Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Bounds”

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 649 records · Page 36
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Submodular optimization problems and greedy strategies: A survey

The greedy strategy is an approximation algorithm to solve optimization problems arising in decision making with multiple actions. How effective is the greedy strategy compared to the optimal solution? In this survey, we mainly consider two classes of optimization problems where the objective function is submodular. The first is set submodular optimization, which is to choose a set of actions to optimize a set submodular objective function, and the second is string submodular optimization, which is to choose an ordered set of actions to optimize a string submodular function. Our emphasis here is on performance bounds for the greedy strategy in submodular optimization problems. Specifically, we review performance bounds for the greedy strategy, more general and improved bounds in terms of curvature, performance bounds for the batched greedy strategy, and performance bounds for Nash equilibria.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Consistent Controls on Trace Metal Micronutrient Speciation in Wetland Soils and Stream Sediments

Trace metal are essential for microbially-mediated biogeochemical processes occurring in anoxic wetland soils and stream bed sediments, but low availability of these elements may inhibit anaerobic element cycling and transformations. Solid-phase speciation is likely a critical control on trace metal availability but has seen limited study in anoxic systems having concentrations similar to geological background levels, where metal limitations may be most prevalent. We have investigated trace metal concentrations and solid-phase speciation in three freshwater subsurface aquatic systems: marsh wetland soils, riparian wetland soils, and the sediments of a streambed. These systems displayed low solid-phase trace metal concentrations, generally at or below geological background levels, which generally followed the trend Zn > Cu ≈ Ni > Co and showed no correlation with major element compositions. All soils and sediments were dominated by quartz but varied in clay mineralogy as well as the organic matter, total sulfur, and total iron contents. X-ray absorption near-edge structure (XANES) spectroscopy shows that sulfur speciation in both wetlands is dominated by organic sulfur. Elemental sulfur and iron sulfides together made up <25% of the sulfur in the wetland soils, but the distribution between inorganic and organic forms was reversed in the stream sediments. Ferrous and ferric iron in clay minerals were common species identified by both XANES and extended X-ray absorption fine structure (EXAFS) spectroscopies at all sites. Iron(III) oxides were substantial components in all but the marsh wetland soils. Quantitative analysis of copper, nickel, and zinc XANES spectra revealed similar metal speciation across all sites. Copper speciation was dominated by sulfides, adsorbed species, and minor amounts of copper bound to organic matter; no metallic copper was detected. Nickel speciation also varied little and was dominated by nickel in clay mineral octahedral sheets and nickel sulfide, with adsorbed species also present. Zinc speciation was slightly more varied, with the marsh wetland soils and stream bed sediments containing adsorbed species, zinc associated with clay mineral structures, and zinc bound to reduced sulfur groups on organic matter, whereas the riparian wetland soils lacked clay-associated zinc but contained zinc sulfide. Trace metals bound to reduced sulfur occurred at every site, with a greater sulfur-bound fraction for copper. The fractional abundance of sulfur-bound species showed no relationship with soil or sediment total sulfur content, which varied by two orders of magnitude. More broadly, the observations in this study suggest that trace metal speciation in freshwater wetland soils and stream sediments is consistently dominated by a small set of recurring components which are distinct for each metal. Furthermore, this may represent a general geochemical phenomenon in anoxic soils and sediments containing trace metals at background concentrations (as low as 3 µg g -1 ) that was not predicted from systems that are contaminated with or naturally-enriched in copper, nickel, or zinc.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Revealing the mechanism of action of a first-in-class covalent inhibitor of $\mathrm{KRASG12C}$ $\mathrm{(ON)}$ and other functional properties of oncogenic $\text{KRAS}$ by 31 P $\mathrm{NMR}$

Individual oncogenic KRAS mutants confer distinct differences in biochemical properties and signaling for reasons that are not well understood. KRAS activity is closely coupled to protein dynamics and is regulated through two interconverting conformations: state 1 (inactive, effector binding deficient) and state 2 (active, effector binding enabled). Here, we use 31 P NMR to delineate the differences in state 1 and state 2 populations present in WT and common KRAS oncogenic mutants (G12C, G12D, G12V, G13D, and Q61L) bound to its natural substrate GTP or a commonly used nonhydrolyzable analog GppNHp (guanosine-5'-[(β,γ)-imido] triphosphate). Our results show that GppNHp-bound proteins exhibit significant state 1 population, whereas GTP-bound KRAS is primarily (90% or more) in state 2 conformation. This observation suggests that the predominance of state 1 shown here and in other studies is related to GppNHp and is most likely nonexistent in cells. We characterize the impact of this differential conformational equilibrium of oncogenic KRAS on RAF1 kinase effector RAS-binding domain and intrinsic hydrolysis. Through a KRAS G12C drug discovery, we have identified a novel small-molecule inhibitor, BBO-8956, which is effective against both GDP- and GTP-bound KRAS G12C. We show that binding of this inhibitor significantly perturbs state 1–state 2 equilibrium and induces an inactive state 1 conformation in GTP-bound KRAS G12C. In the presence of BBO-8956, RAF1–RAS-binding domain is unable to induce a signaling competent state 2 conformation within the ternary complex, demonstrating the mechanism of action for this novel and active-conformation inhibitor.

31P NMR↗
DOE OSTI2021

Controlling Heterogeneous Catalysis with Organic Monolayers on Metal Oxides

A key theme of heterogeneous catalysis research is achieving control of the environment surrounding the active site to precisely steer the reactivity toward desired reaction products. One method toward this goal has been the use of organic ligands or self-assembled monolayers (SAMs) on metal nanoparticles. Metal-bound SAMs are typically employed to improve catalyst selectivity but often decrease the reaction rate as a result of site blocking from the ligands. Recently, the use of metal oxide-bound organic modifiers such as organophosphonic acid (PA) SAMs has shown promise as an additional method for tuning reactions on metal oxide surfaces as well as modifying oxide-supported metal catalysts. In this Account, we summarize recent approaches to enhance catalyst performance with oxide-bound monolayers. These approaches include (1) modification of metal oxide catalysts to tune surface reactions, (2) formation of SAMs on the oxide component of supported metal catalysts to modify sites at the metal–support interface, and (3) enhancement of catalyst performance (e.g., stability) through modification of sites remote from the active sites. Further, both the headgroups and organic tail groups of PA SAMs or other ligands can influence reactions on metal oxide surfaces. Binding of the headgroup can selectively poison certain active sites, altering the selectivity in a manner analogous to metal-bound ligands (at the expense of active site quantity). Moreover, tail groups can be functionalized to interact favorably with reactants and intermediates, for instance through dipole–dipole interactions. On supported metal catalysts like Pt/Al 2 O 3 , PA SAMs can selectively form on the oxide support. This selective deposition allows for modification of the metal–support interface with minimal blockage of metal sites. PA headgroups were shown to provide tunable acid sites at the interface, dramatically improving hydrodeoxygenation rates of various alcohols. Additionally, organic tail functionality was used to activate or stabilize specific reactants at the interface, such as with the use of amine-functionalized PAs to stabilize chemisorption of CO 2 during the reverse water gas shift reaction. PAs have also been found to affect the electronic properties of bulk metal sites through long-range electron withdrawal via the oxide, providing an additional avenue to tune catalytic behavior. Finally, organic modifiers were shown to enhance catalytic performance without directly modifying the active site. For instance, in biphasic liquid environments the modification of catalyst particles with hydrophobic or hydrophilic SAMs shifts the selectivity of multipath reactions on the basis of the hydrophobicities of different intermediates and products. As another “long-range” effect, the deposition of ligands on oxide supports improved catalyst stability through both improved resistance to sintering and suppression of active site poisoning. The recent contributions discussed in this Account demonstrate the versatility and significant potential for the approach of modifying catalysts with oxide-bound organic monolayers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Strain-Modulated Exciton Localization and Enhanced Emission in Multilayer GaSe

Strain engineering is one of the most effective routes for tuning the electrical and optical properties of two-dimensional layered materials. Besides reproducing the results of other groups on the tunability and photoluminescence (PL) enhancement of free and bound excitons under mechanical deformation or thermal effects, we systematically studied the mechanical strain (wrinkle) and local thermal strain (laser heating) effects on the PL lifetime and polarization in GaSe multilayers and their interplay, revealing their coupled impact on excitonic dynamics. Here, the PL intensity of localized excitons in the wrinkle region of GaSe increases superlinearly with the excitation laser power. The polarization effect has been observed for the bound exciton in GaSe under mechanical strain, but not in GaSe under thermal strain. Fluorescence lifetime imaging (FLIM) measurements reveal strain-tunable lifetimes for both free and bound excitons, and the lifetime of the bound exciton is longer than the free exciton in the mechanical strain region, correlating with the enhanced emission of the bound exciton. These results highlight previously uncharacterized optoelectronic tunability in GaSe and broaden the design space for strain (or thermally)-controlled 2D layered devices.

, GaSe, Exciton localization↗
DOE OSTI2021

Erratum: Planck 2018 results: VI. Cosmological parameters

In the original version, the bounds given in Eqs. (87a) and (87b) on the contribution to the early-time optical depth, (15,30), contained a numerical error in deriving the 95th percentile from the Monte Carlo samples. The corrected 95% upper bounds are: τ(15,30) < 0:018 (lowE, flat τ(15, 30), FlexKnot), (1) τ(15, 30) < 0:023 (lowE, flat knot, FlexKnot): (2) These bounds are a factor of 3 larger than the originally reported results. Consequently, the new bounds do not significantly improve upon previous results from Planck data presented in Millea & Bouchet (2018) as was stated, but are instead comparable. Equations (1) and (2) give results that are now similar to those of Heinrich & Hu (2021), who used the same Planck 2018 data to derive a 95% upper bound of 0.020 using the principal component analysis (PCA) model and uniform priors on the PCA mode amplitudes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Automorphic spectra and the conformal bootstrap

We describe a new method for constraining Laplacian spectra of hyperbolic surfaces and 2-orbifolds. The main ingredient is consistency of the spectral decomposition of integrals of products of four automorphic forms. Using a combination of representation theory of PSL 2 (R) and semidefinite programming, the method yields rigorous upper bounds on the Laplacian spectral gap. In several examples, the bound is nearly sharp. For instance, our bound on all genus-2 surfaces is λ 1 ≤ 3.8388976481, while the Bolza surface has λ 1 ≈ 3.838887258. The bounds also allow us to determine the set of spectral gaps attained by all hyperbolic 2-orbifolds. Our methods can be generalized to higher-dimensional hyperbolic manifolds and to yield stronger bounds in the two-dimensional case. The ideas were closely inspired by modern conformal bootstrap.

Kravchuk, Petr↗
DOE OSTI2025

Sharp detection of low-dimensional structure in probability measures via dimensional logarithmic Sobolev inequalities

Identifying low-dimensional structure in high-dimensional probability measures is an essential pre-processing step for efficient sampling. To identify this structure, we approximate the target measure as a perturbation of an arbitrary reference measure along a few directions in $\mathbb{R}^{d}$. These directions are determined by minimizing an upper bound on the Kullback–Leibler (KL) divergence between the target and its approximation. Our contribution improves upon previous works by leveraging dimensional logarithmic Sobolev inequalities to refine the bound on the KL divergence. These inequalities lead to a uniformly tighter bound on the KL divergence, thereby enhancing the identification of the most significant perturbation directions. In particular, when the target and reference are both Gaussian, minimizing the resulting bound is equivalent to minimizing the KL divergence. We further demonstrate the applicability of this analysis to the squared Hellinger distance, where analogous reasoning shows that the dimensional Poincaré inequality offers improved bounds.

Bayesian inference↗
DOE OSTI2026

Quantum Routing and Entanglement Dynamics Through Bottlenecks

To implement arbitrary quantum circuits in architectures with restricted interactions, one may effectively simulate all-to-all connectivity by routing quantum information. We consider the entanglement dynamics and routing between two regions only connected through an intermediate “bottleneck” region with few qubits. In such systems, where the entanglement rate is restricted by a vertex boundary rather than an edge boundary of the underlying interaction graph, existing results such as the small incremental entangling theorem give only a trivial constant lower bound on the routing time (the minimum time to perform an arbitrary permutation). We significantly improve the lower bound on the routing time in systems with a vertex bottleneck. Specifically, for any system with two regions 𝐿,𝑅 with 𝑁 𝐿 ,𝑁 𝑅 qubits, respectively, coupled only through an intermediate region 𝐶 with 𝑁 𝐶 qubits, for any 𝛿 > 0 we show a lower bound of Ω⁢(𝑁$^{1−𝛿}_{𝑅}$/√𝑁 𝐿⁢ 𝑁 𝐶 ) on the Hamiltonian quantum routing time when using piecewise time-independent Hamiltonians, or time-dependent Hamiltonians subject to a smoothness condition. We also prove an upper bound on the average amount of bipartite entanglement between 𝐿 and 𝐶,𝑅 that can be generated in time 𝑡 by such architecture-respecting Hamiltonians in systems constrained by vertex bottlenecks, improving the scaling in the system size from 𝑂⁡(𝑁 𝐿⁢ 𝑡) to 𝑂⁡(√𝑁 𝐿⁢ 𝑡). As a special case, when applied to the star graph (i.e., one vertex connected to 𝑁 leaves), we obtain an Ω⁡(√𝑁 1−𝛿 ) lower bound on the routing time and on the time to prepare 𝑁/2 Bell pairs between the vertices. We also show that, in systems of free particles, we can route optimally on the star graph in time Θ⁡(√𝑁) using Hamiltonian quantum routing, obtaining a speedup over gate-based routing, which takes time Θ⁡(𝑁).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Optimal sensing on an asymmetric exceptional surface

We study the connection between exceptional points (EPs) and optimal parameter estimation, in a simple system consisting of two counterpropagating traveling wave modes in a microring resonator. The unknown parameter to be estimated is the strength of a perturbing cross-coupling between the two modes. Partially reflecting the output of one mode into the other creates a non-Hermitian Hamiltonian that exhibits a family of EPs, creating an exceptional surface (ES). We use a fully quantum treatment of field inputs and noise sources to obtain a quantitative bound on the estimation error by calculating the quantum Fisher information (QFI) in the output fields, whose inverse gives the Cramér-Rao lower bound on the mean-squared error of any unbiased estimator. We determine the bounds for two input states, namely, a semiclassical coherent state and a highly nonclassical NOON state. We find that the QFI is enhanced in the presence of an EP for both of these input states and that both states can saturate the Cramér-Rao bound. We then identify idealized yet experimentally feasible measurements that achieve the minimum bound for these two input states. We also investigate how the QFI changes for parameter values that do not lie on the ES, finding that these can have a larger QFI, suggesting alternative routes to optimize the parameter estimation for this problem.

Exceptional points↗
DOE OSTI2026

Trajectory-independent speed limits for controlled open quantum systems

Existing quantum speed limits for controlled open quantum systems depend on the specified trajectory. For example, lower bounds on quantum annealing times in the presence of dissipation depend explicitly on the chosen annealing schedule. Recently, schedule-independent speed limits have been derived for annealing in the closed quantum system setting [L. P. García-Pintos et al ., SciPost Phys. 18 , 159 (2025)]. In this work, we generalize these results to open quantum systems, deriving schedule-independent lower bounds for quantum annealing times in systems described by a Lindblad master equation. We analyze the interplay between coherent control and dissipation in single- and two-qubit examples, demonstrating that the derived lower bounds capture key scaling behavior with respect to the strength of the dissipator. Finally, we apply the bound to thermal state preparation and show that the bound matches the expected asymptotic behavior for an Ising model in the high-temperature limit.

open quantum systems & decoherence↗
DOE OSTI2020

Fundamental limitations on photoisomerization from thermodynamic resource theories

Small, out-of-equilibrium, and quantum systems defy simple thermodynamic expressions. Such systems are exemplified by molecular switches, which exchange heat with a bath. These molecules can photoisomerize, or change conformation, or switch, on absorbing light. The photoisomerization probability depends on kinetic details that couple the molecule’s energetics to its dissipation. Therefore, a simple, general, thermodynamic-style bound on the photoisomerization probability seems out of reach. We derive such a bound using a resource theory. The resource-theory framework is a set of mathematical tools, developed in quantum information theory, used to generalize thermodynamics to small and quantum settings. From this toolkit has been derived a generalization of the second law, the thermomajorization preorder. We use thermomajorization to upper-bound the photoisomerization probability. Then, we compare the bound with an equilibrium prediction and with a Lindbladian model. We identify a realistic parameter regime in which the Lindbladian evolution saturates the thermomajorization bound. We also quantify the energy coherence in the electronic degree of freedom, and we argue that this coherence cannot promote photoisomerization. Overall, this work illustrates how quantum-information-theoretic thermodynamics can elucidate complex quantum processes in nature, experiments, and synthetics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Electronic density of states of a U ( 1 ) quantum spin liquid with spinon Fermi surface. I. Orbital magnetic field effects

A quantum spin liquid with a spinon Fermi surface is an exotic insulator that hosts neutral Fermi surfaces inside the insulating gap. In an external magnetic field, it has been pointed out that the neutral Fermi surfaces are Landau quantized to form Landau levels due to the coupling to the induced emergent gauge magnetic field. In this paper, we calculate the electronic density of states (as observed in tunneling experiments) of the quantum spin liquid in an orbital magnetic field. Here, we find that the Landau levels from the neutral Fermi surfaces give rise to a set of steps emerging at the upper and lower Hubbard band edges. Each of the Hubbard band edge steps further develop into a band edge resonance peak when a weak gauge binding arising from the gauge field fluctuations is taken into account. Importantly, each Hubbard band edge step and its resulting resonance peak in the weak gauge binding are found to have a corresponding Landau level from the neutral Fermi surfaces, so the Hubbard band edge steps and the band edge resonance peaks provide signatures to the unique feature that characterizes the Landau quantization of the in-gap neutral Fermi surfaces in the spin liquid. We further consider the strong gauge-binding regime where the band edge resonance peaks move into the Mott gap and develop into true in-gap bound states. In the strong gauge binding regime, we solve the Landau-level spectrum of the in-gap bound states in an orbital magnetic field. For the in-gap bound state with a Mexican-hat-like band dispersion, we find that the envelop energy to have a state excited from the bound state Landau levels decreases quadratically with the magnetic field. The quadratic decrease behavior of the envelop energy is consistent with the intuition that applying magnetic field localizes the states and energetically promotes the in-gap bound states formation. Finally, we discuss the connection of our results to the electronic density of states spectra measured in the layered 1T-TaS 2 . We point out that a quantum spin liquid with a quasibound state in the upper Hubbard band can give the density of states spectra similar to the one measured in the experiment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Unbound spectra of neutron-rich oxygen isotopes predicted by the Gamow shell model

The Gamow shell model has shown to efficiently describe weakly bound and unbound nuclear systems, as internucleon correlations and continuum coupling are both taken into account in this model. In the present work, we study neutron-dripline oxygen isotopes. It is hereby demonstrated that the presence of continuum coupling is important for the description of oxygen isotopes at dripline, and especially to assess the eventual bound or unbound character of 28 O. Our results suggest that the ground state of 28 O is weakly unbound and is similar to the narrow resonant 26 O ground state. Predictions of weakly bound and resonance excited states in 24–26 O are also provided. The asymptotes of the studied many-body states are analyzed via one-body densities, whereby the different radial properties of well bound, loosely bound, resonance states are clearly depicted.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Updated systematics of intermediate-energy single-nucleon removal cross sections

The body of experimental measurements of intermediate-energy reactions that remove a single nucleon from a secondary beam of neutron- or proton-rich nuclei continues to grow. These data have been analyzed consistently using an approximate, eikonal-model treatment of the reaction dynamics combined with appropriate shell-model descriptions of the projectile initial state, the bound final states spectrum of the reaction residue, and single-particle removal strengths computed from their wave-function overlaps. Here, the systematics of the ratio R s of the measured inclusive cross section to all bound final states and the calculated cross section to bound shell-model states—in different regions of the nuclear chart and involving both very weakly bound and strongly bound valence nucleons—is important in relating the empirically deduced orbital occupancies to those from the best available shell-model predictions. Importantly, several new higher-energy measurements, for which the sudden-approximation aspect of the dynamical description is placed on an even stronger footing, now supplement the previously analyzed measurements. These additional data sets are discussed. Their R s values are shown to conform to and reinforce the earlier-observed systematics, with no indication that the approximately linear reduction in R s with increasing nucleon separation energy is a consequence of a breakdown of the sudden approximation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Influence of the symmetry energy on the nuclear binding energies and the neutron drip line position

A clear connection can be established between properties of nuclear matter and finite-nuclei observables, such as the correlation between the slope of the symmetry energy and the dipole polarizability, or between compressibility and the isoscalar monopole giant resonance excitation energy. Establishing a connection between realistic atomic nuclei and an idealized infinite nuclear matter leads to a better understanding of underlying physical mechanisms that govern nuclear dynamics. In this work, we aim to study the dependence of the binding energies and related quantities (e.g., location of drip lines, the total number of bound even-even nuclei) on the symmetry energy S 2 (ρ). The properties of finite nuclei are calculated by employing the relativistic Hartree-Bogoliubov model, assuming even-even axial and reflection symmetric nuclei. Calculations are performed by employing two families of relativistic energy density functionals, based on different effective Lagrangians, constrained to a specific symmetry energy at the saturation density J within the interval of 30–36 MeV. Nuclear binding energies and related quantities of bound nuclei are calculated between 8 ≤ Z ≤ 104 from the two-proton to the two-neutron drip line. As the neutron drip line is approached, the interactions with stiffer J tend to predict more bound nuclei, resulting in a systematic shift of the two-neutron drip line towards more neutron-rich nuclei. Consequentially, a correlation between the number of bound nuclei N nucl and S 2 (ρ) is established for a set of functionals constrained using the similar optimization procedures. Furthermore the direction of the relationship between the number of bound nuclei and the symmetry energy highly depends on the density under consideration.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Theory of Trotter Error with Commutator Scaling

The Lie-Trotter formula, together with its higher-order generalizations, provides a simple approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly understood. We develop a theory of Trotter error that overcomes the limitations of truncating the Baker-Campbell-Hausdorff expansion. Our analysis directly exploits the commutativity of operator summands, producing tighter error bounds for both real- and imaginary-time evolutions. Whereas previous work achieves similar goals for systems with geometric locality or Lie-algebraic structure, our approach holds in general. We give a host of improved algorithms for digital quantum simulation and quantum Monte Carlo methods, nearly matching or even outperforming the best previous results. Our applications include: (i) a simulation of second-quantized plane-wave electronic structure, nearly matching the interaction-picture algorithm of Low and Wiebe; (ii) a simulation of $k$-local Hamiltonians almost with induced one-norm scaling, faster than the qubitization algorithm of Low and Chuang; (iii) a simulation of rapidly decaying power-law interactions, outperforming the Lieb-Robinson-based approach of Tran et al.; (iv) a hybrid simulation of clustered Hamiltonians, dramatically improving the result of Peng, Harrow, Ozols, and Wu; and (v) quantum Monte Carlo simulations of the transverse field Ising model and quantum ferromagnets, tightening previous analyses of Bravyi and Gosset. We obtain further speedups using the fact that product formulas can preserve the locality of the simulated system. Specifically, we show that local observables can be simulated with complexity independent of the system size for power-law interacting systems, which implies a Lieb-Robinson bound nearly matching a recent result of Tran et al. Our analysis reproduces known tight bounds for first- and second-order formulas. We further investigate the tightness of our bounds for higher-order formulas. For quantum simulation of a one-dimensional Heisenberg model with an even-odd ordering of terms, our result overestimates the complexity by only a factor of $5$. Our bound is also close to tight for power-law interactions and other orderings of terms. This suggests that our theory can accurately characterize Trotter error in terms of both the asymptotic scaling and the constant prefactor.

quantum computing, numerical analysis↗