Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Hamiltonians”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

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↗
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↗
DOE OSTI2025

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↗
DOE OSTI2025

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↗
DOE OSTI2026

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↗
DOE OSTI2025

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↗
DOE OSTI2024

Hamiltonian learning using machine-learning models trained with continuous measurements

Here, we build upon recent work on the use of machine-learning models to estimate Hamiltonian parameters using continuous weak measurement of qubits as input. We consider two settings for the training of our model: (1) supervised learning, where the weak-measurement training record can be labeled with known Hamiltonian parameters, and (2) unsupervised learning, where no labels are available. The first has the advantage of not requiring an explicit representation of the quantum state, thus potentially scaling very favorably to a larger number of qubits. The second requires the implementation of a physical model to map the Hamiltonian parameters to a measurement record, which we implement using an integrator of the physical model with a recurrent neural network to provide a model-free correction at every time step to account for small effects not captured by the physical model. We test our construction on a system of two qubits and demonstrate accurate prediction of multiple physical parameters in both the supervised context and the unsupervised context. We demonstrate that the model benefits from larger training sets, establishing that it is “learning,” and we show robustness regarding errors in the assumed physical model by achieving accurate parameter estimation in the presence of unanticipated single-particle relaxation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Compressing Hamiltonians with ab initio downfolding for simulating strongly-correlated materials on quantum computers

The accurate first-principles description of strongly correlated materials is an important and challenging problem in condensed matter physics. Ab initio downfolding has emerged as a way of deriving compressed many-body Hamiltonians that maintain the essential physics of strongly correlated materials. The solution of these material-specific models is still exponentially difficult to generate on classical computers, but quantum algorithms allow for a significant speed-up in obtaining the ground states of these compressed Hamiltonians. Here, we demonstrate that using quantum algorithms to obtain the properties of downfolded Hamiltonians can indeed yield high-fidelity solutions. By combining ab initio downfolding and variational quantum eigensolvers, we correctly predict the antiferromagnetic state of one-dimensional cuprate Ca 2 Cu O 3 , the excitonic ground state of monolayer W Te 2 , and the charge-ordered state of correlated metal Sr VO 3 . Numerical simulations using a classical tensor network implementation of variational quantum eigensolvers allow us to simulate large models with up to 54 qubits and encompassing up to four bands in the correlated subspace, which is indicative of the complexity that our framework can address. Through these methods we demonstrate the potential of classical preoptimization and downfolding techniques for enabling efficient materials simulation using quantum algorithms.

Alvertis, Antonios M. [NASA, Ames; LBNL, Berkeley]↗
DOE OSTI2024

Toward a Ginsparg-Wilson lattice Hamiltonian

To address quantum computation of quantities in quantum chromodynamics (QCD) for which chiral symmetry is important, it would be useful to have the Hamiltonian for a fermion satisfying the Ginsparg-Wilson (GW) equation. I work with a solution to the GW equation which is fractional linear in time derivatives. The resulting Hamiltonian is nonlocal and has ghosts, but is free of doublers and has the correct continuum limit. This construction works in general odd spatial dimensions, and I provide an explicit expression for the Hamiltonian in one spatial dimension. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2024

Neutrino oscillations in matter using the adjugate of the Hamiltonian

We revisit neutrino oscillations in constant matter density for a number of different scenarios: three flavors with the standard Wolfenstein matter potential, four flavors with standard matter potential and three flavors with non-standard matter potentials. To calculate the oscillation probabilities for these scenarios one must determine the eigenvalues and eigenvectors of the Hamiltonians. We use a method for calculating the eigenvalues that is well known, determination of the zeros of determinant of matrix (λI - H), where H is the Hamiltonian, I the identity matrix and λ is a scalar. To calculate the associated eigenvectors we use a method that is little known in the particle physics community, the calculation of the adjugate (transpose of the cofactor matrix) of the same matrix, (λI - H). This method can be applied to any Hamiltonian, but provides a very simple way to determine the eigenvectors for neutrino oscillation in matter, independent of the complexity of the matter potential. This method can be trivially automated using the Faddeev–LeVerrier algorithm for numerical calculations. For the above scenarios we derive a number of quantities that are invariant of the matter potential, many are new such as the generalization of the Naumov–Harrison–Scott identity for four or more flavors of neutrinos. We also show how these matter potential independent quantities become matter potential dependent when off-diagonal non-standard matter effects are included.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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 OSTI2025

Efficient Hamiltonian encoding algorithms for extracting quantum control mechanism as interfering pathway amplitudes in the Dyson series

Hamiltonian encoding is a methodology for revealing the mechanism behind the dynamics governing controlled quantum systems. In this paper, following Mitra and Rabitz \cite{abhra_1}, we define mechanism via pathways of eigenstates that describe the evolution of the system, where each pathway is associated with a complex-valued amplitude corresponding to a term in the Dyson series. The evolution of the system is determined by the constructive and destructive interference of these pathway amplitudes. Pathways with similar attributes can be grouped together into pathway classes. The amplitudes of pathway classes are computed by modulating the Hamiltonian matrix elements and decoding the subsequent evolution of the system rather than by direct computation of the individual terms in the Dyson series. The original implementation of Hamiltonian encoding was computationally intensive and became prohibitively expensive in large quantum systems. This paper presents two new encoding algorithms that calculate the amplitudes of pathway classes by using techniques from graph theory and algebraic topology to exploit patterns in the set of allowed transitions, greatly reducing the number of matrix elements that need to be modulated. These new algorithms provide an exponential decrease in both computation time and memory utilization with respect to the Hilbert space dimension of the system. To demonstrate the use of these techniques, they are applied to two illustrative state-to-state transition problems.

Abrams, Erez [Princeton University, Massachusetts ↗
DOE OSTI2025

Optimizing lossy state preparation for quantum sensing using Hamiltonian engineering

One of the most prominent platforms for demonstrating quantum sensing below the standard quantum limit is the spinor Bose–Einstein condensate. While a quantum advantage using several tens of thousands of atoms has been demonstrated in this platform, it faces an important challenge: atom loss. Atom loss is a Markovian error process modeled by Lindblad jump operators, and a no-go theorem, which we also show here, states that the loss of atoms in all spin components reduces the quantum advantage to a constant factor. Here, we show that this no-go theorem can be circumvented if we constrain atom losses to a single spin component. Moreover, we show that in this case, the maximum quantum Fisher information with N atoms scales as N 3/2 , establishing that a scalable quantum advantage can be achieved despite atom loss. Although Lindblad jump operators are generally non-Hermitian and non-invertible, we use their Moore–Penrose inverse to develop a framework for constructing several states with this scaling of Fisher information in the presence of losses. We use Hamiltonian engineering with realistic Hamiltonians to develop experimental protocols for preparing these states. Finally, we discuss possible experimental techniques to constrain the losses to a single spin mode.

74 ATOMIC AND MOLECULAR PHYSICS↗
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↗