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.

SourceResearch connectionFrom yearThrough year

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

At least 37 records · Page 2

All sources NASA NTRS DOE OSTI

NASA NTRSDate not supplied

Self-consistent Quantum Iteratively Sparsified Hamiltonian Algorithm (SQuISH)

Due to coherence time limitations, reducing the resources required to run quantum algorithms and simulate physical systems on a quantum computer is crucial. With regards to Hamiltonian simulation, a significant effort has focused on building efficient algorithms using various factorizations and truncations, typically derived from the Hamiltonian alone. We introduce a new paradigm for improving Hamiltonian simulation and reducing the cost of ground state problems based on ideas recently developed for classical chemistry simulations. The key idea is that one can find efficient ways to reduce resources needed by quantum algorithms by making use of two key pieces of information: the Hamiltonian operator and an approximate ground state wavefunction. We refer to our algorithm as the self-consistent quantum iteratively sparsified Hamiltonian (SQuISH). By performing our scheme iteratively, one can drive SQuISH to create an accurate wavefunction using a truncated, resource-efficient Hamiltonian. By utilizing this more compact Hamiltonian, our algorithm provides an approach to reduce the gate complexity of ground state calculations on quantum hardware. As proof of principle, we implement SQuISH using configuration interaction for small molecules and coupled cluster for larger systems. Through our combination of approaches, we demonstrate how it performs on a range of systems, the largest of which would require more than 200 qubits to run on quantum hardware.

Diana Chamaki↗

NASA NTRSDate not supplied

Downfolding Complex Materials Problems Onto Model Hamiltonians for Quantum Computers

Simulating the properties of quantum materials is expected to be one of the exciting applications for quantum computers and where we hope to see advantages over classical hardware. The complexity of ab initio Hamiltonians describing the physics of application-relevant materials places them beyond the realm of possibility for solution on near-term hardware with a limited number of qubits. Various Hamiltonian approximations, including Hamiltonian downfolding, offers a possibility towards simulating complex materials on near-term hardware. This is accomplished by approximating the relevant physics of a given material through their representation by simpler model Hamiltonians, such as the Hubbard Hamiltonian or extensions of it. Here we employ a well-defined first-principles methodology for deriving downfolded multi-band extended Hubbard Hamiltonians of materials, capturing strong electronic correlation and electron-phonon coupling, based on the formalism of Wannier functions and the calculation of the screened Coulomb interaction. We demonstrate for a variety of systems that quantum simulation of these downfolded Hamiltonians reproduces key properties, thus establishing downfolding as a promising route to achieve near-term simulation of application-relevant systems on quantum hardware.

Antonios Markos Alvertis↗

NASA NTRSDate not supplied

Downfolding complex materials problems onto model Hamiltonians for quantum computers

Antonios M. Alvertis↗

DOE OSTI2024

An efficient quantum circuit for block encoding a pairing Hamiltonian

We present an efficient quantum circuit for block encoding a pairing Hamiltonian often studied in nuclear physics. Our block encoding scheme does not require mapping the creation and annihilation operators to the Pauli operators and representing the Hamiltonian as a linear combination of unitaries. Instead, we show how to encode the Hamiltonian directly using controlled swap operations. We analyze the gate complexity of the block encoding circuit and show that it scales polynomially with respect to the number of qubits required to represent a quantum state associated with the pairing Hamiltonian. We also show how the block encoding circuit can be combined with the quantum singular value transformation to construct an efficient quantum circuit for approximating the density of states of a pairing Hamiltonian. The techniques presented can be extended to encode more general second-quantized Hamiltonians.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Lie–Poisson Neural Networks (LPNets): Data-based computing of Hamiltonian systems with symmetries

An accurate data-based prediction of the long-term evolution of Hamiltonian systems requires a network that preserves the appropriate structure under each time step. Every Hamiltonian system contains two essential ingredients: the Poisson bracket and the Hamiltonian. Hamiltonian systems with symmetries, whose paradigm examples are the Lie–Poisson systems, have been shown to describe a broad category of physical phenomena, from satellite motion to underwater vehicles, fluids, geophysical applications, complex fluids, and plasma physics. The Poisson bracket in these systems comes from the symmetries, while the Hamiltonian comes from the underlying physics. We view the symmetry of the system as primary, hence the Lie–Poisson bracket is known exactly, whereas the Hamiltonian is regarded as coming from physics and is considered not known, or known approximately. Using this approach, we develop a network based on transformations that exactly preserve the Poisson bracket and the special functions of the Lie–Poisson systems (Casimirs) to machine precision. We present two flavors of such systems: one, where the parameters of transformations are computed from data using a dense neural network (LPNets), and another, where the composition of transformations is used as building blocks (G-LPNets). We also show how to adapt these methods to a larger class of Poisson brackets. We apply the resulting methods to several examples, such as rigid body (satellite) motion, underwater vehicles, a particle in a magnetic field, and others. The methods developed in this paper are important for the construction of accurate data-based methods for simulating the long-term dynamics of physical systems.

Data-based modeling↗

DOE OSTI2022

A canonical Hamiltonian for open quantum systems

Abstract If an open quantum system is initially uncorrelated from its environment, then its dynamics can be written in terms of a Lindblad-form master equation. The master equation is divided into a unitary piece, represented by an effective Hamiltonian, and a dissipative piece, represented by a hermiticity-preserving superoperator; however, the division of open system dynamics into unitary and dissipative pieces is non-unique. For finite-dimensional quantum systems, we resolve this non-uniqueness by specifying a norm on the space of dissipative superoperators and defining the canonical Hamiltonian to be the one whose dissipator is minimal. We show that the canonical Hamiltonian thus defined is equivalent to the Hamiltonian initially defined by Lindblad, and that it is uniquely specified by requiring the dissipator’s jump operators to be traceless, extending a uniqueness result known previously in the special case of Markovian master equations. For a system weakly coupled to its environment, we give a recursive formula for computing the canonical effective Hamiltonian to arbitrary orders in perturbation theory, which we can think of as a perturbative scheme for renormalizing the system’s bare Hamiltonian.

Physics↗

DOE OSTI2021

Twisted symmetric trilayer graphene: Single-particle and many-body Hamiltonians and hidden nonlocal symmetries of trilayer moiré systems with and without displacement field

Here, we derive the Hamiltonian for trilayer moiré systems with the Coulomb interaction projected onto the bands near the charge neutrality point. Motivated by the latest experimental results, we focus on the twisted symmetric trilayer graphene (TSTG) with a mirror symmetry with respect to the middle layer. We provide a full symmetry analysis of the noninteracting Hamiltonian with a perpendicular displacement field coupling the band structure made otherwise of the twisted bilayer graphene (TBG) and the high-velocity Dirac fermions, and we identify a hidden nonlocal symmetry of the problem. In the presence of this displacement field, we construct an approximate single-particle model, akin to the tripod model for TBG, capturing the essence of noninteracting TSTG. We also derive more quantitative perturbation schemes for the low-energy physics of TSTG with displacement field, obtaining the corresponding eigenstates. This allows us to obtain the Coulomb interaction Hamiltonian projected in the active band TSTG wave functions and derive the full many-body Hamiltonian of the system. We also provide an efficient parametrization of the interacting Hamiltonian. Finally, we show that the discrete symmetries at the single-particle level promote the U (2) × U (2) spin-valley symmetry to enlarged symmetry groups of the interacting problem under different limits. The interacting part of the Hamiltonian exhibits a large U (4) × U (4) × U (4) × U (4) symmetry in the chiral limit. Moreover, by identifying a symmetry which we dub spatial many-body charge conjugation, we show that the physics of TSTG is symmetric around charge neutrality.

2-dimensional systems↗

DOE OSTI2023

Quantum simulations in effective model spaces: Hamiltonian-learning variational quantum eigensolver using digital quantum computers and application to the Lipkin-Meshkov-Glick model

Quantum simulations offer the potential to predict the structure and dynamics of nuclear many-body systems that are beyond the capabilities of classical computing. Generally, preparing the ground state of strongly-interacting many-body systems relevant to nuclear physics is however inefficient, even using ideal quantum computers. In addition, currently available NISQ-era quantum devices possess modest numbers of qubits, limiting the size of quantum many-body systems that can be simulated. In this context, a reformulation of the quantum many-body problems using truncated model spaces and Hamiltonians is desirable to make them more amenable to near-term quantum computers. The importance of symmetries in low-energy theories, including effective field theories (EFTs), lattice quantum chromodynamics (QCD), and effective model spaces for nuclear systems, in particular their interplay with the reduction of active Hilbert spaces, is well known. Lesser known is the fact that the non-commutivity of some symmetries and truncations of the model space can be profitably combined with variational calculations to rearrange the entanglement into localized structures and enable more efficient simulations. Here, the goal of the present study is to explore and utilize the non-commutivity of symmetries and model-space truncations of quantum many-body systems important to nuclear physics, particularly in combination with variational algorithms for quantum simulations and effective Hamiltonian learning. We introduce an iterative hybrid classical-quantum algorithm, Hamiltonian learning variational quantum eigensolver (HL-VQE), that simultaneously optimizes an effective Hamiltonian, thereby rearranging entanglement into the effective model space, and the associated ground-state wavefunction. Quantum simulations, using classical computers and IBM's superconducting-qubit quantum computers, are performed to demonstrate the HL-VQE algorithm, in the context of the Lipkin-Meshkov-Glick (LMG) model of interacting fermions, where the Hamiltonian transformation corresponds to an orbital rotation. We use a mapping where the number of qubits scales with the $\log$ of the size of the effective model space, rather than the particle number. HL-VQE is found to provide an exponential improvement in LMG-model calculations of the ground-state energy and wavefunction, compared to naive truncations without Hamiltonian learning, throughout a significant fraction of the Hilbert space. In the context of EFT, this corresponds to counterterms scaling exponentially with the cut-off as opposed to power law. Implementations on IBM's QExperience quantum computers and simulators for 1- and 2-qubit effective model spaces are shown to provide accurate and precise results, reproducing classical predictions. For a range of parameters defining the LMG model, the HL-VQE algorithm is found to have better scaling of quantum resources requirements than previously explored algorithms. In particular, the HL-VQE scales efficiently over a large fraction of the model space, in contrast to VQE alone. This work constitutes a step in the development of entanglement-driven quantum algorithms for descriptions of nuclear many-body systems. This, in part, leverages the potential of noisy intermediate-scale quantum (NISQ) devices. The exponential scaling of counterterms observed in this study suggests the possibility of more general applicability to other non-perturbative EFTs.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Machine learning a molecular Hamiltonian for predicting electron dynamics

We develop a computational method to learn a molecular Hamiltonian matrix from matrix-valued time series of the electron density. As we demonstrate for three small molecules, the resulting Hamiltonians can be used for electron density evolution, producing highly accurate results even when propagating 1,000 time steps beyond the training data. As a more rigorous test, we use the learned Hamiltonians to simulate electron dynamics in the presence of an applied electric field, extrapolating to a problem that is beyond the field-free training data. We find that the resulting electron dynamics predicted by our learned Hamiltonian are in close quantitative agreement with the ground truth. Our method relies on combining a reduced-dimensional, linear statistical model of the Hamiltonian with a time-discretization of the quantum Liouville equation within time-dependent Hartree Fock theory. In conclusion, we train the model using a least-squares solver, avoiding numerous, CPU-intensive optimization steps. For both field-free and field-on problems, we quantify training and propagation errors, highlighting areas for future development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Hartree–Fock–Bogoliubov theory for number-parity-violating fermionic Hamiltonians

It is usually asserted that physical Hamiltonians for fermions must contain an even number of fermion operators. This is indeed true in electronic structure theory. However, when the Jordan–Wigner (JW) transformation is used to map physical spin Hamiltonians to Hamiltonians of spinless fermions, terms that contain an odd number of fermion operators may appear. The resulting fermionic Hamiltonian thus does not have number parity symmetry and requires wave functions that do not have this symmetry either. In this work, we discuss the extension of standard Hartree–Fock–Bogoliubov (HFB) theory to the number-parity-nonconserving case. These ideas had appeared in the literature before but, perhaps for lack of practical applications, had, to the best of our knowledge, never been employed. We here present a useful application for this more general HFB theory based on coherent states of the SO(2M + 1) Lie group, where M is the number of orbitals. Here, we also show how using these unusual mean-field states can provide significant improvements when studying the JW transformation of chemically relevant spin Hamiltonians.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Quantum simulation of second-quantized Hamiltonians in compact encoding

We describe methods for simulating general second-quantized Hamiltonians using the compact encoding, in which qubit states encode only the occupied modes in physical occupation number basis states. These methods apply to second-quantized Hamiltonians composed of a constant number of interactions, i.e., linear combinations of ladder operator monomials of fixed form. Compact encoding leads to qubit requirements that are optimal up to logarithmic factors. Here, we show how to use sparse Hamiltonian simulation methods for second-quantized Hamiltonians in compact encoding, give explicit implementations for the required oracles, and analyze the methods. We also describe several example applications including the free boson and fermion theories, the φ 4 -theory, and the massive Yukawa model, all in both equal-time and light-front quantization. Our methods provide a general-purpose tool for simulating second-quantized Hamiltonians, with optimal or near-optimal scaling with error and model parameters.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Large classes of quantum scarred Hamiltonians from matrix product states

Motivated by the existence of exact many-body quantum scars in the Affleck-Kennedy-Lieb-Tasaki (AKLT) chain, in this work we explore the connection between matrix product state (MPS) wave functions and many-body quantum scarred Hamiltonians. We provide a method to systematically search for and construct parent Hamiltonians with towers of exact eigenstates composed of quasiparticles on top of an MPS wave function. These exact eigenstates have low entanglement in spite of being in the middle of the spectrum, thus violating the strong eigenstate thermalization hypothesis. Using our approach, we recover the AKLT chain starting from the MPS of its ground state, and we derive the most general nearest-neighbor Hamiltonian that shares the AKLT quasiparticle tower of exact eigenstates. We further apply this formalism to other simple MPS wave functions, and derive families of Hamiltonians that exhibit AKLT-like quantum scars. As a consequence, we also construct a scar-preserving deformation that connects the AKLT chain to the integrable spin-1 pure biquadratic model. Finally, we also derive other families of Hamiltonians that exhibit types of exact quantum scars, including a $\textit{U}$(1)-invariant perturbed Potts model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Effective Gaps Are Not Effective: Quasipolynomial Classical Simulation of Obstructed Stoquastic Hamiltonians

All known examples suggesting an exponential separation between classical simulation algorithms and stoquastic adiabatic quantum computing (StoqAQC) exploit symmetries that constrain adiabatic dynamics to effective, symmetric subspaces. The symmetries produce large effective eigenvalue gaps, which in turn make adiabatic computation efficient. We present a classical algorithm to subexponentially sample from an effective subspace of any k -local stoquastic Hamiltonian H , without a priori knowledge of its symmetries (or near symmetries). Our algorithm maps any k -local Hamiltonian to a graph G = ( V , E ) with | V | = O (poly (n)) , where n is the number of qubits. Given the well-known result of Babai [Graph isomorphism in quasipolynomial time, in Proceedings of the Forty-Eighth Annual ACM Symposium on Theory of Computing (2016), pp. 684–697], we exploit graph isomorphism to study the automorphisms of G and arrive at an algorithm quasipolynomial in | V | for producing samples from effective subspace eigenstates of H . Our results rule out exponential separations between StoqAQC and classical computation that arise from hidden symmetries in k -local Hamiltonians. Our graph representation of H is not limited to stoquastic Hamiltonians and may rule out corresponding obstructions in nonstoquastic cases, or be useful in studying additional properties of k -local Hamiltonians.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Stability of PT and anti- PT -symmetric Hamiltonians with multiple harmonics

Hermitian Hamiltonians with time-periodic coefficients can be analyzed via Floquet theory, and have been extensively used for engineering Floquet Hamiltonians in standard quantum simulators. Generalized to non-Hermitian Hamiltonians, time periodicity offers avenues to engineer the landscape of Floquet quasienergies across the complex plane. We investigate two-level non-Hermitian PT and anti- PT -symmetric Hamiltonians with coefficients that have multiple harmonics using Floquet theory. By analytical and numerical calculations, we obtain their regions of stability, defined by real Floquet quasienergies, and contours of exceptional point (EP) degeneracies. We extend our analysis to study the phases that accompany these cyclic changes with the biorthogonality approach. Our results demonstrate that these time-periodic Hamiltonians generate a rich landscape of stable (real) and unstable (complex) regions. Published by the American Physical Society 2024

Cen, Julia (ORCID:0000000299353943)↗

DOE OSTI2025

Genesis: A Compiler Framework for Hamiltonian Simulation on Hybrid CV-DV Quantum Computers

We introduce Genesis, the first compiler designed to support Hamiltonian Simulation on hybrid continuous-variable (CV) and discrete-variable (DV) quantum computing systems. Genesis is a two-level compilation system. At the first level, it decomposes an input Hamiltonian into basis gates using the native instruction set of the target hybrid CV-DV quantum computer. At the second level, it tackles the mapping and routing of qumodes/qubits to implement long-range interactions for the gates decomposed from the first level. Rather than a typical implementation that relies on SWAP primitives similar to qubit-based (or DV-only) systems, we propose an integrated design of connectivity-aware gate synthesis and beamsplitter SWAP insertion tailored for hybrid CV-DV systems. We also introduce an OpenQASM-like domain-specific language (DSL) named CVDV-QASM to represent Hamiltonian in terms of Pauli-exponentials and basic gate sequences from the hybrid CVDV gate set. Genesis has successfully compiled several important Hamiltonians, including the Bose-Hubbard model, Z2−Higgs model, Hubbard-Holstein model, Heisenberg model and Electron-vibration coupling Hamiltonians, which are critical in domains like quantum field theory, condensed matter physics, and quantum chemistry. Our implementation is available at Genesis-CVDV-Compiler https://github.com/ruadapt/Genesis-CVDV-Compiler

Chen, Henry↗

DOE OSTI2024

On the hardness of learning ground state entanglement of geometrically local Hamiltonians

Characterizing the entanglement structure of ground states of local Hamiltonians is a fundamental problem in quantum information. In this work we study the computational complexity of this problem, given the Hamiltonian as input. Our main result is that to show it is cryptographically hard to determine if the ground state of a geometrically local, polynomially gapped Hamiltonian on qudits (d=O(1)) has near-area law vs near-volume law entanglement. This improves prior work of Bouland et al. (arXiv:2311.12017) showing this for non-geometrically local Hamiltonians. In particular we show this problem is roughly factoring-hard in 1D, and LWE-hard in 2D. Our proof works by constructing a novel form of public-key pseudo-entanglement which is highly space-efficient, and combining this with a modification of Gottesman and Irani's quantum Turing machine to Hamiltonian construction. Our work suggests that the problem of learning so-called "gapless" quantum phases of matter might be intractable.

Computational Complexity (cs.CC)↗

DOE OSTI2025

Ginsparg-Wilson Hamiltonians with Improved Chiral Symmetry

We construct a family of Ginsparg-Wilson Hamiltonians with improved chiral properties, starting from a construction of Creutz-Horvath-Neuberger that provides a doubler-free Hamiltonian lattice regularization for Dirac fermions in even spacetime dimensions. We use a higher-order generalization of the Ginsparg-Wilson relation due to Fujikawa, which yields an order-$k$ Hamiltonian overlap operator for each integer $k \geq 0$, with an exactly conserved but nonquantized chiral charge that becomes quantized as $k \to \infty$. Our construction provides physical insight into how Fujikawa's higher-order Ginsparg-Wilson relation improves chiral symmetry while reproducing the anomaly, highlighting the trade-offs inherent in any Hamiltonian lattice realization of an anomalous chiral symmetry. This class of Hamiltonian lattice regularizations, with their tunable chiral symmetry properties, offers potential advantages for quantum and tensor-network simulations.

Singh, Hersh [Fermilab]↗

NASA NTRS1972

Hamiltonian cosmology.

The study of cosmological models by means of equations of motion in Hamiltonian form is considered. Hamiltonian methods applied to gravity seem to go back to Rosenfeld (1930), who constructed a quantum-mechanical Hamiltonian for linearized general relativity theory. The first to notice that cosmologies provided a simple model in which to demonstrate features of Hamiltonian formulation was DeWitt (1967). Applications of the ADM formalism to homogeneous cosmologies are discussed together with applications of the Hamiltonian formulation, giving attention also to Bianchi-type universes. Problems involving the concept of superspace and techniques of quantization are investigated.

Ryan, M.↗