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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

MFANS 2024 - Formally Proving Characteristics of Cyber-Physical Systems

Cyber-physical systems (CPS) are engineered systems that rely on the smooth integration of computational algorithms and physical elements. This integration presents new challenges for verifying that systems will behave as expected. The goal of this presentation is to present current challenges and potential solutions for the formal verification of cyber-physical systems. For cyber systems, formal methods refer to systematically rigorous mathematical techniques employed in the specification, development, analysis, and verification of both software and hardware systems. Recent advancements in computer science have yielded sophisticated tools specifically designed to address challenges associated with formal methods in complex systems. These tools leverage various foundational concepts such as logic, formal languages, program semantics, type systems, type theory, and automata theory. A notable achievement in the application of formal methods is the seL4 microkernel, claimed to be the first general-purpose operating-system kernel to be verified. Its proof implies the absence of bugs and guarantees that the kernel meets specifications. For physical systems, dynamic and control theory has a history of using rigorous analytic techniques to prove functional correctness. Lyapunov, optimal, classical, modern, and robust control theories all provide rigorous mathematical methods both to analyze system performance and to design controller that can be guaranteed to meet certain objectives. Recent computational techniques like level set theory and reachability analysis provide assertions that a system's state will avoid unsafe regions. Even though success has been independently achieved for cyber systems and physical systems, the integration of such systems creates new challenges. In particular, there is an obvious discrepancy between finite-state machines and infinite-state systems, resulting in different approaches for modeling and analyzing these system. While it is possible to simulate hybrid systems, this provides only a demonstration of a performance and not proof. For hybrid systems, current formal methods and system analysis approaches typically require a workarounds to work on hybrid systems like CPS. This paper will outline the state of the art and limits of current practice for formally verifying CPS and will identify possible research directions that require attention.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Prediction of Above-Room-Temperature Superconductivity in Lanthanide/Actinide Extreme Superhydrides

Achieving superconductivity at or above room temperature has been a century long held dream for physicists since the discovery of superconductivity in mercury in 1911. Following the recent predictions and ensuing synthesis of clathrate superhydride LaH 10 under pressure exhibiting extraordinary superconducting critical temperatures (T c ) of 250 260 K, we predict via advanced crystal structure search methods a new class of extremely hydrogen rich clathrate superhydrides. These MH 18 (M: rare earth/actinide metal atom) stoichiometric compounds consisting of H36 cage networks are predicted to host T c values above room temperature up to 330 K at pressures of 350 GPa. The bonding and electronic properties of these MH 18 clathrate superhydrides parallel those of atomic metallic hydrogen, giving rise to the highest superconducting temperatures predicted thus far for a thermodynamically stable hydride compound. In depth examination of these extreme superhydrides offers key insights for elucidating and further exploring phonon mediated superconductivity above room temperature in hydrogen rich and other low Z materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Nuclear cusps and singularities in the nonadditive kinetic potential bifunctional from analytical inversion

The non-additive kinetic potential $v^{\text{NAD}}$ is a key quantity in density-functional theory (DFT) embedding methods, such as frozen density embedding theory and partition DFT. $v^{\text{NAD}}$ is a bi-functional of electron densities $\rho_{\rm B}$ and $\rho_{\rm tot} = \rho_{\rm A} + \rho_{\rm B}$. It can be evaluated using approximate kinetic-energy functionals, but accurate approximations are challenging. The behavior of $v^{\text{NAD}}$ in the vicinity of the nuclei has long been questioned, and singularities were seen in some approximate calculations. In this article, the existence of singularities in $v^{\text{NAD}}$ is analyzed analytically for various choices of $\rho_{\rm B}$ and $\rho_{\rm tot}$, using the nuclear cusp conditions for the density and Kohn-Sham potential. It is shown that no singularities arise from smoothly partitioned ground-state Kohn-Sham densities. We confirm this result by numerical calculations on diatomic test systems HeHe, HeLi$^+$, and H$_2$, using analytical inversion to obtain a numerically exact $v^{\rm NAD}$ for the local density approximation. We examine features of $v^{\rm NAD}$ which can be used for development and testing of approximations to $v^{\rm NAD}[\rho_{\rm B},\rho_{\rm tot}]$ and kinetic-energy functionals.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Time-dependent equation-of-motion coupled-cluster simulations with a defective Hamiltonian

Here simulations of laser-induced electron dynamics in a molecular system are performed using time-dependent (TD) equation-of-motion (EOM) coupled-cluster (CC) theory. The target system has been chosen to highlight potential shortcomings of truncated TD-EOM-CC methods [represented in this work by TD-EOM-CC with single and double excitations (TD-EOM-CCSD)], where unphysical spectroscopic features can emerge. Specifically, we explore driven resonant electronic excitations in magnesium fluoride in the proximity of an avoided crossing. Near the avoided crossing, the CCSD similarity-transformed Hamiltonian is defective, meaning that it has complex eigenvalues, and oscillator strengths may take on negative values. When an external field is applied to drive transitions to states exhibiting these traits, unphysical dynamics are observed. For example, the stationary states that make up the time-dependent state acquire populations that can be negative, exceed one, or even complex-valued.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Importance of Dispersion in the Molecular Geometries of Mn(III) Spin-Crossover Complexes

The computational investigation of the molecular geometries of a pair of manganese(III) spin-crossover complexes is reported. For the geometry of the quintet high-spin state, density functionals significantly overestimate Mn–Namine bond distances, although the geometry for the triplet intermediate-spin state is well described. Here, comparisons with several wave function-based methods demonstrate that this error is due to the limited ability of commonly used density functionals to recover dispersion beyond a certain extent. Among the methods employed for geometry optimization, restricted open-shell Møller–Plesset perturbation theory (MP2) appropriately describes the high-spin geometry but results in a slightly shorter Mn–O distance in both spin states. On the other hand, extended multistate complete active space second-order perturbation theory (XMS-CASPT2) provides a good description of the geometry for the intermediate-spin state but also sufficiently recovers dispersion, performing well for the high-spin state. Despite the fact that the electronic structure of both spin states is dominated by one-electron configuration, XMS-CASPT2 offers a balanced approach, leading to molecular geometries with much better agreement with experiment than MP2 and DFT. A scan along the Mn–N amine bond demonstrates that for these complexes coupled cluster methods (i.e., DLPNO-CCSD(T)) also yield bond distances in agreement with experiment while multiconfiguration pair density functional theory (MC-PDFT) is unable to recover dispersion well enough, analogous to single-reference DFT.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Multi-Scale Integrated Monitoring System for Enhancing Methane Emission Detection, Quantification & Prediction

This report details the progress and findings of a comprehensive study on reviewing existing solutions, identifying technology gaps, and formulating an “all-in-one” integrated strategy for developing the next-generation multiscale methane monitoring and modeling platform, conducted under grant number DE-FE0032292. Co-led by Dr. David Ebert, Dr. Binbin Weng, and Dr. Chenghao Wang at the University of Oklahoma, the project’s goal was to develop an integrated approach for building this engineering platform to detect, quantify, and mitigate methane emissions across various temporal scale, spatial scales, and sectors. The planning grant study began with an extensive review of various methane sensing and monitoring technologies and systems, surveying over 100 technology providers globally. This review revealed the prevalence of optical methods over chemical methods in commercially available sensors, with Non-Dispersive Infrared (NDIR), Tunable Diode Laser Absorption Spectroscopy (TDLAS), and Optical Gas Imaging (OGI) cameras being the most prevalent options. A trend towards more advanced optical techniques was observed, driven by increased regulatory focus and technological advancements. The technical evaluation of these sensing technologies provided crucial insights into their capabilities and limitations. The study examined emerging technologies such as Differential Absorption LiDAR (DIAL), which show promise for high-precision and long-range detection. The team then investigated the features and application bandwidth of various sensing platforms, including handheld, fixed/stationary, mobile, aerials, and spaceborne monitors. Pilot field studies were conducted to assess the capabilities of solutions for different emission scenarios. Field work with sensor deployments was conducted at three distinct site types: an oil & gas industry site, a cattle ranching operation, and a waste processing facility. The team also conducted a thorough review of methane flux inverse modeling approaches, focused on physically based methods. These approaches were categorized into simple, intermediate, and advanced methods. A realtime WRF-GHG (Weather Research and Forecasting-Greenhouse Gas) modeling system was developed and applied, incorporating multiple data sources to guide field experiments and inform methane plume detection. The project identified and analyzed numerous categories of methane data sources, including satellite measurements, ground-based sensors, and inventory databases. Key platforms examined include EDGAR, EPA GHGI, NASA TROPOMI, Carbon Mapper, and Climate TRACE, among others. The team proposed an architecture for a comprehensive methane monitoring platform. This system incorporates multi-source data acquisition, advanced data processing and assimilation, interactive visualization tools, and analytical capabilities for emissions forecasting and scenario analysis. The proposed platform aims to provide a user-friendly interface catering to various stakeholders, from researchers to policymakers. The architecture includes sophisticated data ingestion methods, a centralized data warehouse, and advanced analytical tools for data fusion and interpretation. To ensure the relevance and effectiveness of the proposed system, a comprehensive survey was conducted to gather stakeholder input on system requirements. Key findings include a strong need for integrating various data types and formats, a preference for real-time data updates and advanced visualization tools, and a demand for user-friendly interfaces catering to different expertise levels.

03 NATURAL GAS↗
DOE OSTI2024

Pseudospectral particle-in-cell formulation with arbitrary charge and current-density time dependencies for the modeling of relativistic plasmas

This paper introduces a formulation of the particle-in-cell (PIC) method for the modeling of relativistic plasmas, that leverages the ability of the pseudospectral analytical time-domain solver (PSATD) to handle arbitrary time dependencies of the charge and current densities during one PIC cycle (applied to second-order polynomial dependencies here). Here, the formulation is applied to a modified set of Maxwell's equations that was proposed earlier in the context of divergence cleaning, and to recently proposed extensions of the PSATD-PIC algorithm. Detailed analysis and testings revealed that, under some condition, the formulation can expand the range of numerical parameters under which PIC simulations are stable and accurate when modeling relativistic plasmas such as, e.g., plasma-based particle accelerators.

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Near-field radiative heat transfer between irregularly shaped dielectric particles modeled with the discrete system Green's function method

Near-field radiative heat transfer (NFRHT) between irregularly shaped dielectric particles made of SiO 2 and morphology characterized by Gaussian random spheres is studied. Particles are modeled using the discrete system Green's function (DSGF) approach, which is a volume integral numerical method based on fluctuational electrodynamics. This method is applicable to finite, three-dimensional objects, and all system interactions are defined independent of thermal excitation by a generalized system Green's function. The DSGF method is deemed suitable to model NFRHT between irregularly shaped particles after verification against the analytical solution for chains of two and three SiO 2 spheres. The NFRHT results reveal that geometric irregularity in particles leads to a reduction of the total conductance from that of comparable perfect spheres at vacuum separation distances smaller than the particle size, a regime in which NFRHT is a surface phenomenon. At vacuum separation distances larger than the particle size, NFRHT becomes a volumetric process, and the total conductance between irregularly shaped particles converges to that of comparable perfect spheres. Spectral analysis reveals, however, that particle irregularity leads to damping and broadening of resonances at all separation distances, thereby highlighting the importance of the DSGF method for spectral engineering in the near field. The reduced spectral coherence when particle size is larger than the vacuum separation distance is attributed to coupling of surface phonon-polaritons within the randomly generated, distorted particle features. For particle size smaller than the vacuum separation distance, resonance broadening and damping are linked with the multiple localized surface phonon modes supported by the composite spherical harmonic morphologies of the Gaussian random spheres. In conclusion, this paper has direct implications for thermal management of packed particle systems, with applications in radiative property control, electronics, energy conversion, and nanomanufacturing.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Trace Chemical Detection Using Intercalated MXenes as a Signal Enhancing Substrate in Optical Probes

MXenes are 2D materials composed of layered transition metal nitrides or carbides. These materials are synthesized by HF exfoliation from MAX phases (Ti{sub 3}AlC{sub 2}). The 2D nanomaterial was synthesized by the removal of the 'A' element, resulting in a Mxene product (Ti{sub 3}C{sub 2}). MXenes have the general formula M{sub n+1}X{sub n}T{sub x}, where M is an early transition metal, X is Carbon and/or Nitrogen, and T accounts for surface terminated functional groups such as Fluoride, hydroxyl, and oxygen. These materials have very unique properties, similar to graphene, that allows them to be applied in a variety of trace detection techniques including surface-enhanced Raman spectroscopy (SERS). MXenes have also been demonstrated to selectively uptake uranyl ion, UO{sub 2}{sup 2+}. If this property can be combined with SERS or fluorescence detection, it may be possible to use MXenes as the basis for an alternative method to kinetic phosphorescence analysis (KPA) for trace uranyl measurements. Objectives: To confirm that MXene Nano materials are suitable substrates for SERS and sensor development by enhancing Raman signaling. To determine if certain MXene preparation methods yield materials that are more suitable for trace sensing methods. To determine uranyl uptake properties of these MXene materials and test them for analytical signals. Sample Preparation: Preparation of Ti{sub 3}C{sub 2}MXene (at FSU). MXenes were prepared by etching Al from Ti{sub 3}AlC{sub 2} (MAX phase)material. Two etching techniques yield different MXene products: LiF/HCl: Milder reaction, larger MXene flakes. HF: Harsher reaction, smaller flakes, larger layer separation. Products washed to remove etchant, vacuum filtered, and dried. Dried MXene flakes are air-stable. Film preparation for sensor testing (at SRNL): Suspend powder in diH{sub 2}O, purge with Ar, sonicate for 30 min. Centrifuge and collect supernate with suspended particles. Observed LiF-etched Mxene yielded a higher density of particles and darker collected solution. Drop-cast (4 ml) supernate onto slides and dried with Ar. For Rhodamine B (RhB) testing, drop-cast 4 ml drops onto Mxene spots and dried with Ar. Scanning Electron Microscopy conditions: 10 kV Beam energy, high vacuum; Working distance of 8 mm; beam penetration depth appx. 4 microns, beam spot size appx. 2 nanometers. Results: Detection of aluminum correlates with bright spots on image. Presence of aluminum shows that LiF/HCl etching was less thorough than HF etching. Trace Cl detection in LiF images suggests incomplete rinsing. HF has smaller feature size, more layer structure, and increased homogeneity, consistent with expectations. Macroscopic Raman spectroscopy measurements: 532 nm excitation, ∼50 mW with a ∼100 micron spot size (InPhotonics RPB probe). Kaiser Optical Holospec f/1.8 spectrometer with cooled (-60 deg.C) Andor iDus OE420 CCD. LiF 1x supernate showed good signal for trace measurements of Rhodamine B. HF and 1/4x LiF supernates showed little Mxene or Rhodamine B signal. Low deposition densities led to excess background signal from glass slides. For LiF film, response is linear with Rhodamine B concentration over range tested. Will retest with Raman microscope (∼1 micron spot size) to characterize SERS of more dilute LiF and HF etched Mxenes. Conclusions: The LiF etched material was more suitable for macroscopic SERS measurements because it was more concentrated, resulting in a thicker film than the HF etched Mxene and diluted LiF sample. However, the other materials may give greater SERS enhancements, which we hope to determine from measurements with the Raman microscope. From characterization with SEM we concluded that the HF etched Mxene is more uniform/homogenous and has smaller particle size than the LiF etched Mxene. There is still aluminum present in both samples indicating that etching wasn't complete, but the removal of the aluminum was more efficient in the HF method. Path Forward: Observe SERS with Raman microscopy, to obtain better signals for the more diluted samples and be able to compare enhancement effects for the different MXenes. Characterize uranyl sorption into MXene films and test Raman and fluorescence signals. Revisit the etching conditions to improve removal of aluminum. FSU and SRNL will continue to collaborate to create and characterize different Mxene materials and test their usefulness for sensor applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Recent Advances in the Chemistry of Hydrometallurgical Methods

Producing pure substances has been the obsession of scientists for centuries and has defined chemistry as we know it. Nowadays, most of our economy still relies on the chemist ability to extract and purify metallic elements from raw or recycled materials, which, in most cases, is done partly or entirely via hydrometallurgical methods. In this work, the authors present the critical aspects of this relatively overlooked, yet critical, chemistry discipline. This review article highlights the importance of hydrometallurgical processes for strategic industrial sectors, put in perspective traditional separation methods with emerging ones (new metal-binding chelators, ionic liquids, deep eutectic solvents, microfluidic devices, biomaterials, etc.), critically reviews progress made on separation methods over the past two decades, and highlights the challenges lying ahead for the hydrometallurgists in academia and the industry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Semi-Implicit Computation of Fast Modes in a Scheme Integrating Slow Modes by a Leapfrog Method Based on a Selective Implicit Time Filter

Abstract A scheme for integration of atmospheric equations containing terms with differing time scales is developed. The method employs a filtered leapfrog scheme utilizing a fourth-order implicit time filter with one function evaluation per time step to compute slow-propagating phenomena such as advection and rotation. The terms involving fast-propagating modes are handled implicitly with an unconditionally stable method that permits application of larger time steps and faster computations compared to fully explicit treatment. Implementation using explicit and recurrent formulation is provided. Stability analysis demonstrates that the method is conditionally stable for any combination of frequencies involved in the slow and fast terms as they approach the origin. The implicit filter used in the method damps the computational modes without noticeably sacrificing the accuracy of the physical mode. TheO[(Δt 4 )] accuracy for amplitude errors achieved by the implicitly filtered leapfrog is preserved in applications where terms responsible for fast propagation are integrated with a semi-implicit method. Detailed formulation of the method for soundproof nonhydrostatic anelastic equations is provided. Procedures for implementation in global spectral shallow-water models are also given. Examples comparing numerical and analytical solutions for linear gravity waves demonstrate the accuracy of the scheme. The performance is also shown in more practical nonlinear applications, where numerical solutions accomplished by the method are evaluated against those computed from a scheme where the slow terms are handled by the third-order Runge–Kutta scheme. It demonstrates that the method is able to accurately resolve fine-scale dynamics of Kelvin–Helmholtz shear instabilities, the evolution of density current, and nonlinear drifts of twin tropical cyclones.

Meteorology & Atmospheric Sciences↗
DOE OSTI2021

Reactive Flows in Porous Media: Challenges in Theoretical and Numerical Methods

We review theoretical and computational research, primarily from the past 10 years, addressing the flow of reactive fluids in porous media. The focus is on systems where chemical reactions at the solid–fluid interface cause dissolution of the surrounding porous matrix, creating nonlinear feedback mechanisms that can often lead to greatly enhanced permeability. Here, we discuss insights into the evolution of geological forms that can be inferred from these feedback mechanisms, as well as some geotechnical applications such as enhanced oil recovery, hydraulic fracturing, and carbon sequestration. Until recently, most practical applications of reactive transport have been based on Darcy-scale modeling, where averaged equations for the flow and reactant transport are solved. We summarize the successes and limitations of volume averaging, which leads to Darcy-scale equations, as an introduction to pore-scale modeling. Pore-scale modeling is computationally intensive but offers new insights as well as tests of averaging theories and pore-network models. We include recent research devoted to validation of pore-scale simulations, particularly the use of visual observations from microfluidic experiments.

wormhole formation↗
DOE OSTI2020

Efficient Step-Merged Quantum Imaginary Time Evolution Algorithm for Quantum Chemistry

In this work, we develop a resource-efficient step-merged quantum imaginary time evolution approach (smQITE) to solve for the ground state of a Hamiltonian on quantum computers. This heuristic method features a fixed shallow quantum circuit depth along the state evolution path. We use this algorithm to determine the binding energy curves of a set of molecules, including H 2 , H 4 , H 6 , LiH, HF, H 2 O, and BeH 2 , and find highly accurate results. The required quantum resources of smQITE calculations can be further reduced by adopting the circuit form of the variational quantum eigensolver (VQE) technique, such as the unitary coupled cluster ansatz. We demonstrate that smQITE achieves a similar computational accuracy as VQE at the same fixed-circuit ansatz, without requiring a generally complicated high-dimensional nonconvex optimization. Finally, smQITE calculations are carried out on Rigetti quantum processing units, demonstrating that the approach is readily applicable on current noisy intermediate-scale quantum devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Mechanism of $\mathrm{E}$-bridge formation by various $\mathrm{PAH}$ molecules: A theoretical study

Potential energy surfaces (PES) for dimerization of acepyrene-pyrene, aceanthracene-anthracene, and acenaphthalene-naphthalene were computed by the G3(MP2,CC) and ONIOM2(G3(MP2,CC):B3LYP/6-31G(d)) methods. Close agreement of relative energies of corresponding species along reaction paths for different reactions was found suggesting that the PES for E-bridge formation depends weakly on the number of rings in the interacting monomers. Our results indicate that the reaction rate is controlled by the dynamics of the initial collision, which may depend on the monomer size. The ONIOM approach is proposed as an accurate tool for calculations of PES in large PAH systems being more reliable than various DFT methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Rank-reduced coupled-cluster. III. Tensor hypercontraction of the doubles amplitudes

In this work, we develop a quartic-scaling implementation of coupled-cluster singles and doubles (CCSD) based on low-rank tensor hypercontraction (THC) factorizations of both the electron repulsion integrals (ERIs) and the doubles amplitudes. This extends our rank-reduced (RR) coupled-cluster method to incorporate higher-order tensor factorizations. The THC factorization of the doubles amplitudes accounts for most of the gain in computational efficiency as it is sufficient, in conjunction with a Cholesky decomposition of the ERIs, to reduce the computational complexity of most contributions to the CCSD amplitude equations. Further THC factorization of the ERIs reduces the complexity of certain terms arising from nested commutators between the doubles excitation operator and the two-electron operator. We implement this new algorithm using graphical processing units and demonstrate that it enables CCSD calculations for molecules with 250 atoms and 2500 basis functions using a single computer node. Furthermore, we show that the new method computes correlation energies with comparable accuracy to the underlying RR-CCSD method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Deeply uncertain: comparing methods of uncertainty quantification in deep learning algorithms

We present a comparison of methods for uncertainty quantification (UQ) in deep learning algorithms in the context of a simple physical system. Three of the most common uncertainty quantification methods - Bayesian Neural Networks (BNN), Concrete Dropout (CD), and Deep Ensembles (DE) - are compared to the standard analytic error propagation. We discuss this comparison in terms endemic to both machine learning ("epistemic" and "aleatoric") and the physical sciences ("statistical" and "systematic"). The comparisons are presented in terms of simulated experimental measurements of a single pendulum - a prototypical physical system for studying measurement and analysis techniques. Our results highlight some pitfalls that may occur when using these UQ methods. For example, when the variation of noise in the training set is small, all methods predicted the same relative uncertainty independently of the inputs. This issue is particularly hard to avoid in BNN. On the other hand, when the test set contains samples far from the training distribution, we found that no methods sufficiently increased the uncertainties associated to their predictions. This problem was particularly clear for CD. In light of these results, we make some recommendations for usage and interpretation of UQ methods.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

A circuit-generated quantum subspace algorithm for the variational quantum eigensolver

Recent research has shown that wavefunction evolution in real and imaginary time can generate quantum subspaces with significant utility for obtaining accurate ground state energies. Inspired by these methods, we propose combining quantum subspace techniques with the variational quantum eigensolver (VQE). In our approach, the parameterized quantum circuit is divided into a series of smaller subcircuits. The sequential application of these subcircuits to an initial state generates a set of wavefunctions that we use as a quantum subspace to obtain high-accuracy groundstate energies. We call this technique the circuit subspace variational quantum eigensolver (CSVQE) algorithm. By benchmarking CSVQE on a range of quantum chemistry problems, we show that it can achieve significant error reduction in the best case compared to conventional VQE, particularly for poorly optimized circuits, greatly improving convergence rates. Furthermore, we demonstrate that when applied to circuits trapped at local minima, CSVQE can produce energies close to the global minimum of the energy landscape, making it a potentially powerful tool for diagnosing local minima.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗