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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.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
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↗
DOE OSTI2022

Analytical solution for nonadiabatic quantum annealing to arbitrary Ising spin Hamiltonian

Abstract Ising spin Hamiltonians are often used to encode a computational problem in their ground states. Quantum Annealing (QA) computing searches for such a state by implementing a slow time-dependent evolution from an easy-to-prepare initial state to a low energy state of a target Ising Hamiltonian of quantum spins, H I . Here, we point to the existence of an analytical solution for such a problem for an arbitrary H I beyond the adiabatic limit for QA. This solution provides insights into the accuracy of nonadiabatic computations. Our QA protocol in the pseudo-adiabatic regime leads to a monotonic power-law suppression of nonadiabatic excitations with time T of QA, without any signature of a transition to a glass phase, which is usually characterized by a logarithmic energy relaxation. This behavior suggests that the energy relaxation can differ in classical and quantum spin glasses strongly, when it is assisted by external time-dependent fields. In specific cases of H I , the solution also shows a considerable quantum speedup in computations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Hamiltonian simulation in the low-energy subspace

Abstract We study the problem of simulating the dynamics of spin systems when the initial state is supported on a subspace of low energy of a Hamiltonian H . This is a central problem in physics with vast applications in many-body systems and beyond, where the interesting physics takes place in the low-energy sector. We analyze error bounds induced by product formulas that approximate the evolution operator and show that these bounds depend on an effective low-energy norm of H . We find improvements over the best previous complexities of product formulas that apply to the general case, and these improvements are more significant for long evolution times that scale with the system size and/or small approximation errors. To obtain these improvements, we prove exponentially decaying upper bounds on the leakage to high-energy subspaces due to the product formula. Our results provide a path to a systematic study of Hamiltonian simulation at low energies, which will be required to push quantum simulation closer to reality.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Synthesizing efficient circuits for Hamiltonian simulation

Abstract We provide an approach for compiling quantum simulation circuits that appear in Trotter, qDRIFT and multi-product formulas to Clifford and non-Clifford operations that can reduce the number of non-Clifford operations. The total number of gates, especially CNOT, reduce in many cases. We show that it is possible to implement an exponentiated sum of commuting Paulis with at most m (controlled)-rotation gates, where m is the number of distinct non-zero eigenvalues (ignoring sign). Thus we can collect mutually commuting Hamiltonian terms into groups satisfying one of several symmetries identified in this work. This allows an inexpensive simulation of the entire group of terms. We further show that the cost can in some cases be reduced by partially allocating Hamiltonian terms to several groups and provide a polynomial time classical algorithm that can greedily allocate the terms to appropriate groupings.

Mukhopadhyay, Priyanka (ORCID:0000000164639100)↗
DOE OSTI2023

Variable-moment fluid closures with Hamiltonian structure

Abstract Based on ideas due to Scovel–Weinstein, I present a general framework for constructing fluid moment closures of the Vlasov–Poisson system that exactly preserve that system’s Hamiltonian structure. Notably, the technique applies in any space dimension and produces closures involving arbitrarily-large finite collections of moments. After selecting a desired collection of moments, the Poisson bracket for the closure is uniquely determined. Therefore data-driven fluid closures can be constructed by adjusting the closure Hamiltonian for compatibility with kinetic simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Extracting the excitonic Hamiltonian of a chlorophyll dimer from broadband two-dimensional electronic spectroscopy

We apply Frenkel exciton theory to model the entire Q-band of a tightly bound chlorophyll dimer inspired by the photosynthetic reaction center of photosystem II. The potential of broadband two-dimensional electronic spectroscopy experiment spanning the Qx and Qy regions to extract the parameters of the model dimer Hamiltonian is examined through theoretical simulations of the experiment. We find that the local nature of Qx excitation enables identification of molecular properties of the delocalized Qy excitons. Specifically, we demonstrate that the cross-peak region, where excitation energy is resonant with Qy while detection is at Qx, contains specific spectral signatures that can reveal the full real-space molecular Hamiltonian, a task that is impossible by considering the Qy transitions alone. System–bath coupling and site energy disorder in realistic systems may limit the resolution of these spectral signatures due to spectral congestion.

Chemistry↗
DOE OSTI2024

Hamiltonian switching control of noisy bipartite qubit systems

Abstract We develop a Hamiltonian switching ansatz for bipartite control that is inspired by the quantum approximate optimization algorithm, to mitigate environmental noise on qubits. We demonstrate the control for a central spin coupled to bath spins via isotropic Heisenberg interactions, and then make physical applications to the protection of quantum gates performed on superconducting transmon qubits coupling to environmental two-level-systems (TLSs) through dipole-dipole interactions, as well as on such qubits coupled to both TLSs and a Lindblad bath. The control field is classical and acts only on the system qubits. We use reinforcement learning with policy gradient to optimize the Hamiltonian switching control protocols, using a fidelity objective for specific target quantum gates. We use this approach to demonstrate effective suppression of both coherent and dissipative noise, with numerical studies achieving target gate implementations with fidelities over 0.9999 (four nines) in the majority of our test cases and showing improvement beyond this to values of 0.999 999 999 (nine nines) upon a subsequent optimization by GRadient Ascent Pulse Engineering (GRAPE). We analyze how the control depth, total evolution time, number of environmental TLS, and choice of optimization method affect the fidelity achieved by the optimal protocols and reveal some critical behaviors of bipartite control of quantum gates.

Physics↗
DOE OSTI2021

Parametrized Hamiltonian simulation using quantum optimal control

Analog quantum simulation offers a hardware-specific approach to studying quantum dynamics, but mapping a model Hamiltonian onto the available device parameters requires matching the hardware dynamics. In this work, we introduce a paradigm for quantum Hamiltonian simulation that leverages digital decomposition techniques and optimal control to perform analog simulation. We validate this approach by constructing the optimal analog controls for a superconducting transmon device to emulate the dynamics of an extended Bose-Hubbard model. We demonstrate the role of control time, digital error, and pulse complexity, and we explore the accuracy and robustness of these controls. We conclude by discussing the opportunity for implementing this paradigm in near-term quantum devices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Stochastic quantum Krylov protocol with double-factorized Hamiltonians

Here we propose a class of randomized quantum Krylov diagonalization (rQKD) algorithms capable of solving the eigenstate estimation problem with modest quantum resource requirements. Compared to previous real-time evolution quantum Krylov subspace methods, our approach expresses the time evolution operator e –i$\widehat{H}$$\tau$ as a linear combination of unitaries and subsequently uses a stochastic sampling procedure to reduce circuit depth requirements. While our methodology applies to any Hamiltonian with fast-forwardable subcomponents, we focus on its application to the explicitly double-factorized electronic-structure Hamiltonian. To demonstrate the potential of the proposed rQKD algorithm on near-term quantum devices, we provide numerical benchmarks for a variety of molecular systems with circuit-based state-vector simulators including the effects of sampling noise, achieving ground-state energy errors of less than 1 kcal mol -1 with circuit depths orders of magnitude shallower than those required for low-rank deterministic Trotter-Suzuki decompositions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Scattering solution of an interacting Hamiltonian for the electronic control of molecular spin qubits

We theoretically study how a scattered electron can entangle molecular spin qubits (MSQs). This requires solving the inelastic transport of a single electron through a scattering region described by a tight-binding interacting Hamiltonian. We accomplish this using a Green's-function solution. We can model realistic physical implementations of MSQs by parametrizing the tight-binding Hamiltonian with first-principles descriptions of magnetic anisotropy and exchange interactions. As a result, we find that, for two-MSQ systems with inversion symmetry, projective measurement of the spin degree of freedom of the scattered electron offers probabilistic control of the degree of entanglement between the MSQs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Variational Adiabatic Gauge Transformation on Real Quantum Hardware for Effective Low-Energy Hamiltonians and Accurate Diagonalization

Effective low-energy theories represent powerful theoretical tools to reduce the complexity in modeling interacting quantum many-particle systems. However, common theoretical methods rely on perturbation theory, which limits their applicability to weak interactions. Here we introduce the Variational Adiabatic Gauge Transformation (VAGT), a nonperturbative hybrid quantum algorithm that can use nowadays quantum computers to learn the variational parameters of the unitary circuit that brings the Hamiltonian to either its block-diagonal or full-diagonal form. If a Hamiltonian can be diagonalized via a shallow quantum circuit, then VAGT can learn the optimal parameters using a polynomial number of runs. The accuracy of VAGT is tested through numerical simulations, as well as simulations on Rigetti and IonQ quantum computers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Bogoliubov Fermi surfaces in spin-$\frac{1}{2}$ systems: Model Hamiltonians and experimental consequences

Bogoliubov Fermi surfaces (BFSs) are topologically protected regions of zero energy excitations in a superconductor whose dimension equals that of the underlying normal state Fermi surface. Examples of Hamiltonians exhibiting this “ultranodal” phase are known to preserve charge-conjugation ($\textit{C}$) and parity ($\textit{P}$) but break time-reversal ($\textit{T}$). In this work, we provide examples of model Hamiltonians that do not necessarily preserve this symmetry pattern but have well-defined sign-changing Pfaffians yielding BFSs. While their topological character has not been recognized previously, some of the models we present have been extensively studied in prior literature. Here, we further examine thermodynamic and electronic properties arising from the ultranodal state. In particular, we study the effect of a weak Zeeman field close to the topological transition and propose distinguishing features of BFSs using residual specific heat and tunneling conductance. Our calculation of the superfluid density in a toy multiband model indicates a window of interband pairing strength where BFSs are stable with a positive superfluid density. We also present additional signatures of BFSs in spin-polarized spectral weight and total magnetization measurements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Quantum phase transitions in a model Hamiltonian exhibiting entangled simultaneous fermion-pair and exciton condensations

Quantum states of a novel Bose-Einstein condensate, in which both fermion-pair and exciton condensations are simultaneously present, have recently been realized theoretically in a model Hamiltonian system. Here, in this study, we identify quantum phase transitions in that model between fermion-pair and exciton condensations based on a geometric analysis of the convex set of ground-state two-particle reduced density matrices (2-RDMs). The 2-RDM set provides a finite representation of the infinite parameter space of Hamiltonians that readily reveals a fermion-pair condensate phase and two distinct exciton condensate phases, as well as the emergence of first- and second-order phase transitions as the particle number of the system is increased. The set, furthermore, shows that the fermion-exciton condensate (FEC) lies along the second-order phase transition between the exciton and fermion-pair condensate phases. The detailed information about the exciton and fermion-pair phases, the forces behind these phases, as well as their associated transitions provides additional insight into the formation of the FEC condensate, which we anticipate will prove useful in its experimental realization.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Effect of off-diagonal elements in the Wannier Hamiltonian on DFT + DMFT for low-symmetry materials: Study of Li 2 MnO 3

Here, we study the effect of the off-diagonal elements of the Wannier Hamiltonian on the electronic structure of the low-symmetry material Li 2 MnO 3 ( C2/m ), using dynamical mean field theory calculations with a continuous-time quantum Monte Carlo impurity solver. The presence of significant off-diagonal elements leads to a pronounced suppression of the energy gap. The off-diagonal elements are largest when the Wannier projection is used based on the global coordinate, and they remain substantial even with the projection using the local coordinate close to the direction of Mn-O bonds. We show that the energy gap is enhanced by the diagonalization of the Mn d block in the full p-d Hamiltonian with the application of a unitary rotation matrix. Additionally, the inclusion of small double counting energy is crucial for achieving the experimental gap by reducing p-d hybridization. Furthermore, we establish the efficiency of a low-energy (d-only basis) model for studying the electronic structure of Li 2 MnO 3 , as the Wannier basis represents a hybridized state of Mn d and O p orbitals. These findings suggest an appropriate approach for investigating low-symmetry materials using the density functional theory plus dynamical mean field theory (DFT + DMFT) method. We also find that the antiferromagnetic ground state $\Gamma$ 2u is stable with U ≤ 2 eV within density functional theory+$U$ calculations, which is much smaller than the widely used U = 5 eV.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Topological triviality of flat Hamiltonians

Landau levels play a key role in theoretical models of the quantum Hall effect. Each Landau level is degenerate, flat, and topologically nontrivial. Motivated by Landau levels, we study tight-binding Hamiltonians whose energy levels are all flat. Here, we demonstrate that in two dimensions, for such Hamiltonians, the flat bands must be topologically trivial. To that end, we show that the projector onto each flat band is necessarily strictly local. Our conclusions do not need the assumption of lattice translational invariance.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Ab initio multishell valence-space Hamiltonians and the island of inversion

In the shell-model framework, valence-space Hamiltonians connecting multiple major-oscillator shells are of key interest for investigating the physics of neutron-rich nuclei, which have been the subject of intense experimental activity for decades. Here we present an extension of the ab initio valence-space in-medium similarity renormalization group, which allows the derivation of such Hamiltonians nonperturbatively. Starting from initial two- and three-nucleon forces from chiral effective field theory, we then calculate properties of nuclei in the important island-of-inversion region above oxygen, so far unexplored with ab initio methods. In this work, our results in the neon and magnesium isotopes indicate the importance of neutron excitation from the $\textit{sd}$ to $\textit{pf}$ shells and ground states dominated by intruder configurations around $\textit{N}$ = 20, consistent with the conclusions from phenomenological studies. We also benchmark the excitation spectrum of 16 O with coupled-cluster theory, finding generally good agreement, and discuss implications for ground-state energies and charge radii in oxygen and calcium isotopes. Finally we outline the proper procedure for treating the longstanding issue of center-of-mass contamination, and show that with a particular choice of valence space, these spurious states can be removed successfully.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Fermion-bag inspired Hamiltonian lattice field theory for fermionic quantum criticality

Motivated by the fermion-bag approach, in this work we construct a new class of Hamiltonian lattice field theories that can help us to study fermionic quantum critical points, particularly those with four-fermion interactions. Although these theories are constructed in discrete time with a finite temporal lattice spacing ϵ, when ϵ → 0, conventional continuous-time Hamiltonian lattice field theories are recovered. The fermion-bag algorithms run relatively faster when ϵ = 1 as compared to ϵ → 0 but still allow us to compute universal quantities near the quantum critical point even at such a large value of ϵ. As an example of this new approach, here we study the $N_f$ = 1 Gross-Neveu chiral-Ising universality class in 2 + 1 dimensions by calculating the critical scaling of the staggered mass order parameter. We show that we are able to study lattice sizes up to 100 2 sites when ϵ = 1, while with comparable resources we can reach lattice sizes of only up to 64 2 when ϵ → 0. The critical exponents obtained in both these studies match within errors.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗