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Magnet-superconductor hybrid quantum systems: a materials platform for topological superconductivity

Magnet–superconductor hybrid (MSH) systems have recently emerged as one of the most significant developments in condensed matter physics. This has generated, in the last decade, a steadily rising interest in the understanding of their unique properties. They have been proposed as one of the most promising platforms for the establishment of topological superconductivity, which holds high potential for application in future quantum information technologies. Their emergent electronic properties stem from the exchange interaction between the magnetic moments and the superconducting condensate. Given the atomic-level origin of such interaction, it is of paramount importance to investigate new magnet–superconductor hybrids at the atomic scale. In this regard, scanning tunneling microscopy (STM) and spectroscopy are playing a crucial role in the race to unveil the fundamental origin of the unique properties of MSH systems, with the aim to discover new hybrid quantum materials capable of hosting topologically non-trivial unconventional superconducting phases. In particular, the combination of STM studies with tight-binding model calculations have represented, so far, the most successful approach to unveil and explain the emergent electronic properties of MSHs. The scope of this review is to offer a broad perspective on the field of MSHs from an atomic-level investigation point-of-view. The focus is on discussing the link between the magnetic ground state hosted by the hybrid system and the corresponding emergent superconducting phase. This is done for MSHs with both one-dimensional (atomic chains) and two-dimensional (atomic lattices and thin films) magnetic systems proximitized to conventional s-wave superconductors. We present a systematic categorization of the experimentally investigated systems with respect to defined experimentally accessible criteria to verify or falsify the presence of topological superconductivity and Majorana edge modes. The discussion will start with an introduction to the physics of Yu–Shiba–Rusinov bound states at magnetic impurities on superconducting surfaces. This will be used as a base for the discussion of magnetic atomic chains on superconductors, distinguishing between ferromagnetic, antiferromagnetic and non-collinear magnetic ground states. A similar approach will be used for the discussion of magnetic thin film islands on superconductors. Given the vast number of publications on the topic, we limit ourselves to discuss works which are most relevant to the search for topological superconductivity.

Majorana states

Dissipative Phase Transition in the Two-Photon Dicke Model

We explore the dissipative phase transition of the two-photon Dicke model, a topic that has garnered significant attention recently. Our analysis reveals that while single-photon loss does not stabilize the intrinsic instability in the model, the inclusion of two-photon loss restores stability, leading to the emergence of superradiant states, which coexist with the normal vacuum states. Using a second-order cumulant expansion for the photons, we derive an analytical description of the system in the thermodynamic limit, which agrees well with the exact calculation results. Additionally, we present the Wigner function for the system, shedding light on the breaking of the 𝑍4 symmetry inherent in the model. These findings offer valuable insights into stabilization mechanisms in open quantum systems and pave the way for exploring complex nonlinear dynamics in two-photon Dicke models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Kondo effect in ferromagnetic quantum critical CeRh 6 ⁢Ge 4

The mechanism of a pressure-induced quantum critical point in the heavy fermion ferromagnet CeRh 6 ⁢Ge 4 has attracted interest, as ferromagnetic quantum criticality in a clean itinerant Ce compound is typically avoided. The localized versus itinerant character of the 4⁢𝑓 electrons is a key aspect for understanding this behavior. We investigated the electronic structure of the 4⁢𝑓 shell in CeRh 6 ⁢Ge 4 using core-level photoelectron and x-ray absorption spectroscopy, demonstrating the hybridization of Ce 4⁢𝑓 with the conduction electrons. Linearly polarized x-ray absorption reveals a temperature-dependent linear dichroism consistent with the crystal-electric-field sequence as inferred from the static susceptibility. This dichroism cannot be described by an ionic full-multiplet model alone, but is reproduced by including the Kondo effect within a single-impurity Anderson model in the noncrossing approximation. The Kondo effect mixes higher-lying crystal-field states into a resulting multiorbital ground state with 4⁢𝑓 occupancy, 𝑛 𝑓 ∼ 0.9. Deviations at low temperatures between the measured linear dichroism and calculated dichroism suggest an orbital-dependent Kondo effect. A scenario in which there is a multiorbital ground state and orbital-dependent Kondo hybridization should be a starting point for a model of pressure-induced criticality in CeRh 6 ⁢Ge 4 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Classical-Quantum Algorithm for Solving Stochastic Programs

Stochastic programming provides a rigorous mathematical framework for making decisions under uncertainty in a risk-aware manner. Two-stage stochastic programming is, perhaps, the simplest form of this framework. Here the first-stage variables represent decisions that must be made "here and now" in the face of uncertainty, while the second-stage variables are decisions made after uncertain events. However, the broad adoption of stochastic programming has been hindered by computational challenges caused by the two-stage stochastic programming formulation which requires solving an ensemble of optimization problems. Using quantum amplitude estimation (QAE), quantum computers have shown the theoretic ability to compute expectations with Monte-Carlo methods with quadratically fewer samples than classical methods. In this work, we present a quantum algorithm for computing the expectation term using QAE for given first-stage decisions. Further, we detail methods of computing gradient information from the quantum calculation enabling the application of classical gradient-based optimization techniques. The result is a classical-quantum hybrid method of solving two-stage stochastic programs. These techniques are demonstrated with computational experiments based an engineering optimization problem.

97 MATHEMATICS AND COMPUTING

Scattering theory of frequency-entangled biphoton states facilitated by cavity polaritons

The use of quantum light to probe exciton properties in semiconductor and molecular nanostructures typically occurs in the low-intensity regime. A substantial enhancement of exciton-photon coupling can be achieved with photonic cavities, where excitons hybridize with cavity modes to form polariton states. Here, to provide a theoretical framework for interpreting emerging experimental efforts in this direction, we develop a scattering theory describing the interaction of frequency-entangled photon pairs with cavity polariton and bipolariton states under various coupling regimes. Employing the Tavis-Cummings model in combination with our scattering approach, we present a quantitative analysis of how the interaction of the entangled photon pair with the polariton or bipolariton modifies its joint spectral amplitude (JSA). Specifically, we examine the effects of the cavity-mode steady-state population, exciton-cavity coupling strength, and different forms of the input photon JSA. Our results show that the entanglement entropy of the scattered photons is highly sensitive to the interplay between the input JSA and the spectral line shapes of the polariton resonances, emphasizing the cavity filtering effects. We suggest that biphoton-scattering quantum light spectroscopy best serves as a sensitive probe of polariton and bipolariton states in the photon-vacuum cavity state. Our approach is not only robust to various regimes of cavity-exciton coupling, but also amenable to extensions beyond the Tavis-Cummings model, enabling the representation of a broad class of molecular systems and solid state quantum materials.

36 MATERIALS SCIENCE

Thermalization and criticality on an analogue–digital quantum simulator

Abstract Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators 1,2 . Unlocking the full potential of such systems towards this goal requires flexible initial state preparation, precise time evolution and extensive probes for final state characterization. Here we present a quantum simulator comprising 69 superconducting qubits that supports both universal quantum gates and high-fidelity analogue evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. This hybrid platform features more versatile measurement capabilities compared with analogue-only simulators, which we leverage here to reveal a coarsening-induced breakdown of Kibble–Zurek scaling predictions 3 in theXYmodel, as well as signatures of the classical Kosterlitz–Thouless phase transition 4 . Moreover, the digital gates enable precise energy control, allowing us to study the effects of the eigenstate thermalization hypothesis 5–7 in targeted parts of the eigenspectrum. We also demonstrate digital preparation of pairwise-entangled dimer states, and image the transport of energy and vorticity during subsequent thermalization in analogue evolution. These results establish the efficacy of superconducting analogue–digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.

Science & Technology - Other Topics

Subscale Hardware-In-The-Loop Results for Hybrid Electric Turbofan Controls Use Cases

NASA is investigating hybrid electric turbine engine systems for commercial transport aircraft due to the potentially significant improvements hybrid electric technology offers in performance, fuel consumption, and operational and design flexibility. Recently, the technology has been tested at full scale in partnership with industry and advanced to Technology Readiness Level 4. This presentation will focus on a recent subscale hardware-in-the-loop test of an open source turbofan engine model developed by NASA. The Advanced Geared Turbofan 30,000 lbf – electrified (AGTF30-e) engine is used as a reference model to demonstrate control system design and use cases for an example mild hybrid electric system with no large-scale energy storage. This model is run in real-time in NASA’s Hybrid Propulsion Emulation Rig (HyPER) and is used to drive an emulation of the turbomachinery system using subscale electric machines. This dynamic scaled shaft emulation interacts with a subscale (<100 kW) hybrid system consisting of electric machines, motor controllers, and a programmable electronic load. Specific use cases demonstrated include the use of Turbine Electrified Energy Management to improve operation during transients, megawatt-scale power extraction from the AGTF30-e, and power transfer between engine spools. Results related to the effectiveness of hybrid systems are qualitatively compared to results from industry testing.

Hybrid

Analysis and Overview of Hybrid Wired and Wireless Bi-Directional EV Charger Systems

Here, this paper analyzes and overviews hybrid wired and wireless bi-directional Electric Vehicle (EV) charging systems with a primary focus on resonant compensation methods that enable a unified power conversion architecture. Four compensation configurations based on series–series and LCC–LCC resonant networks are systematically evaluated for both wired transformer-based and wireless coupler-based operation. The analysis examines how coupling conditions, resonant component selection, and auxiliary compensation tuning influence voltage gain characteristics, resonant tank current magnitude and phase, and operating frequency requirements. Normalized frequency-domain results are presented to directly compare reactive current behavior and voltage regulation capability under wired and wireless operating conditions. A 60 kW bi-directional charger case study is used to demonstrate the feasibility of retaining a common hardware platform while accommodating distinct coupling scenarios through compensation tuning rather than structural modification. The presented results provide design-oriented insights into resonant network selection and compensation strategies for scalable and flexible hybrid EV charging systems.

Hybrid

Li-ion Battery Aging with Hybrid Physics-Informed Neural Networks and Fleet-wide Data

In this work, we propose a hybrid model for Li-ion battery discharge and aging prediction that leverages fleet-wide data to predict future capacity drops.The model is built upon an hybrid approach merging physics-based and empirical equations, as well as neural network models in a recurrent neural network cell. The hybrid physics-informed neural network can predict voltage discharge cycles given the loading profile, and estimate the used capacity of the battery under random-loading conditions by tracking aging parameters connected to the residual capacity of the battery. By merging information on the battery aging parameters with existing fleet-wide aging data, the model can predict the future residual capacity of the battery that is being monitored, and therefore enable predictions of voltage discharge curves far ahead in the battery life cycle. We validated the approach using the NASA Prognostics Data Repository Battery data-set, which contains experimental data on Li-ion batteries discharged at random loading conditions in a controlled environment. The approach also allows the identification of discrepancies between the battery aging trend and the trend observed at the fleet level, so that batteries behaving differently from the rest of the fleet can be subject to closer monitoring and further testing to refine predictions.

PINN

Market participation strategy of hybrid energy resources: A New York ISO case study

Drawing on existing market designs with independent resource participation in electricity markets, this study analyzes participation models for hybrid resources combining renewable generation and storage. Two models are considered: in the first, the components operate independently, with the Independent System Operator (ISO) managing the storage state of charge (SoC); in the second, the hybrid resource acts as an integrated unit, submitting offers as a “black box” and managing its SoC internally. Using a production cost model for the zonal New York Bulk Power System, we evaluate trade-offs in system reliability, market efficiency, and asset profitability. Our results provide several key insights for policymakers, showing that the ISO-managed granular model enhances social welfare through explicit SoC management, while the simpler integrated model is more computationally efficient, but may cause more real-time violations and lower overall profits.

Bansal, Rajni Kant

Overview of initial research into the effects of strong vortex flow on hybrid rocket combustion and performance

An examination of the effect of vortex flow on hybrid rocket combustion and performance is underway. Emphasis is on response of the fuel regression rate when subjected to vortex flow. Initial results show that there is a definite effect of the vortex on fuel regression rate. Future work will focus on quantitatively measuring this regression rate. This work is part of an overall program to develop an ultra low cost fuel system for hybrid rocket engines.

P Gloyer

Optimization of the FRIB beam dump: a hybrid genetic algorithm and reinforcement learning approach

The operational envelope of high-power-density systems, such as particle accelerators and advanced nuclear energy systems, is critically constrained by the need to manage extreme thermal loads. To address this, we present a novel hybrid optimization framework combining a genetic algorithm (GA) with a soft actor-critic (SAC) deep reinforcement learning agent. This framework was applied to a practical high-heat-flux problem: redesigning the beam dump at the Facility for Rare Isotope Beams (FRIB) for a power upgrade from 20 kW to 50 kW. The resulting design, validated by three-dimensional conjugate heat transfer simulations, suppresses hazardous hot spots and yields a markedly more uniform temperature distribution. This provides a robust operating margin, increasing the average power-handling capability by 72% relative to the current design, demonstrating the framework’s potential to solve complex thermal management challenges in both accelerator technology and advanced nuclear systems.

Accelerator

Turbofan Engine Power Extraction Demonstration Final Report

As GE Aerospace advances toward a revolutionary step change in propulsion efficiency, the integration and demonstration of new engine architectures and technology systems are essential. The NASA Turbofan Engine Power Extraction Demonstration (PEx), conducted through the Hybrid Thermally Efficient Core (HyTEC) project, aims to develop and demonstrate megawatt-class hybrid electric capability on a modern commercial turbofan engine. The hybrid electric system is critical to meeting the needs of the U.S. aviation industry for next-generational propulsion systems with greater efficiency, durability, and range. This supports energy independence and helps ensure the security and resilience of one of America's largest export industries. The PEx project specifically targets three key objectives: mechanically integrating hybrid electric capability into a commercial turbofan engine, integrating electric machine control with turbofan control for advanced power management, and de-risking performance modeling of future hybrid electric architectures. To mature these technologies to Technology Readiness Level (TRL) 6, a series of electric power system component tests and a baseline engine performance test campaign were conducted. These efforts culminated in an integrated hybrid electric turbofan test campaign demonstrating power extraction, power insertion, and power transfer between spools. Tests of the electric power system were completed at GE Aerospace’s Electrical Power Integrated Systems Center in Dayton, Ohio and engine tests were completed at Peebles Test Operation in Peebles, Ohio. Hybrid electric trade studies extended the demonstrated capability to altitude using the validated cycle model from the PEx test campaigns, allowing for comments on expanded mission benefits not demonstrated in the ground campaign. The knowledge gained from PEx also supports GE Aerospace’s Compact Core Demonstrator as part of HyTEC Phase 2 and ultimately informs the implementation of hybrid electric systems in the next generation of GE Aerospace commercial engine products. This report provides a summary of the program background, test campaigns, trade studies, and insights into the technical maturation required to support future commercial products.

Hybrid Electric

EXERGETIC: De-Risking Next-Generation Resilient Geothermal Hybrids via At-Scale Evaluation Using Virtual Emulation Digital Twin Environment for Efficient Operation

The DOE-GTO-funded project, award number 5.1.2.12, entitled "EXERGETIC - De-risking Next Generation Resilient Geothermal Hybrids via at-Scale Evaluation Using a Virtual Emulation Digital Twin Environment for Efficient Operation," advances the solution to these challenges by developing and validating a geothermal co-emulation environment implemented at the National Laboratory of the Rockies (NLR)'s Advanced Research on Integrated Energy Systems (ARIES) platform. This framework enables the de-risking of next-generation geothermal and geothermal hybrid systems through high-fidelity modeling, real-time digital emulation, advanced control strategies, and techno-economic assessment. The project focused on geothermal hybrid configurations that integrate geothermal power plants with concentrated solar power and underground thermal energy storage, enabling enhanced efficiency, flexibility, and grid support capabilities. The main goal of this project was the development of a geothermal digital co-emulation environment to demonstrate the technical and economic value of geothermal hybrid systems and their contribution to grid stability and flexibility. The EXERGETIC framework combined physics-based models, controls, and real assets at ARIES, including digital real-time simulators (DRTS), a 20-MW-scale controllable grid interface (CGI), and a 2-MW conventional generator. Detailed transient models were developed for the key subsystems of a hybrid geothermal plant, including parabolic trough solar collectors, reservoir thermal energy storage (RTES), and a binary Organic Rankine Cycle (ORC) power plant. The ORC model explicitly captured thermal inertia and off-design operation and integrated control strategies to dynamically respond to electric load profiles. The models were validated against published experimental and numerical studies, demonstrating strong agreement and confirming the accuracy and robustness of the modeling approach. The resulting digital twin represents geothermal-solar-storage systems at multiple scales (1 MW to 100 MW) and enables realistic emulation of grid-connected operation. The control architecture allows the geothermal resource to provide stable baseload generation, while solar and stored thermal energy supply flexible, dispatchable support during periods of high demand or variable grid conditions. A key contribution of the EXERGETIC project is the demonstration that geothermal hybrid systems can be designed to be active grid assets rather than passive baseload generators. Using the ARIES platform, the digital twin was evaluated under multiple grid scenarios, including load following, voltage support at the distribution level, and frequency response at the transmission level. Results show that hybrid geothermal systems can respond effectively to dynamic grid conditions, providing inertia-like behavior, primary frequency support, and voltage regulation through coordinated control. In addition to the performance and grid services capability analysis of geothermal and hybrid geothermal systems, the EXERGETIC project also focused on scalability and techno-economic analysis of geothermal hybrid plants. In particular, for the scalability analysis, machine-learning (ML)-based surrogate models were trained using data generated from the geothermal digital twin under different grid-connected scenarios and plant capacities. These ML models demonstrated strong interpolation and extrapolation capabilities across plant sizes, accurately reproducing both steady-state and transient responses with very low errors. Regarding the techno-economic analysis, plant performance results were integrated with cost models for hybrid geothermal systems, and the levelized cost of electricity (LCOE) was used as the main economic metric to evaluate system performance across a range of system capacities, solar shares, solar multiples, and storage durations. Results indicate that economies of scale significantly reduce geothermal LCOE as plant capacity increases, with large-scale systems (25-100 MW) achieving substantially lower costs than small plants. Hybridization with solar thermal energy and storage further improves economic performance by increasing capacity utilization and enabling flexible dispatch. In addition, thermal storage plays a critical role in reducing LCOE by maximizing geothermal, solar, and stored energy resources. In summary, the results from this project demonstrate that geothermal hybrid systems represent a promising alternative for increasing the energy conversion efficiency of geothermal technologies, contributing to the preservation of geothermal resources, and supporting the transition of geothermal plants from traditional baseload resources into flexible, resilient, and cost-competitive energy conversion technologies.

15 GEOTHERMAL ENERGY

Trajectory-independent speed limits for controlled open quantum systems

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

open quantum systems & decoherence

Hybrid biophysical systems for atmospheric CO 2 capture

Negative emissions technologies will be essential for limiting anthropogenic global temperature increases to 2 °C in the later years of the 21st century. Carbonic anhydrase (CA) metalloenzymes catalyze the otherwise slow conversion of CO 2 into carbonic acid (H 2 CO 3 ), suggesting their utility in the rapid hydration and downstream capture of dissolved CO 2 in aqueous media for a variety of CO 2 capture methods, such as thermal and pH swings and mineralization. The possibility of driving the rapid capture of CO 2 by catalyzing the CO 2 hydration bottleneck carries real potential for realizing efficient direct air capture (DAC) and direct ocean capture (DOC) systems. However, scaled application of CAs will be dependent on some way of economically sourcing the enzymes at volumes relevant to scaled DAC/DOC operations. In this perspective, we consider the prospect of catalyzing CO 2 hydration using a CA that is bound to the outer membrane of a cyanobacterial host, engineered constructs we call CyCAMs. Coupling extracellular CA expression to a marine, photosynthetic cyanobacterial host results in a CO 2 hydration catalyst that is continuously refreshed during the bacterial growth cycle, without the need for enzyme purification or harvesting steps. In the case of marine cyanobacteria, sunlight and the solutes native to seawater provide the respective energy, nutrients and sources of inorganic carbon essential to maintaining the bacterial population. We consider the potential impact of CA-mediated CO 2 hydration on a variety of DAC processes, with CO 2 mineralization explored as a primary use case.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments

In this work, we introduce an efficient method, TTN-HEOM, for exactly calculating the open quantum dynamics for driven quantum systems interacting with highly structured bosonic baths by combining the tree tensor network (TTN) decomposition scheme with the bexcitonic generalization of the numerically exact hierarchical equations of motion (HEOM). The method yields a series of quantum master equations for all core tensors in the TTN that efficiently and accurately capture the open quantum dynamics for non-Markovian environments to all orders in the system–bath interaction. These master equations are constructed based on the time-dependent Dirac–Frenkel variational principle, which isolates the optimal dynamics for the core tensors given the TTN ansatz. The dynamics converges to the HEOM when increasing the rank of the core tensors, a limit in which the TTN ansatz becomes exact. We introduce TENSO, tensor equations for non-Markovian structured open systems, as a general-purpose Python code to propagate the TTN-HEOM dynamics. We implement three general propagators for the coupled master equations: two fixed-rank methods that require a constant memory footprint during the dynamics and one adaptive-rank method with a variable memory footprint controlled by the target level of computational error. We exemplify the utility of these methods by simulating a two-level system coupled to a structured bath containing one Drude–Lorentz component and eight Brownian oscillators, which is beyond what can presently be computed using the standard HEOM. Our results show that the TTN-HEOM is capable of simulating both dephasing and relaxation dynamics of driven quantum systems interacting with structured baths, even those of chemical complexity, with an affordable computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH