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DOE OSTI2026

MFC 5.0: An exascale many-physics flow solver

Many problems of interest in engineering, medicine, and the fundamental sciences rely on high-fidelity flow simulation, making performant computational fluid dynamics solvers a mainstay of the open-source software community. Previous work MFC 3.0 was made a published, documented, and open-source solver via Bryngelson et al. Comp. Phys. Comm. (2021) with numerous physical features, numerical methods, and scalable infrastructure. MFC 5.0 is a significant update to MFC 3.0, featuring a broad set of well-established and novel physical models and numerical methods, as well as the introduction of GPU and APU (or superchip) acceleration. Here, we exhibit state-of-the-art performance and ideal scaling on the first two exascale supercomputers, OLCF Frontier and LLNL El Capitan. Combined with MFC’s single-accelerator performance, MFC achieves exascale computation in practice, and achieved the largest-to-date public CFD simulation at 200 trillion grid points as a 2025 ACM Gordon Bell Prize finalist. New physical features include the immersed boundary method, N-fluid phase change, Euler–Euler and Euler–Lagrange sub-grid bubble models, fluid-structure interaction, hypo- and hyper-elastic materials, chemically reacting flow, two-material surface tension, magnetohydrodynamics (MHD), and more. Numerical techniques now represent the current state-of-the-art, including general relaxation characteristic boundary conditions, WENO variants, Strang splitting for stiff sub-grid flow features, and low Mach number treatments. Weak scaling to tens of thousands of GPUs on OLCF Summit and Frontier and LLNL El Capitan achieves efficiencies within 5% of ideal to over 90% of their respective system sizes. Strong scaling results for a 16-times increase in device count show parallel efficiencies over 90% on OLCF Frontier. MFC’s software stack has undergone further improvements, including continuous integration, which ensures code resilience and correctness through over 300 regression tests; metaprogramming, which reduces code length while maintaining performance portability; and code generation for computing chemical reactions

Computational fluid dynamics↗

DOE OSTI2026

Enhancing photoionization rate calculations in low-temperature plasmas using spectral methods

Photoionization plays a central role in the development of streamer discharges and other non-equilibrium plasma phenomena. It creates seed electrons, which are essential for positive streamer propagation, allowing the ionization front to move forward. Because of this, accurate modeling of photoionization is very important for predicting streamer behavior and plasma evolution. The photoionization process in air (N 2 – O 2 mixture) is often described by the Zheleznyak model (1982). This model is usually solved through Helmholtz-type equations that approximate the Zheleznyak photoionization model (Zheleznyak et al. 1982) as Partial Differential Equations (PDEs). Conventional numerical methods, such as the Finite Difference Method (FDM) or Finite Volume Method (FVM), are widely used to solve these equations. Although they are prevalent, the computational cost of these methods due to their need for matrix operations and iterative solver is demanding. To address this challenge, this work develops a spectral solver based on the Fast Fourier Transform (FFT) combined with Discrete Cosine Transform (DCT) and Discrete Sine Transform (DST) to calculate the photoionization rate efficiently in an axisymmetric cylindrical domain. This method naturally satisfies the boundary conditions used in the model and converts the PDE into algebraic ones in spectral space. Thus, avoids the need for iterative matrix solvers. When compared with FDM results, it is demonstrated that the new solver not only maintains accuracy, but also reduces the computational cost, showing a performance increase of approximately 100 compared to FDM over a wide range of problem sizes. The method is parallelized using Message Passing Interface (MPI) and has been integrated into a fluid plasma model for streamer simulation. Here, this FFT-based approach provides a fast and reliable alternative for calculating photoionization in fluid models, helping large-scale plasma simulations run faster and efficiently, and allows higher-resolution simulation without extra computational cost.

Axisymmetric system↗

DOE OSTI2024

Combinatorial transcription factor binding encodes cis -regulatory wiring of mouse forebrain GABAergic neurogenesis

Transcription factors (TFs) bind combinatorially to cis-regulatory elements, orchestrating transcriptional programs. Although studies of chromatin state and chromosomal interactions have demonstrated dynamic neurodevelopmental cis-regulatory landscapes, parallel understanding of TF interactions lags. To elucidate combinatorial TF binding driving mouse basal ganglia development, we integrated chromatin immunoprecipitation sequencing (ChIP-seq) for twelve TFs, H3K4me3-associated enhancer-promoter interactions, chromatin and gene expression data, and functional enhancer assays. We identified sets of putative regulatory elements with shared TF binding (TF-pRE modules) that orchestrate distinct processes of GABAergic neurogenesis and suppress other cell fates. The majority of pREs were bound by one or two TFs; however, a small proportion were extensively bound. These sequences had exceptional evolutionary conservation and motif density, complex chromosomal interactions, and activity as in vivo enhancers. Our results provide insights into the combinatorial TF-pRE interactions that activate and repress expression programs during telencephalon neurogenesis and demonstrate the value of TF binding toward modeling developmental transcriptional wiring.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Dataset of simulated vibrational density of states and X-ray diffraction profiles of mechanically deformed and disordered atomic structures in Gold, Iron, Magnesium, and Silicon

This dataset is comprised of a library of atomistic structure files and corresponding X-ray diffraction (XRD) profiles and vibrational density of states (VDoS) profiles for bulk single crystal silicon (Si), gold (Au), magnesium (Mg), and iron (Fe) with and without disorder introduced into the atomic structure and with and without mechanical loading. Included with the atomistic structure files are descriptor files that measure the stress state, phase fractions, and dislocation content of the microstructures. All data was generated via molecular dynamics or molecular statics simulations using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) code. This dataset can inform the understanding of how local or global changes to a materials microstructure can alter their spectroscopic and diffraction behavior across a variety of initial structure types (cubic diamond, face-centered cubic (FCC), hexagonal close-packed (HCP), and body-centered cubic (BCC) for Si, Au, Mg, and Fe, respectively) and overlapping changes to the microstructure (i.e., both disorder insertion and mechanical loading).

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

DOE OSTI2025

Monitoring pipeline integrity of underground gas storage facilities using membrane-based electrochemical sensors

Effective monitoring of internal corrosion risk is crucial to ensuring the safety and longevity of natural gas pipeline infrastructure. While electrochemical sensors are commonly used to assess corrosion rates and corrosion indicators in aqueous fluids, they are rarely used in gas pipelines as these fluids lack the ionic conductivity needed for electrochemical measurements. The inclusion of ion-conductive membranes into electrochemical sensors can extend their functionality into humidified gas streams, providing critical information about emerging corrosion events that are common during withdrawal season in pipeline systems downstream from underground storage facilities. In parallel, new protective films, like those obtained through cold spray coating, are being developed to protect oil and gas pipelines and recover losses in structural integrity due to corrosion damage. Herein, we demonstrate how membrane-based electrochemical sensors (MBES) can be used to monitor fluid corrosivity by examining their response to changes in water content for a wide range of fluid compositions. It was found that MBES readings were highly sensitive to water content changes with membrane conductivity measurements varying from 10 –6 to 10 –1 S cm -1 , and corrosion rate measurements which varied from 10 –7 to 1 mm y -1 . Electron microscopy confirmed that the self-healing characteristics of metal coating films were still active despite their inclusion into an MBES probe. In conclusion, these findings indicate that membrane-based corrosion monitoring can be expanded to monitor coated-pipeline materials and provide early detection of emerging corrosion upsets relevant to underground gas storage facilities.

Electrochemical sensor↗

DOE OSTI2025

Effect of cell compression on the performance and the structure of proton exchange membrane water electrolyzer (PEMWE) assembly

Here, in the field of water electrolysis, the proton exchange membrane water electrolyzer (PEMWE) is currently the most advanced technology for producing hydrogen without emitting CO 2 . Although PEMWE plants are already in operation, further research is needed to improve cell efficiency and reduce the use of rare materials, such as iridium oxide catalysts for the oxygen evolution reaction (OER). One of the main causes of performance loss in PEMWE is the relatively low electric conductivity of the porous transport layer (PTL) and of the anode catalyst layer, which results in ohmic losses and low catalyst utilization during high current density operation. The objective of this study is to investigate how optimization of the PTL and electrode interface can increase the cell performance. To this end, we tested different cell assemblies using fibrous and sintered PTLs, decreasing membrane thickness, reducing iridium loading, and inserting a microporous layer to increase contact surface area. Electrochemical characterization of each cell configuration was systematically performed at various compression levels as the pressure is a crucial parameter influencing the electrode/PTL contact area. In parallel, X-ray microcomputed tomography (micro-CT) was employed to investigate the effects of cell hydration and compression on the structure of PEMWE components. This study combining electrochemistry and micro-CT imaging presents how optimizing the electrode/PTL contact surface area, minimizes ohmic losses, and enables PEMWE operation with low iridium loading at high current densities.

Catalyst - PTL interface↗

DOE OSTI2024

District heating utilizing waste heat of a data center: High-temperature heat pumps

Data centers are energy-intensive facilities with substantial low-grade waste heat. High-temperature heat pumps can be critical in boosting the data center’s waste heat for district heating, improving the system-level energy efficiency of data centers, and reducing CO 2 emissions in district heating. This study built thermodynamic models to assess high-temperature heat pumps with six configurations using low global warming potential refrigerants to supply heat up to 120 °C. The heat pump configurations include single-stage or two-stage cycles with advanced components, such as internal heat exchanger, economizer, flash tank, or parallel compressor. The refrigerants include R1234ze(Z), R1233ed(E), R1224yd(Z), R600, and R600a, and R245fa is used as a reference. A case study was carried out to recover the waste heat from the Frontier high-performance computing data center and provide hot water for district heating at the US Department of Energy’s Oak Ridge National Laboratory campus. The optimized performance of high-temperature heat pumps is characterized with various effectiveness of internal heat exchangers, and the operating parameters of economizer or flash tank, as well as their combination. The results show that the configurations of two-stage cycles with internal heat exchanger + flash tank and internal heat exchanger + economizer/parallel-compressor provide the highest coefficient of performance under scenarios of the maximum allowable value and a fixed value (0.3) of the internal heat exchangers’ effectiveness, respectively. R1234ze(Z) and R600a are the most promising refrigerants, considering trade-offs between the coefficient of performance and the volumetric heating capacity. The single-stage cycle with internal heat exchanger + economizer/parallel-compressor using R1234ze(Z) is recommended for utilizing Fronter’s waste heat in district heating. A one mega-watt high-temperature heat pump will reduce 33,100–33,200 metric tons of CO2 emission annually, corresponding to 85.4 %–85.6 % of equivalent CO2 emissions from natural gas boilers. Here, this study provides good guidelines for designing and deploying high-temperature heat pumps to support sustainable data centers and decarbonize district heating in the US.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2025

The value of integrating a geothermal district heating system into a microgrid

As electrical grids increasingly rely on variable renewable energy, maintaining reliability and cost efficiency becomes more complex. To address these challenges, this study analyzed the integration of geothermal district heating as a grid-responsive thermal resource within a microgrid in Tuttle, Oklahoma. Building energy modeling using EnergyPlus estimated annual district heating demand at 2.9 GWh, with a peak load of 2.8 MW th . Techno-economic analyses were conducted to meet the heating demand under three geothermal scenarios, varying by production depth, flow rate, and thermal output, each supplemented by natural gas peaking boilers. In parallel, equivalent electrical load profiles were developed using typical coefficients of performance (COPs) for air-source heat pumps and electric boilers to establish an electrified baseline scenario. A complete end-use electrical load profile was also developed for the microgrid using Cambium dataset. The modeling results demonstrated reliable and economic operation of the geothermal systems over 30 years, with COPs ranging from 2.6 to 8.9 and the lowest levelized heating cost at $\$$54.6/MWh. Geothermal integration reduced electricity consumption by up to 94.7 % compared to the non-geothermal base case, yielding annual energy savings of up to $\$$803 k. Avoided grid costs ranged from $\$$65 k–$\$$147 k per year, with individual events avoiding up to $\$$4,863 per hour. Grid-responsive operation further reduced wholesale energy costs by 53–56 %. These findings demonstrate geothermal heating, traditionally treated as a non-grid-responsive thermal resource, can be reconfigured to support dynamic grid services, offering a scalable pathway to enhance reliability and reduce costs in renewable-rich microgrids and district heating networks.

15 GEOTHERMAL ENERGY↗

DOE OSTI2024

Stress intensity factor models using mechanics-guided decomposition and symbolic regression

The finite element method can be used to compute accurate stress intensity factors (SIFs) for cracks with complex geometries and boundary conditions. In contrast, handbook solutions act as surrogate SIF models that provide significantly faster evaluation times. However, the development of conventional surrogate SIF models relies on manual development based on low-order parameterizations. This limits surrogate model accuracy and generalizability. Here, in this paper, we develop a framework for the automated development of mechanics-guided handbook SIF solutions by using interpretable machine learning via genetic programming for symbolic regression (GPSR). Formalizing the mechanics-based approach of Raju and Newman, SIF training data is decomposed into multiple subsets. This decomposition enables parallel GPSR model development of subfunctions, each of which accounts for specific geometrical corrections with respect to a known analytical model. Using this mechanics-based approach with GPSR allows for equations to be learned with improved accuracy and reduced complexity relative to the Raju Newman equations while maintaining the inherent interpretability of mathematical expressions. In this paper, we present equations that match the complexity of the Raju Newman equations while having reduced error, as well as equations with similar errors and reduced complexity.

42 ENGINEERING↗

DOE OSTI2025

Characterizing Hazardous Gases from NMC811 Materials and Coin Cells with TGA and Tube-Furnace FTIR-MS Evolved-Gas-Analysis

Abuse testing is useful for informing the risks of different battery chemistries but has been limited to larger formats. This paper conducted thermal abuse tests at the smaller coin cell level to determine its relevance in specifying vent gas flammability and toxicity. A nitrogen purge carried the evolved gases into a parallel Fourier-transform infrared spectrometer (FTIR) and a mass spectrometer (MS) downstream of the tube furnace. The experimental system was validated by comparing evolved gas data for single components between the tube furnace system and a thermogravimetric analysis (TGA) instrument. Multiple samples were tested during validation, including CaCO3, electrolyte, delithiated NMC 811 cathode, and lithiated graphite anode. Temperature-resolved gas evolution of HF, CO2, CO, H2, and hydrocarbons from isolated components helped to characterize the emission sources. A previously unreported H2 generation mechanism was found. It was shown that the reduced NMC cathode acts as a catalyst to crack polypropylene-decomposed hydrocarbons into H2 at around 450 degrees C. It was also shown, while studying LiPF6 thermal decomposition, that using the tube furnace with a coin cell casing as the sample holder has some advantages for evolved-gas analysis of environmentally sensitive samples relative to testing in TGA instruments. After validation with single components, a fully charged NMC 811 coin cell was failed in the tube furnace. The measured evolved gases were found to be a combination of the species measured from the single component tests. H2 formation related to the reduced cathode was found to have greater abundance than H2 formed from the anode. Hydrogen fluoride emission factors and diethyl carbonate conversion emission factors assist in understanding the gaseous hazards for larger format cells.

25 ENERGY STORAGE↗

DOE OSTI2025

Earthquake-triggered submarine canyon flushing transfers young terrestrial and marine organic carbon into the deep sea

Submarine canyons transfer substantial amounts of sediment and organic carbon (OC) into the deep ocean, nourishing deep-sea ecosystems and contributing to the global carbon cycle through OC burial and sequestration. Tracking lateral OC transport through submarine canyon systems is challenged by the deep-ocean setting, difficulties with constraining episodic depositional events, and the need to assess the composition and age of marine and terrestrial organic matter. We apply innovative parallel ramped pyrolysis oxidation accelerator mass spectrometry and pyrolysis-gas chromatography-mass spectrometry with isotope analyses to track OC age and sources in the 2016 Kaikoura earthquake-triggered, canyon-flushing event that deposited along >1300 km of a submarine canyon-channel system, offshore Aotearoa New Zealand. Specifically, these techniques allow us to determine the ages, sources, and partitioning of OC within the Kaikoura turbidite deposit and test hypotheses of how submarine canyon systems contribute to lateral OC flux and burial. Our results show that, despite considerable canyon floor erosion, substantial amounts of young OC were flushed into the deep sea, with relatively little (~2%) pre-Holocene OC contributions. Even without a direct connection between rivers and submarine canyons, most (~55%) of the OC in the Kaikoura event bed is from terrestrial sources. However, the deposit also contains substantial amounts (~22%) of marine-derived OC and ~23% of the material is of unassignable origin. Particle sorting imparts variability on the age and composition of OC within turbidite deposits and along the turbidity current flow path. Terrestrial-derived OC is preferentially older than marine-derived OC and concentrated in coarser particle sizes found more commonly at the deposit base and in proximal settings. Young, marine-derived OC is concentrated at the surface of the deposits and tends to be enriched in finer particle sizes. Such OC partitioning in turbidites supports the relevance of depositional models for predicting and quantifying distribution of OC in deep-sea deposits. Earthquake-triggered, canyon flushing events and resulting turbidites enhance OC burial efficiency and can sequester OC effectively, contributing an important carbon sink to the sedimentary carbon cycle.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Long duration battery sizing, siting, and operation under wildfire risk using progressive hedging

Battery sizing and siting problems are computationally challenging due to the need to make long-term planning decisions that are cognizant of short-term operational decisions. This paper considers sizing, siting, and operating batteries in a power grid to maximize their benefits, including price arbitrage and load shed mitigation, during both normal operations and periods with high wildfire ignition risk. Here we formulate a multi-scenario optimization problem for long duration battery storage while considering the possibility of load shedding during Public Safety Power Shutoff (PSPS) events that de-energize lines to mitigate severe wildfire ignition risk. To enable a computationally scalable solution of this problem with many scenarios of wildfire risk and power injection variability, we develop a customized temporal decomposition method based on a progressive hedging framework. Extending traditional progressive hedging techniques, we consider coupling in both placement variables across all scenarios and state-of-charge variables at temporal boundaries. This enforces consistency across scenarios while enabling parallel computations despite both spatial and temporal coupling. The proposed decomposition facilitates efficient and scalable modeling of a full year of hourly operational decisions to inform the sizing and siting of batteries. With this decomposition, we model a year of hourly operational decisions to inform optimal battery placement for a 240-bus WECC model in under 70 min of wall-clock time.

25 ENERGY STORAGE↗

DOE OSTI2027

Nodal capacity expansion planning with flexible large-scale load siting

We propose explicitly incorporating large-scale load siting into a stochastic nodal power system capacity expansion planning model that concurrently co-optimizes generation, transmission, and storage expansion. The potential operational flexibility of some of these large loads is also taken into account by considering them as consisting of a set of tranches with different reliability requirements, which are modeled as a constraint on expected served energy across operational scenarios. We implement our model as a two-stage stochastic mixed-integer optimization problem with cross-scenario expectation constraints. To overcome the challenge of scalability, we build upon existing work to implement this model on a high performance computing platform and exploit scenario parallelization using an augmented Progressive Hedging Algorithm. The algorithm is implemented using the bounding features of mpisppy, which have shown to provide satisfactory provable optimality gaps despite the absence of theoretical guarantees of convergence. We test our approach and assess the value of this proactive planning framework on total system cost and reliability metrics using realistic testcases geographically assigned to San Diego and South Carolina, with datacenter and direct air capture facilities as large loads.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

A microfluidic spore chamber for long-term imaging of single-spore hyphal development.

Understanding the life cycle of fungal spores is essential for elucidating their roles in pathogenesis, dispersal, and survival. However, studying spore development under controlled, spatially defined conditions remains challenging. Here, we present the Spore Chamber, a custom-built microfluidic platform engineered for parallel trapping and long-term imaging of individual spores under defined media conditions, enabling real-time visualization of hyphal development. Using Aspergillus fumigatus as a model organism, we demonstrate that sparse trapping of individual spores within size-matched trap geometries enables long-term time-lapse imaging of key developmental stages, including germination, polarized hyphal elongation, branching, and conidiophore formation. To assess the device's capacity to resolve morphogenetic responses to exogenous signals, we introduced lipochitooligosaccharides (LCOs) and short-chain chitooligosaccharides (COs). Rhizobium-derived, non-sulfated LCO (nsLCO) mixtures induced enhanced secondary branching (hyperbranching), a response not previously reported in A. fumigatus under these signal conditions, to our knowledge, whereas sulfated LCOs and CO4 did not significantly alter branching patterns. In addition, long-term confinement and imaging revealed rare developmental morphologies previously described primarily in mutant strains, including split conidiophore formation, elongated phialides, and stress-associated phenomena such as microcyclic conidiation, and chlamydospore development. Together, these results establish the Spore Chamber as a targeted microfluidic platform for single-spore phenotyping and long-term developmental analysis, with applications in fungal biology, chemical signaling studies, and host–microbe interaction research.

Antifungal screening↗

DOE OSTI2025

A scoping study of far-SOL main-wall protection limiters for steady-state operation of compact pilot plant tokamaks

We present a novel method for handling steady-state heat fluxes incident on the main wall of pilot plant-scale magnetic fusion devices, based on the utilization of protection limiters in the far scrape-off layer (SOL). This method helps avoid large plasma-wall gaps, without excessively compromising blanket performance. We present an optimization algorithm for determining the appropriate size and scale of these protection limiters given (1) probability distributions of SOL plasma parameters and (2) assumed risk tolerance. As part of this optimization, we have developed an analytic description of parallel heat fluxes across limiter shadows, and an objective cost function (the ‘Far-SOL Marginal Cost’) to quantify the impact that different main-wall thermal management design choices have on reactor capital cost. Applying the model to a midscale fusion pilot plant concept shows that making use of far-SOL protection limiters can reduce capital costs on the order of $500 M, relative to naively increasing the plasma-wall gap. Our analysis demonstrates that the far-SOL power decay length is the highest-leverage plasma assumption for thermal loading of the first wall, and the primary cost driver for main wall thermal management. The relative cost efficiency of protection limiters increases as assumptions on the far-SOL heat flux become more pessimistic. The concepts described in this paper motivate the further development of far-SOL protection limiters as part of larger efforts to design economical core-edge-wall compatible solutions for a fusion pilot plant.

Design under uncertainty↗

DOE OSTI2025

Computing material volume fractions on a superimposed mesh as applied to Monte Carlo particle transport simulations

Here, we present a newly implemented ray tracing algorithm in OpenMC for efficiently computing material volume fractions on superimposed meshes in complex geometries. By firing rays along each coordinate direction through the geometry, the approach accumulates track-length data in each mesh element, thereby determining the fractional composition of each material. Scaling studies on three different models—a random tetrahedra configuration, the Frascati Neutron Generator ITER dose rate benchmark, and a stellarator design—show excellent parallel performance, with nearly linear speedup on modern multi-threaded and distributed-memory systems. An analysis of the residual error relative to high-resolution reference solutions demonstrated that under optimal conditions it decreases as 1/R, where R is the number of rays fired, making it straightforward to achieve user-prescribed accuracy. This new functionality enables practical, mesh-based approaches for detailed nuclear analyses in production Monte Carlo workflows without resorting to expensive, fully conformal or unstructured meshing.

Monte Carlo↗

DOE OSTI2024

A survey on checkpointing strategies: Should we always checkpoint à la Young/Daly?

The Young/Daly formula provides an approximation of the optimal checkpointing period for a parallel application executing on a supercomputing platform. It was originally designed to handle fail-stop errors for preemptible tightly-coupled applications, but has been extended to other application and resilience frameworks. Here, we provide some background and survey various scenarios to assess the usefulness and limitations of the formula, both for preemptible applications and workflow applications represented as a graph of tasks. We also discuss scenarios with uncertainties, and extend the study to silent errors. We exhibit cases where the optimal period is of a different order than that dictated by the Young/Daly formula, and finally we explain how checkpointing can be further combined with replication.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

LuGo: An enhanced quantum phase estimation implementation

Quantum Phase Estimation (QPE) is a cardinal algorithm in quantum computing that plays a crucial role in various applications, including cryptography, molecular simulation, and solving systems of linear equations. However, the standard implementation of QPE faces challenges related to time complexity and circuit depth, which limit its practicality for large-scale computations. We introduce LuGo, a novel framework designed to enhance the performance of QPE by reducing circuit duplication, as well as using parallelization techniques to achieve faster generation of the QPE circuit and gate reduction. We validate the effectiveness of our framework by generating quantum linear solver circuits, which require both QPE and inverse QPE, to solve linear systems of equations. LuGo achieves significant improvements in both computational efficiency and hardware requirements without compromising on accuracy. Compared to a standard QPE implementation, LuGo reduces time consumption to generate a circuit that solves a 2 6 × 2 6 system matrix by a factor of 50.68 and over 31× reduction of quantum gates and circuit depth, with no fidelity loss on an ideal quantum simulator. Furthermore, we demonstrated the versatility and scalability of LuGo enabled HHL algorithm by simulating a canonical Hele-Shaw fluid problem using a quantum simulator. With these advantages, LuGo paves the way for more efficient implementations of QPE, enabling broader applications across several quantum computing domains.

Quantum algorithm↗