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631 records · Page 12

Exact block encoding of imaginary time evolution with universal quantum neural networks

We develop a constructive approach to generate quantum neural networks capable of representing the exact thermal states of all many-body qubit Hamiltonians. The Trotter expansion of the imaginary time propagator is implemented through an exact block encoding by means of a unitary, restricted Boltzmann machine architecture. Marginalization over the hidden-layer neurons (auxiliary qubits) creates the nonunitary action on the visible layer. Then, we introduce a unitary deep Boltzmann machine architecture in which the hidden-layer qubits are allowed to couple laterally to other hidden qubits. We prove that this wave-function is closed under the action of the imaginary time propagator and, more generally, can represent the action of a universal set of quantum gate operations. We provide analytic expressions for the coefficients for both architectures, thus enabling exact network representations of thermal states without stochastic optimization of the network parameters. In the limit of large imaginary time, the yields the ground state of the system. The number of qubits grows linearly with the number of interactions and total imaginary time for a fixed interaction order. Both networks can be readily implemented on quantum hardware via midcircuit measurements of auxiliary qubits. If only one auxiliary qubit is measured and reset, the circuit depth scales linearly with imaginary time and number of interactions, while the width is constant. Alternatively, one can employ a number of auxiliary qubits linearly proportional to the number of interactions, and circuit depth grows linearly with imaginary time only. Every midcircuit measurement has a postselection success probability, and the overall success probability is equal to the product of the probabilities of the midcircuit measurements.

97 MATHEMATICS AND COMPUTING

Erosion Results of the MISSE 9-15 Polymers and Composites Experiment 1-4 (PCE 1-4)

Polymers and other oxidizable materials on the exterior of spacecraft in the low Earth orbit (LEO) space environment can be eroded from reaction with atomic oxygen (AO). Therefore, in order to design durable spacecraft it is important to know the extent of erosion that will occur during a mission. This can be determined by knowing the LEO AO erosion yield, E y (volume loss per incident oxygen atom), of materials susceptible to AO reaction. In addition, recent flight experiments have shown that the AO E y can vary with the AO fluence and/or solar exposure. Therefore, obtaining AO E y data for materials flown on various spaceflight missions is important. NASA Glenn Research Center has flown numerous experiments as part of the Materials International Space Station Experiment (MISSE) missions on the exterior of the International Space Station (ISS) to characterize the LEO E y of polymers, composites, protective coatings, and other spacecraft materials. Recently, four Glenn experiments with 365 flight (F) samples were flown on ISS’s MISSE-Flight Facility (MISSE-FF). These experiments are the Polymers and Composites Experiment-1 (PCE-1) flown as part of the MISSE-9 mission, the PCE-2 flown as part of the MISSE-10 mission, the PCE-3 flown as part of the MISSE-12 and MISSE-15 missions, and the PCE-4 flown as part of the MISSE-13 mission. Although each experiment had numerous sample objectives, the primary objective was to determine the LEO AO E y of various spacecraft materials as a function of solar irradiation and AO fluence. This paper provides a summary of the erosion data for the PCE 1-4 AO E y samples. The AO E y for 150 samples flown in either the LEO ram, wake, zenith or nadir directions are provided. The AO ram fluence varied from 2.97×10 20 atoms/cm 2 after 0.89 years of direct space exposure (with relatively high levels of Si contamination) on MISSE 12 to 3.93×10 20 atoms/cm 2 after 1.17 years of direct space exposure on MISSE-10. The ram AO E y values for uncoated polymers range from 3.81×10 –25 cm 3 /atom for polytetrafluoroethylene (M9R-C20 F) exposed to an AO fluence of 3.44×10 20 atoms/cm 2 on MISSE-9 to 4.43×10 –23 cm 3 /atom for AO etched low density polyimide aerogel (M12R-C21 F) exposed to an AO fluence of 2.97×10 21 atoms/cm 2 on MISSE-12. Because of the low AO fluence and relatively high Si contamination, a number of PCE-3 wake samples experienced mass gain. Thus, AO E y values are not provided for these samples. Although there are calculated AO E y values for the zenith, wake and nadir samples, the ram AO E y for a particular material is a more reliable value in terms of AO exposure because the zenith, wake and nadir directions were exposed to either no or very little AO fluence and thus other space environmental factors (i.e. vacuum, thermal extremes and thermal cycling, and/or various types of radiation) are responsible for the mass loss.

Erosion yield

Aerosol-deep convection interaction based on joint cell-thermal tracking in Large Eddy Simulations during the TRACER campaign

In cumulus clouds, aerosol concentrations control cloud droplet concentrations, modifying cloud radiative properties, precipitation processes, and cloud electrification. However, mechanisms of aerosol-deep convection interactions are not well understood due to complex cloud dynamics and microphysics. We investigate the interaction of aerosols with isolated deep convection using Large Eddy Simulations of two cases during the TRacking Aerosol Convection interactions ExpeRiment (TRACER) near Houston, Texas, using a joint cell-thermal tracking algorithm. Cumulus thermals are droplet generators, since supersaturation and droplet nucleation coincide with thermal centers, where the strongest updrafts occur. Primary ice crystal formation does not take place inside thermals, but at layers where previous thermals detrained moisture. As subsequent thermals containing supercooled droplets penetrate these layers, hail and graupel form at or near these thermals. Higher aerosol concentrations result in higher droplet concentrations that suppress drizzle, delay warm rain processes, and transport more moisture aloft. This increases snow and ice amount, as well as graupel and hail, leading to more lightning. Polluted thermals initiate at slightly higher altitudes, and are slightly larger and faster, suggesting a weak invigoration. We also find more thermals per cell, but fewer isolated cells, since convection is more aggregated and intense, especially near the end of the 24 h simulation. Non-linear mesoscale feedback likely triggered by temperature and moisture responses to aerosol-thermal interactions causes the aggregation. Time-lagged aerosol-reinitialization experiments show that the mesoscale response is the predominant forcing for the invigoration. These changes happen within one day, on a smaller scale than previously suggested.

54 ENVIRONMENTAL SCIENCES

2005 NASA Seal/Secondary Air System Workshop

The 2005 NASA Seal/Secondary Air System workshop covered the following topics: (i) Overview of NASA’s new Exploration Initiative program aimed at exploring the Moon, Mars, and beyond; (ii) Overview of the NASA-sponsored Propulsion 21 Project; (iii) Overview of NASA Glenn’s seal project aimed at developing advanced seals for NASA’s turbomachinery, space, and reentry vehicle needs; (iv) Reviews of NASA prime contractor, vendor, and university advanced sealing concepts including tip clearance control, test results, experimental facilities, and numerical predictions; and (v) Reviews of material development programs relevant to advanced seals development. Turbine engine studies have shown that reducing high-pressure turbine (HPT) blade tip clearances will reduce fuel burn, lower emissions, retain exhaust gas temperature margin, and increase range. Several organizations presented development efforts aimed at developing faster clearance control systems and associated technology to meet future engine needs. The workshop also covered several programs NASA is funding to develop technologies for the Exploration Initiative and advanced reusable space vehicle technologies. NASA plans on developing an advanced docking and berthing system that would permit any vehicle to dock to any on-orbit station or vehicle. Seal technical challenges (including space environments, temperature variation, and seal-on-seal operation) as well as plans to develop the necessary “androgynous” seal technologies were reviewed. Researchers also reviewed tests completed for the shuttle main landing gear door seals.

Hypersonic

Validation Data for Benchmarking Wire Arc Additive Manufacturing Process Simulations

Residual stresses cause geometric distortion and affect mechanical performance of additively manufactured structures, yet they are notoriously difficult to assess and predict. Distortion (warpage) can drive parts outside dimensional tolerance limits, leading to part rejection or rework. For parts that meet tolerance, locked-in residual stress fields can affect structural integrity during operation, particularly subcritical cracking by fatigue, creep, or corrosion. This work develops benchmark data for a common additive manufacturing process (Wire Arc Additive Manufacturing) that can be applied for calibration and validation of physical process models that predict residual stress fields. The work includes design of two different samples of differing geometry, detailed manufacturing records for a set of physical samples, and an extensive set of residual stress measurement data developed using two diverse techniques (the contour method and neutron diffraction). An initial application of the work is also reported, where a modeling challenge was issued to secure residual stress model predictions from two independent laboratories that were blind to residual stress measurement data. These initial blind residual stress predictions show significant discrepancies relative to the measurement data, illustrating the potential value of the underlying validation data. An open repository for this work, including the sample designs, manufacturing process records, and the residual stress data, is also provided for future application in non-blind validation efforts.

36 MATERIALS SCIENCE

Smart Charging of Fleet and Personal Electric Vehicles through Joint Vehicle-to-Grid Optimization

As electric vehicle (EV) adoption accelerates, vehicle-to-grid (V2G) strategies offer advantages over unmanaged charging (V0G) by enhancing grid stability, reducing fleet operation costs, and supporting integration of variable generation resources. This research develops a day-ahead optimization framework linked with agent-based simulations to evaluate coordinated V2G participation by fleet and personal EVs under 5 energy-pricing settings in Austin, Texas. Three scenarios (V0G, fleet-only V2G, and joint-V2G) are examined, considering real-time price and grid profiles, health-damage costs, and operational constraints for both fleet and personal EVs. Results show how V2G scenarios shift fleet EV charging to mid-day while enabling strategic battery-discharge during evening peaks, mitigating grid stress and lowering EV energy costs. V2G delivers close to 80% energy-cost savings for a 2000-EV fleet in Austin on grid-stressed days, with 55% lower charging pollutant outputs. Joint-V2G amplifies system-level benefits by complementing fleet discharge, but smart-charging equipment costs can offset those benefits.

Electric vehicle

Mechanical Properties of Carbon Fiber Reinforced Composites Exposed to Cryogenic Conditions and Space Radiation via Simulation and Testing

As NASA missions extend beyond low Earth orbit, increasing reliance is placed on carbon fiber reinforced polymer (CFRP) composites for spacecraft structures where mass efficiency, durability, and long-term reliability are critical. In service, these materials are subjected to a combination of ultraviolet radiation, vacuum, ionizing radiation, atomic oxygen, and extreme thermal excursions under sustained mechanical loading. Flight systems such as the Boeing Starliner and SpaceX Dragon employ external composite structures that will experience these environments for extended durations. Although prior spaceflight and ground studies have reported limited changes in bulk mechanical properties, the synergistic effects of these environments on composite microstructure, particularly at the fiber matrix interphase, remain insufficiently characterized and represent a potential qualification and reliability risk. This study investigates the effects of short-term cryogenic exposure on a radiation shielding carbon epoxy composite, SC2020, as a ground-based analog for space relevant thermal extremes. The SC2020 material system has previously flown on the International Space Station under the Materials International Space Station Experiment (MISSE) program. Composite specimens were exposed to liquid nitrogen for 6 and 24 hours and evaluated using a multiscale characterization framework that combined ASTM D3039 tensile testing, Atomic Force Microscopy (AFM) based interphase analysis, and helium gas permeability measurements. Tensile testing showed no statistically significant or permanent degradation in global strength or modulus following cryogenic exposure. In contrast, AFM measurements revealed reductions in interphase modulus, weakened adhesion, and increased nanoscale heterogeneity, indicating localized degradation mechanisms not captured by conventional bulk testing. Gas permeability measurements showed a progressive increase in helium diffusion with exposure duration, consistent with micro-void formation or partial interfacial debonding. The results indicate that cryogenic exposure initiates degradation at the fiber matrix interphase while leaving global mechanical properties largely unchanged over short durations. These findings underscore the importance of multiscale diagnostics for identifying early-stage damage mechanisms that may influence long term performance and qualification margins for spaceflight composite structures. The data presented establish a cryogenic baseline for comparison with forthcoming MISSE flight exposure results and support ongoing NASA Established Program to Stimulate Competitive Research (EPSCoR) efforts aimed at improving composite qualification methodologies, risk assessment, and reliability prediction for space environments.

composite reliability

Galaxy Size and Rotation Curve Diversity in ΛCDM with Baryons

The observed rotation curves of dwarf galaxies exhibit significant diversity at fixed halo mass, challenging galaxy formation within the cold dark matter (CDM) model. Previous cosmological galaxy formation simulations with baryonic physics fail to reproduce the full diversity of rotation curves, suggesting that there is a flaw in baryonic feedback models, observational bias, or that an alternative to CDM must be invoked. In this work, we use the Marvelous Massive Dwarf zoom-in simulations, a suite of high-resolution dwarf simulations with M 200 ∼ 10 10 –10 11 M ⊙ and M * ∼ 10 7 –10 9 M ⊙ , designed to target the mass range where the galaxy rotation curve diversity is maximized, i.e., between and 100 km s −1 . We add to this a set of low-mass galaxies from the Marvel Dwarf Zoom Volumes to extend the galaxy mass range to lower values. Our fiducial star formation and feedback models produce simulated dwarfs with a broader range of rotation curve shapes, similar to observations. These simulations both create dark matter cores via baryonic feedback, reproducing the slower-rising rotation curves, while also allowing for compact galaxies and steeply rising rotation curves. Our simulated dwarfs also reproduce the observed size–M * relation, including scatter, producing both extended and compact dwarfs for the first time in simulated field dwarfs. However, the slowly rising and high baryon mass fraction, as well as the steeply rising and low baryon mass fraction, remain missing. We explore star formation and feedback models and conclude that previous simulations may have had feedback that was too strong to produce compact dwarfs.

Cruz, Akaxia [Flatiron Institute, New York, NY (Un

The phase diagram of quantum chromodynamics in one dimension on a quantum computer

The quantum chromodynamics (QCD) phase diagram, which reveals the state of strongly interacting matter at different temperatures and densities, is key to answering open questions in physics, ranging from the behaviour of particles in neutron stars to the conditions of the early universe. However, classical simulations of QCD face significant computational barriers, such as the sign problem at finite matter densities. Quantum computing offers a promising solution to overcome these challenges. Here, we take an important step toward exploring the QCD phase diagram with quantum devices by preparing thermal states in one-dimensional non-Abelian gauge theories. We experimentally simulate the thermal states of SU(2) and SU(3) gauge theories at finite densities on a trapped-ion quantum computer using a variational method. This is achieved by introducing two features: Firstly, we add motional ancillae to the existing qubit register to efficiently prepare thermal probability distributions. Secondly, we introduce charge-singlet measurements to enforce colour-neutrality constraints. This work pioneers the quantum simulation of QCD at finite density and temperature for two and three colours, laying the foundation to explore QCD phenomena on quantum platforms.

Quantum information

Improvement in the Thermal-to-Structural Model Mapping Process for Integrated Modeling for the Roman Space Telescope

Integrated Modeling has been a key component of verifying optical requirements for the Nancy Grace Roman Space Telescope (RST) that are either impossible or impractical to verify exclusively through ground testing. Two major areas for integrated Modeling are Jitter and Thermal Distortion that require the exchanges of model performance predictions across disciplines. In both cases, distortions are impressed on optical models to evaluate the impact on boresight alignment and wave front error. In the case of Jitter, the disturbances are driven by reactions to motions most often from actuators; however, in the case of thermal distortion, the motions are driven by thermal expansion or contraction as a result of changing temperatures. This then requires a link further upstream to the thermal model, which is used to predict the thermal performance and temperature gradients and stability. The process for mapping temperatures from a thermal model to a corresponding structural model has been performed numerous times through the RST project lifecycle, with improvements in the accuracy, verification, and effort sought throughout. This paper describes some of the recent improvements to the process, including: capture of the visualization parameters, automatic generation of the mapped images for both the thermal and structural model groupings, and reduction in the effort to assemble the full set of mapped temperatures. These upgrades have greatly reduced the manual effort associated with thermal mapping and allowed for faster turn-around of Integrated Modeling predictions.

Thermal Mapping

Evidence for large baryonic feedback at low and intermediate redshifts from kinematic Sunyaev-Zel’dovich observations with ACT and DESI photometric galaxies

Recent advances in cosmological observations have provided an unprecedented opportunity to investigate the distribution of baryons relative to the underlying matter. In this work, we show that the gas is more extended than the dark matter, and the amount of baryonic feedback at $z \lesssim 1$ disfavors low-feedback models such as that of state-of-the-art hydrodynamical simulation IllustrisTNG compared with high-feedback models such as that of the original Illustris simulation. This has important implications for bridging the gap between theory and observations and understanding galaxy formation and evolution. Furthermore, a better grasp of the baryon-dark matter link is critical to future cosmological analyses, which are currently impeded by our limited knowledge of baryonic feedback. Here, we measure the kinematic Sunyaev-Zel'dovich (kSZ) effect from the Atacama Cosmology Telescope (ACT), stacked on the luminous red galaxy (LRG) sample of the Dark Energy Spectroscopic Instrument (DESI) imaging survey. This is the first analysis to use photometric redshifts for reconstructing galaxy velocities. Due to the large number of galaxies comprising the DESI imaging survey, this is the highest signal-to-noise stacked kSZ measurement to date: we detect the signal at 13$σ$, finding strong evidence that the gas is more spread out than the dark matter, as well as a preference for larger feedback compared to some commonly used state-of-the-art hydrodynamical simulations. Here, our work opens up the possibility of recalibrating large hydrodynamical simulations using the kSZ effect. In addition, our findings highlight the importance of properly accounting for baryonic feedback with future surveys such as LSST through direct probes such as the kSZ, and shed light on long-standing enigmas in astrophysics, such as the “missing baryon” problem.

79 ASTRONOMY AND ASTROPHYSICS

Glenn Research Center Propulsion Systems Laboratory 2026 Customer Guide

This guide describes the Propulsion Systems Laboratory (PSL) at the NASA Glenn Research Center. It was written to help customers understand the various components involved in conducting a test program within the PSL. The PSL complex supports two large-engine test cells that simulate altitude flight conditions for a wide range of research and experimental tests. These test cells operate at altitudes up to 90,000 ft and speeds from subsonic to above supersonic. Test points such as pressure, temperature, and Mach number can be set at the engine or test article inlet based on customer requirements. The facility’s support systems include the heated and cooled combustion air systems; altitude exhaust system; hydraulic system; nitrogen, oxygen, and hydrogen systems; thrust measurement system, which includes the facility’s single- and multi-axis thrust stands; inlet system; and electrical systems. In addition to providing a detailed description of PSL systems and capabilities, this guide discusses the facility’s history and past tests and addresses facility safety procedures, pretest requirements, and test operation standards.

Engine Icing Test Facility

CASM Monte Carlo: Calculations of the thermodynamic and kinetic properties of complex multicomponent crystals

Monte Carlo techniques play a central role in statistical mechanics approaches that connect macroscopic thermodynamic and kinetic properties to the electronic structure of a material. This paper describes the implementation of Monte Carlo techniques for the study of multicomponent crystalline materials within the Clusters Approach to Statistical Mechanics (CASM) software suite, and demonstrates their use in model systems to calculate free energies and kinetic coefficients, study phase transitions, and construct phase diagrams from first principles. Many crystal structures are complex, with multiple sublattices occupied by differing sets of chemical species, along with the presence of vacancies or interstitial species. This imposes constraints on concentration variables, the form of thermodynamic potentials, and the values of kinetic transport coefficients. The framework used by CASM to formulate thermodynamic potentials and kinetic transport coefficients accounting for arbitrarily complex crystal structures is presented and demonstrated with examples of increasing complexity. Additionally, an overview of the capabilities of the CASM software specific to Monte Carlo methods is given, and a new CASM software package is introduced, casm-flow, which helps automate the setup, submission, management, and analysis of Monte Carlo simulations.

Cluster expansion

Microgravity Game Changers: Recent Accomplishments of Microgravity Assisted Materials Experiments on the ISS

This paper discusses important new materials, devices and technology produced in low-Earth orbit (LEO) that have been developed with funding from NASA’s In Space Production Applications (InSPA) Portfolio. In coordination with the International Space Station (ISS) National Laboratory, InSPA supports innovative small businesses and other research & development organizations to develop microgravity-assisted applications that make significant impacts in a wide variety of industries on Earth. These technology development efforts are using the microgravity of orbital space to overcome gravity-induced defects on Earth to create high-value products for terrestrial markets in the areas of semiconductors, pharmaceuticals, and communications. Through 24/7/365 operation on ISS for 25 years, coupled with commercial space transportation and services to, in, and from orbit, the microgravity environment has enabled pioneering science and significant commercial applications, including novel medical advances. World-leading researchers, innovators, and space payload developers provide compelling evidence through demonstrations on the ISS that materials processing in microgravity improves outcomes for a wide range of materials and products at all levels of the organization of matter, from quantum entities such as Bose-Einstein condensates, to crystals, alloys, composites, thin films, and photonics, to stem cells, medical diagnoses, medical treatments, and medical devices for humans. As of 2026, numerous examples proved by demonstration on ISS show the potential of these technologies in various fields. In this paper, a summary of four important experiments is presented.

microgravity medical devices

A parametric study of slow dynamic nonlinear elasticity with comparisons to models

Several phenomenological models that aspire to quantitative description of anomalous nonlinear mesoscopic elasticity are reviewed and compared with laboratory measurements. This class of nonlinearity, best known perhaps for slow dynamics and aging, is seen widely in imperfectly consolidated granular solids but is not well understood. Typical slow dynamic tests show that a modest conditioning oscillatory "pump" strain depresses material stiffness, which then recovers like the logarithm of time after conditioning ceases. Several phenomenological models based on physical arguments have been proposed that predict the material stiffness response to arbitrary pump strain histories during conditioning and recovery. Approximate closed form and numerical solutions to the models are presented that predict the quantitative influence of three key pump parameters: the pump's strain amplitude, the pump's strain rate, and the pump’s duration. Laboratory measurements on Berea sandstone, concrete and a confined single aluminum bead find that slow dynamic responses are linear in pump strain and independent of pump frequency. Measurements also show that, after pump-off, stiffness recovers over times far longer than the pump duration. These observations and others are compared to model predictions. One of the considered models, based on a picture of fast brittle damage and slow healing, successfully matches all these behaviors.

36 MATERIALS SCIENCE

The Future of in-Situ Sequencing-Based Microbial Monitoring: Development of a Shelf-Stable Method for Artemis and Beyond

Microbial monitoring onboard the International Space Station (ISS) is essential for assessing the efficiency of the Environmental Control and Life Support Systems (ECLSS) and providing insight into potential risk to both crew and spacecraft. Historically, this monitoring required the need to culture organisms onboard, return these cultures to Earth, and then complete the identifications, a process that would take months. Over the past decade, and through numerous payloads, advances in molecular biology have enabled in-flight microbial identifications using nanopore sequencing. The swab-to-sequencer method resulting from these efforts was transitioned from research to operations for microbial monitoring under the Crew Health Care Systems (CHeCS) BioMole. Collectively, these accomplishments have propelled the swab-to-sequencer method to be selected as the Microbial Surface Monitor (MSM) for Gateway, as well as a payload on Artemis IV. However, the lack of cold stowage availability for Artemis requires modifications to the entire method due to the thermal instability of the reagents required for sample preparation. To achieve this, new development, optimization, and validations were undertaken. Key considerations included enzyme concentration, buffer compatibility, and equal or enhanced sensitivity and specificity. At each step, thorough side-by-side comparisons with the current ISS method were performed. The development of a robust shelf-stable method will ensure continued sequencing-based microbial monitoring for Artemis and beyond, providing data in near real-time, enhancing risk response time, and yielding clear insight into the microbiome of spacecraft.

Christian G Mena

Carbon Utilization and Storage Partnership of the Western United States

This technical report documents research conducted under DOE Award No. DE-FE0031837 focused on evaluating the feasibility of carbon capture, utilization, and storage (CCUS) systems in the central and western United States. The project integrated geologic characterization, reservoir simulation, infrastructure modeling, and economic analysis to assess CO₂ storage potential near industrial sources and develop strategies for transport and sequestration. The work included subsurface modeling, risk assessment, monitoring and verification (MRV) planning, and evaluation of regulatory pathways such as EPA Underground Injection Control (UIC) Class VI permitting and IRS 45Q tax credit eligibility. Results demonstrate the viability of multiple storage approaches, including saline formations, enhanced coalbed methane recovery, and basalt mineralization, supported by data-driven workflows and regional analyses. The project also produced permitting templates, technology transfer activities, and stakeholder engagement efforts to support deployment readiness. These findings contribute to the development of scalable, economically viable CCUS systems and provide a repeatable framework for future carbon management projects.

20 FOSSIL-FUELED POWER PLANTS

Quantum Filtering and Analysis of Multiplicities in Eigenvalue Spectra

Fine-grained spectral properties of quantum Hamiltonians, including both eigenvalues and their multiplicities, provide useful information for characterizing many-body quantum systems as well as for understanding phenomena such as topological order. Extracting such information with small additive error is #BQP-complete in the worst case. In this work, we introduce QFAMES (quantum filtering and analysis of multiplicities in eigenvalue spectra), a quantum algorithm that efficiently identifies clusters of closely spaced dominant eigenvalues and determines their multiplicities under physically motivated assumptions, which allows us to bypass worst-case complexity barriers. QFAMES also enables the estimation of observable expectation values within targeted energy clusters, providing a powerful tool for studying quantum phase transitions and other physical properties. We validate the effectiveness of QFAMES through numerical demonstrations, including its applications to characterizing quantum phases in the transverse-field Ising model and estimating the ground-state degeneracy of a topologically ordered phase in the two-dimensional toric code model. We also generalize QFAMES to the setting of mixed initial states. Our approach offers rigorous theoretical guarantees and significant advantages over existing subspace-based quantum spectral analysis methods, particularly in terms of the sample complexity and the ability to resolve degeneracies.

97 MATHEMATICS AND COMPUTING