold naturally inherits a Hamiltonian structure from the underlying system. After expressing this structure in a simple form, we use it to identify a manifestly Hamiltonian correction to the Vlasov–Darwin model. The derivation of higher-order terms is reduced to computing the corrections of the system Hamiltonian restricted to the slow manifold.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

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↗

Downfolding from ab initio to interacting model Hamiltonians: comprehensive analysis and benchmarking of the DFT+cRPA approach

Abstract Model Hamiltonians are regularly derived from first principles to describe correlated matter. However, the standard methods for this contain a number of largely unexplored approximations. For a strongly correlated impurity model system, here we carefully compare a standard downfolding technique with the best possible ground-truth estimates for charge-neutral excited-state energies and wave functions using state-of-the-art first-principles many-body wave function approaches. To this end, we use the vanadocene molecule and analyze all downfolding aspects, including the Hamiltonian form, target basis, double-counting correction, and Coulomb interaction screening models. We find that the choice of target-space basis functions emerges as a key factor for the quality of the downfolded results, while orbital-dependent double-counting corrections diminish the quality. Background screening of the Coulomb interaction matrix elements primarily affects crystal-field excitations. Our benchmark uncovers the relative importance of each downfolding step and offers insights into the potential accuracy of minimal downfolded model Hamiltonians.

Chemistry↗

A quantum hamiltonian simulation benchmark

Hamiltonian simulation is one of the most important problems in quantum computation, and quantum singular value transformation (QSVT) is an efficient way to simulate a general class of Hamiltonians. However, the QSVT circuit typically involves multiple ancilla qubits and multi-qubit control gates. In order to simulate a certain class of n-qubit random Hamiltonians, we propose a drastically simplified quantum circuit that we refer to as the minimal QSVT circuit, which uses only one ancilla qubit and no multi-qubit controlled gates. We formulate a simple metric called the quantum unitary evolution score (QUES), which is a scalable quantum benchmark and can be verified without any need for classical computation. Under the globally depolarized noise model, we demonstrate that QUES is directly related to the circuit fidelity, and the potential classical hardness of an associated quantum circuit sampling problem. Under the same assumption, theoretical analysis suggests there exists an ‘optimal’ simulation time t opt ≈ 4.81, at which even a noisy quantum device may be sufficient to demonstrate the potential classical hardness.

97 MATHEMATICS AND COMPUTING↗

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↗

Hybridizing pseudo-Hamiltonians and non-local pseudopotentials in diffusion Monte Carlo

An accurate treatment of effective core potentials (ECPs) requires care in continuum quantum Monte Carlo (QMC) methods. While most QMC studies have settled on the use of familiar non-local (NL) pseudopotentials with additional localization approximations, these approaches have been shown to result in moderate residual errors for some classes of molecular and solid state applications. Here, we revisit an idea proposed early in the history of QMC ECPs that does not require localization approximations, namely, a differential class of potentials referred to as pseudo-Hamiltonians. We propose to hybridize NL potentials and pseudo-Hamiltonians to reduce residual non-locality of existing potentials. We derive an approach to recast pseudopotentials for 3d elements as hybrid pseudo-Hamiltonians with optimally reduced NL energy. We demonstrate the fidelity of the hybrid potentials by studying atomic ionization potentials of Ti and Fe and the binding properties of TiO and FeO molecules with diffusion Monte Carlo (DMC). We show that localization errors have been reduced relative to potentials with the same NL channels for Sc–Zn by considering the DMC energy change with respect to the choice of approximate localization. While localization error decreases proportionate to the reduced NL energy without a Jastrow, with a Jastrow, the degree of reduction decreases at higher filling of the d-shell. Our results suggest that a subset of existing ECPs may be recast in this hybrid form to reduce the DMC localization error. They also point to the prospect of further reducing this error by generating ECPs within this hybrid form from the start.

36 MATERIALS SCIENCE↗

Leveraging Hamiltonian simulation techniques to compile operations on bosonic devices

Circuit quantum electrodynamics enables the combined use of qubits and oscillator modes. Despite a variety of available gate sets, many hybrid qubit-boson (i.e. qubit-oscillator) operations are realizable only through optimal control theory, which is oftentimes intractable and uninterpretable. We introduce an analytic approach with rigorously proven error bounds for realizing specific classes of operations via two matrix product formulas commonly used in Hamiltonian simulation, the Lie–Trotter–Suzuki and Baker–Campbell–Hausdorff product formulas. We show how this technique can be used to realize a number of operations of interest, including polynomials of annihilation and creation operators, namely (a) p (a † ) q for integer p, q. We show examples of this paradigm including obtaining universal control within a subspace of the entire Fock space of an oscillator, state preparation of a fixed photon number in the cavity, simulation of the Jaynes–Cummings Hamiltonian, and simulation of the Hong-Ou-Mandel effect. This work demonstrates how techniques from Hamiltonian simulation can be applied to better control hybrid qubit-boson devices.

bosonic qubits↗

Polaritons and excitons: Hamiltonian design for enhanced coherence

The primary questions motivating this report are: Are there ways to increase coherence and delocalization of excitation among many molecules at moderate electronic coupling strength? Coherent delocalization of excitation in disordered molecular systems is studied using numerical calculations. The results are relevant to molecular excitons, polaritons, and make connections to classical phase oscillator synchronization. In particular, it is hypothesized that it is not only the magnitude of electronic coupling relative to the standard deviation of energetic disorder that decides the limits of coherence, but that the structure of the Hamiltonian—connections between sites (or molecules) made by electronic coupling—is a significant design parameter. Inspired by synchronization phenomena in analogous systems of phase oscillators, some properties of graphs that define the structure of different Hamiltonian matrices are explored. The report focuses on eigenvalues and ensemble density matrices of various structured, random matrices. Some reasons for the special delocalization properties and robustness of polaritons in the single-excitation subspace (the star graph) are discussed. The key result of this report is that, for some classes of Hamiltonian matrix structure, coherent delocalization is not easily defeated by energy disorder, even when the electronic coupling is small compared to disorder.

Science & Technology - Other Topics↗

Simulations of frustrated Ising Hamiltonians using quantum approximate optimization

Novel magnetic materials are important for future technological advances. Theoretical and numerical calculations of ground-state properties are essential in understanding these materials, however, computational complexity limits conventional methods for studying these states. Here we investigate an alternative approach to preparing materials ground states using the quantum approximate optimization algorithm (QAOA) on near-term quantum computers. We study classical Ising spin models on unit cells of square, Shastry-Sutherland and triangular lattices, with varying field amplitudes and couplings in the material Hamiltonian. We find relationships between the theoretical QAOA success probability and the structure of the ground state, indicating that only a modest number of measurements (≲100) are needed to find the ground state of our nine-spin Hamiltonians, even for parameters leading to frustrated magnetism. We further demonstrate the approach in calculations on a trapped-ion quantum computer and succeed in recovering each ground state of the Shastry-Sutherland unit cell with probabilities close to ideal theoretical values. The results demonstrate the viability of QAOA for materials ground state preparation in the frustrated Ising limit, giving important first steps towards larger sizes and more complex Hamiltonians where quantum computational advantage may prove essential in developing a systematic understanding of novel materials.

97 MATHEMATICS AND COMPUTING↗

Improved honeycomb and hyperhoneycomb lattice Hamiltonians for quantum simulations of non-Abelian gauge theories

Improved Kogut-Susskind Hamiltonians for quantum simulations of non-Abelian Yang-Mills gauge theories are developed for honeycomb (2+1⁢D) and hyperhoneycomb (3+1⁢D) spatial tessellations. This is motivated by the desire to identify lattices for quantum simulations that involve only 3-link vertices among the gauge field group spaces in order to reduce the complexity in applications of the plaquette operator. For the honeycomb lattice, we derive a classically 𝒪⁡(𝑏 2 )-improved Hamiltonian, with 𝑏 being the lattice spacing. Tadpole improvement via the mean-field value of the plaquette operator is used to provide the corresponding quantum improvements. We have identified the (nonchiral) hyperhoneycomb as a candidate spatial tessellation for 3+1⁢D quantum simulations of gauge theories, and determined the associated 𝒪⁡(𝑏)-improved Hamiltonian.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Systematic Construction of Time-Dependent Hamiltonians for Microwave-Driven Josephson Circuits

Time-dependent electromagnetic drives are fundamental for controlling complex quantum systems, including superconducting Josephson circuits. In these devices, accurate time-dependent Hamiltonian models are imperative for predicting their dynamics and designing high-fidelity quantum operations. Existing numerical methods, such as black-box quantization (BBQ) and energy-participation ratio (EPR), excel at modeling the static Hamiltonians of Josephson circuits. However, these techniques do not fully capture the behavior of driven circuits stimulated by external microwave drives, nor do they include a generalized approach to account for the inevitable noise and dissipation that enter through microwave ports. Here, we introduce numerical techniques that leverage classical microwave simulations, efficiently executable in finite-element solvers, to obtain the time-dependent Hamiltonian of microwave-driven superconducting circuits with arbitrary geometries under charge, flux, or mixed electromagnetic modulation. Importantly, our techniques do not rely on a lumped-element description of the superconducting circuit, in contrast to previous approaches to tackling this problem. We demonstrate the versatility of our approach by characterizing the driven properties of realistic circuit devices in complex electromagnetic environments, including coherent dynamics due to charge and flux modulation, as well as drive-induced relaxation and dephasing. Our techniques offer a powerful toolbox for optimizing circuit designs and advancing practical applications in superconducting quantum computing.

Lu, Yao [Yale U.; Yale U. (main); Fermilab] (ORCID↗

Algebraic compression of quantum circuits for Hamiltonian evolution

Here unitary evolution under a time-dependent Hamiltonian is a key component of simulation on quantum hardware. Synthesizing the corresponding quantum circuit is typically done by breaking the evolution into small time steps, also known as Trotterization, which leads to circuits the depth of which scales with the number of steps. When the circuit elements are limited to a subset of SU(4) - or equivalently, when the Hamiltonian may be mapped onto free fermionic models - several identities exist that combine and simplify the circuit. Based on this, we present an algorithm that compresses the Trotter steps into a single block of quantum gates using algebraic relations between adjacent circuit elements. This results in a fixed depth time evolution for certain classes of Hamiltonians. We explicitly show how this algorithm works for several spin models, and demonstrate its use for adiabatic state preparation of the transverse field Ising model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Strategies for simulating the time evolution of Hamiltonian lattice field theories

Simulating the time evolution of quantum field theories given some Hamiltonian H requires developing algorithms for implementing the unitary operator e -iHt . A variety of techniques exist that accomplish this task, with the most common technique used so far being Trotterization, which is a special case of the application of a product formula. However, other techniques exist that promise better asymptotic scaling in certain parameters of the theory being simulated, the most efficient of which are based on the concept of block encoding. In this work we study the performance of such algorithms in simulating lattice field theories. We derive and compare the asymptotic gate complexities of several commonly used simulation techniques in application to Hamiltonian lattice field theories. Using the scalar $\hat{φ}$ 4 theory as a test, we also perform numerical studies and compare the gate costs required by product formulas and signal-processing-based techniques to simulate time evolution. For the latter, we use the linear combination of unitaries (LCU) construction augmented with the quantum Fourier transform circuit to switch between the field and momentum eigenbases, which leads to immediate order-of-magnitude improvement in the cost of preparing the block encoding. Further, this paper also includes a pedagogical review of the techniques used, in particular product formulas, LCU, qubitization, quantum signal processing, as well as the technique for simulating geometrically-local Hamiltonians developed by Haah, Hastings, Kothari, and Low.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗