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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2017

Robust Exploration and Commercial Missions to the Moon Using LANTR Propulsion and In-Situ Propellants Derived from Lunar Polar Ice (LPI) Deposits

The nuclear thermal rocket (NTR) has frequently been identified as a key space asset required for the human exploration of Mars. This proven technology can also provide the affordable access through cislunar space necessary for commercial development and sustained human presence on the Moon. It is a demonstrated technology capable of generating both high thrust and high specific impulse (Isp 900 s) twice that of todays best chemical rockets. Nuclear lunar transfer vehicles consisting of a propulsion stage using three approx.16.5 klbf "Small Nuclear Rocket Engines (SNREs)", an in-line propellant tank, plus the payload can enable a variety of reusable lunar missions. These include cargo delivery and crewed lunar landing missions. Even weeklong "tourism" missions carrying passengers into lunar orbit for a day of sightseeing and picture taking are possible. The NTR can play an important role in the next phase of lunar exploration and development by providing a robust in-space lunar transportation system (LTS) that can allow initial outposts to evolve into settlements supported by a variety of commercial activities such as in-situ propellant production used to supply strategically located propellant depots and transportation nodes. The processing of LPI deposits (estimated to be approx. 2 billion metric tons) for propellant production - specifically liquid oxygen (LO2) and hydrogen (LH2) can significantly reduce the launch mass requirements from Earth and can enable reusable, surface-based lunar landing vehicles (LLVs) using LO2/LH2 chemical rocket engines. Afterwards, LO2/LH2 propellant depots can be established in lunar polar and equatorial orbits to supply the LTS. At this point a modified version of the conventional NTR called the LO2-augmented NTR, or LANTR would be introduced into the LTS allowing bipropellant operation and leveraging the mission benefits of refueling with lunar-derived propellants (LDPs) for Earth return. The bipropellant LANTR engine utilizes the large divergent section of its nozzle as an afterburner into which oxygen is injected and supersonically combusted with nuclear preheated hydrogen emerging from the engines choked sonic throat essentially scramjet propulsion in reverse. By varying the oxygen-to-hydrogen mixture ratio, LANTR engines can operate over a range of thrust and Isp values while the reactor core power level remains relatively constant. A LANTR-based LTS offers unique mission capabilities including short transit time crewed cargo transports. Even a commuter shuttle service may be possible allowing one-way trip times to and from the Moon on the order of 36 hours or less. If only 1 of the postulated water ice trapped in deep shadowed craters at the lunar poles were available for use in lunar orbit, such a supply could support daily commuter flights to the Moon for many thousands of years! The proposed paper outlines an evolutionary mission architecture and examines a variety of mission types and transfer vehicle designs, along with the increasing demands on LDP production as mission complexity and delta V requirements increase. A comparison of vehicle features and engine operating characteristics are also provided together with a discussion of the propellant production and mining requirements, and issues, associated with using LPI as the source material.

Nuclear Thermal Propulsion↗
NASA NTRS2018

Robust Exploration and Commercial Missions to the Moon Using Nuclear Thermal Rocket Propulsion and Lunar Liquid Oxygen Derived from FeO-Rich Pyroclasitc Deposits

The nuclear thermal rocket (NTR) has frequently been identified as a key space asset required for the human exploration of Mars. This proven technology can also provide the affordable access through cislunar space necessary for commercial development and sustained human presence on the Moon. It is a demonstrated technology capable of generating both high thrust and high specific impulse (I(sub sp) approx. 900 s) twice that of today's best chemical rockets. Nuclear lunar transfer vehicles-consisting of a propulsion stage using three approx. 16.5-klb(sub f) small nuclear rocket engines (SNREs), an in-line propellant tank, plus the payload-are reusable, enabling a variety of lunar missions. These include cargo delivery and crewed lunar landing missions. Even weeklong ''tourism'' missions carrying passengers into lunar orbit for a day of sightseeing and picture taking are possible. The NTR can play an important role in the next phase of lunar exploration and development by providing a robust in-space lunar transportation system (LTS) that can allow initial outposts to evolve into settlements supported by a variety of commercial activities such as in-situ propellant production used to supply strategically located propellant depots and transportation nodes. The use of lunar liquid oxygen (LLO2) derived from iron oxide (FeO)-rich volcanic glass beads, found in numerous pyroclastic deposits on the Moon, can significantly reduce the launch mass requirements from Earth by enabling reusable, surface-based lunar landing vehicles (LLVs)that use liquid oxygen and hydrogen (LO2/LH2) chemical rocket engines. Afterwards, a LO2/LH2 propellant depot can be established in lunar equatorial orbit to supply the LTS. At this point a modified version of the conventional NTR-called the LO2-augmented NTR, or LANTR-is introduced into the LTS allowing bipropellant operation and leveraging the mission benefits of refueling with lunar-derived propellants for Earth return. The bipropellant LANTR engine utilizes the large divergent section of its nozzle as an ''afterburner'' into which oxygen is injected and supersonically combusted with nuclear preheated hydrogen emerging from the engine's choked sonic throat-essentially ''scramjet propulsion in reverse.'' By varying the oxygen-to-hydrogen mixture ratio, LANTR engines can operate over a range of thrust and I(sub sp) values while the reactor core power level remains relatively constant. A LANTR-based LTS offers unique mission capabilities including short-transit-time crewed cargo transports. Even a ''commuter'' shuttle service may be possible allowing ''one-way'' trip times to and from the Moon on the order of 36 hours or less. If only 1% of the extracted LLO2 propellant from identified resource sites were available for use in lunar orbit, such a supply could support daily commuter flights to the Moon for many thousands of years! This report outlines an evolutionary architecture and examines a variety of mission types and transfer vehicle designs, along with the increasing demands on LLO2 production as mission complexity and velocity change delta V requirements increase. A comparison of vehicle features and engine operating characteristics, for both NTR and LANTR engines, is also provided along with a discussion of the propellant production and mining requirements associated with using FeO-rich volcanic glass as source material.

rocket↗
NASA NTRS2018

Robust Exploration and Commercial Missions to the Moon Using Nuclear Thermal Rocket Propulsion and In Situ Propellants Derived from Lunar Polar Ice Deposits

The nuclear thermal rocket (NTR) has frequently been identified as a key space asset required for the human exploration of Mars. This proven technology can also provide the affordable “access through cislunar space” necessary for commercial development and sustained human presence on the Moon. It is a demonstrated technology capable of generating both high thrust and high specific impulse (I(sub sp) ~900 s)— twice that of today’s best chemical rockets. Nuclear lunar transfer vehicles—consisting of a propulsion stage using three ~16.5-klb(sub f) small nuclear rocket engines (SNREs), an in-line propellant tank, plus the payload—can enable a variety of reusable lunar missions. These include cargo delivery and crewed lunar landing missions. Even weeklong “tourism” missions carrying passengers into lunar orbit for a day of sightseeing and picture taking are possible. The NTR can play an important role in the next phase of lunar exploration and development by providing a robust in-space lunar transportation system (LTS) that can allow initial outposts to evolve into settlements supported by a variety of commercial activities such as in situ propellant production used to supply strategically located propellant depots and transportation nodes. The processing of lunar polar ice (LPI) deposits (estimated to be ~2 billion metric tons) for propellant production—specifically liquid oxygen (LO(sub 2)) and hydrogen (LH(sub 2))—can significantly reduce the launch mass requirements from Earth and can enable reusable, surface-based lunar landing vehicles (LLVs) using LO(sub 2)/LH(sub 2) chemical rocket engines. Afterwards, LO(sub 2)/LH(sub 2) propellant depots can be established in lunar polar and equatorial orbits to supply the LTS. At this point a modified version of the conventional NTR called the LO(sub 2)-augmented NTR, or LANTR, would be introduced into the LTS, allowing bipropellant operation and leveraging the mission benefits of refueling with lunar-derived propellants (LDPs) for Earth return. The bipropellant LANTR engine utilizes the large divergent section of its nozzle as an “afterburner” into which oxygen is injected and supersonically combusted with nuclear preheated hydrogen emerging from the engine’s choked sonic throat—essentially “scramjet propulsion in reverse.” By varying the oxygen-to-hydrogen mixture ratio, LANTR engines can operate over a range of thrust and I(sub sp) values while the reactor core power level remains relatively constant. A LANTR-based LTS offers unique mission capabilities including short transit time crewed cargo transports. Even a “commuter” shuttle service may be possible, allowing “one-way” trip times to and from the Moon on the order of 36 hr or less. If only 1% of the postulated trapped water ice were available for use in lunar orbit, such a supply could support routine commuter flights to the Moon for many thousands of years. This report outlines an evolving LTS architecture that uses propellants derived from LPI and examines a variety of mission types and transfer vehicle designs along with their operating characteristics and increasing demands on LDP production as mission complexity and velocity change ΔV requirements increase. A comparison of the LDP production and mining requirements using LPI and volcanic glass to produce lunar-derived liquid oxygen (LUNOX) via the hydrogen reduction process is included, and the synergy with an evolving helium-3 mining industry is also discussed.

Borowski, Stanley K.↗
NASA NTRS2019

Air Mobility Data & Reasoning Fabric

Throughout the world, especially in dense urban environments, the quality of life is being negatively impacted by ever growing commute time. Travel, beyond commuting, is increasingly driven by door-to-door challenges ? not just gate-to-gate considerations. Air Mobility may be an approach to address these challenges, as it can effectively convert our 2D mobility system to a 3D mobility system, vastly increasing mobility options.

Van Dalsem, William R.↗
NASA NTRS2019

Key Technologies, Systems, and Infrastructure Enabling the Commercialization and Human Settlement of the Moon and Cislunar Space

Over 50 years have passed since 2001: A Space Odyssey debuted in April 1968. In the film, Dr. Heywood Floydflies to a large artificial gravity space station orbiting Earth aboard a commercial space plane. He then embarks on acommuter flight to the Moon arriving there 25 hours later. Today, in this the 50th anniversary year of the Apollo 11lunar landing, the images portrayed in 2001 still remain well beyond our capabilities. This paper examines keytechnologies and systems (e.g., in-situ resource utilization, fission power, advanced chemical and nuclearpropulsion), and supporting orbital infrastructure (providing a propellant and cargo transfer function), that could bedeveloped by NASA and industry over the next 30 years allowing the operational capabilities presented in 2001 to beachieved, albeit on a more spartan scale. Lunar-derived propellants (LDPs) will be essential to developing a reusablelunar transportation system that can allow initial outposts to evolve into settlements supporting a variety ofcommercial activities. Deposits of icy regolith discovered at the lunar poles can supply the feedstock material neededto produce liquid oxygen (LO2) and hydrogen (LH2) propellants. On the lunar nearside, near the equator, iron oxiderichvolcanic glass beads from vast pyroclastic deposits, together with mare regolith, can provide the feedstockmaterials to produce lunar-derived LO2 plus other important solar wind implanted (SWI) volatiles, including H2and helium-3. Megawatt-class fission power systems will be essential for providing continuous "24/7" power toprocessing plants, human settlements and commercial enterprises that develop on the Moon and in orbit. Reusablelunar landing vehicles will provide cargo and passenger "orbit-to-surface" access and will also transport LDP toSpace Transportation Nodes (STNs) located in lunar polar (LPO) and equatorial orbits (LLO). Reusable space-based,lunar transfer vehicles (LTVs), operating between STNs in low Earth orbit, LLO, and LPO, and able to refuel withLDPs, offer unique mission capabilities including short transit time crewed cargo transports. Even commuter flightssimilar to that portrayed in 2001 appear possible, allowing 1-way trip times to and from the Moon as short as 24hours. The performance of LTVs using both RL10B-2 chemical rockets, and a variant of the nuclear thermal rocket(NTR), the LO2-Augmented NTR (LANTR), are examined and compared. If only 1% of the LDP obtained from icyregolith, volcanic glass, and SWI volatile deposits were available for use in lunar orbit, such a supply could supportroutine commuter flights to the Moon for many thousands of years. This paper provides a look ahead at what mightbe possible in the not too distant future, quantifies the operational characteristics of key in-space and surfacetechnologies and systems, and provides conceptual designs for the various architectural elements discussed.

Borowski, Stanley K.↗
NASA NTRS2019

Key Technologies, Systems, and Infrastructure Enabling the Commercialization and Human Settlement of the Moon and Cislunar Space

Over 50 years have passed since 2001: A Space Odyssey debuted in April 1968. In the film, Dr. Heywood Floydflies to a large artificial gravity space station orbiting Earth aboard a commercial space plane. He then embarks on acommuter flight to the Moon arriving there 25 hours later. Today, in this the 50th anniversary year of the Apollo 11lunar landing, the images portrayed in 2001 still remain well beyond our capabilities. This paper examines keytechnologies and systems (e.g., in-situ resource utilization, fission power, advanced chemical and nuclearpropulsion), and supporting orbital infrastructure (providing a propellant and cargo transfer function), that could bedeveloped by NASA and industry over the next 30 years allowing the operational capabilities presented in 2001 to beachieved, albeit on a more spartan scale. Lunar-derived propellants (LDPs) will be essential to developing a reusablelunar transportation system that can allow initial outposts to evolve into settlements supporting a variety ofcommercial activities. Deposits of icy regolith discovered at the lunar poles can supply the feedstock material neededto produce liquid oxygen (LO2) and hydrogen (LH2) propellants. On the lunar nearside, near the equator, iron oxiderichvolcanic glass beads from vast pyroclastic deposits, together with mare regolith, can provide the feedstockmaterials to produce lunar-derived LO2 plus other important solar wind implanted (SWI) volatiles, including H2and helium-3. Megawatt-class fission power systems will be essential for providing continuous "24/7" power toprocessing plants, human settlements and commercial enterprises that develop on the Moon and in orbit. Reusablelunar landing vehicles will provide cargo and passenger "orbit-to-surface" access and will also transport LDP to Space Transportation Nodes (STNs) located in lunar polar (LPO) and equatorial orbits (LLO). Reusable space-based,lunar transfer vehicles (LTVs), operating between STNs in low Earth orbit, LLO, and LPO, and able to refuel with LDPs, offer unique mission capabilities including short transit time crewed cargo transports. Even commuter flights similar to that portrayed in 2001 appear possible, allowing 1-way trip times to and from the Moon as short as 24hours. The performance of LTVs using both RL10B-2 chemical rockets, and a variant of the nuclear thermal rocket(NTR), the LO2-Augmented NTR (LANTR), are examined and compared. If only 1% of the LDP obtained from icyregolith, volcanic glass, and SWI volatile deposits were available for use in lunar orbit, such a supply could support routine commuter flights to the Moon for many thousands of years. This paper provides a look ahead at what might be possible in the not too distant future, quantifies the operational characteristics of key in-space and surface technologies and systems, and provides conceptual designs for the various architectural elements discussed.

Borowski, Stanley K.↗
NASA NTRS2017

A Study of the Degradation of Electronic Speed Controllers for Brushless DC Motors

Brushless DC motors are frequently used in electric aircraft and other direct drive applications. As these motors are notactually direct current machines but synchronous alternating current machines; they are electronically commutated by a power inverter. The power inverter for brushless DC motors typically used in small scale UAVs is a semiconductor base delectronic commutator that is external to the motor and is referred to as an electronic speed control (ESC). This paper examines the performance changes of a UAV electric propulsion system resulting from ESC degradation. ESC performance is evaluated in simulation and on a new developed test bed featuring propulsion components from a reference UAV. An increase in the rise fall times of the switched voltages is expected to cause timing issues at high motor speeds. This study paves the way for further development of diagnostic and prognostic methods for inverter circuits which are part of the overall electric UAV system.

Gorospe, George E., Jr.↗
NASA NTRS2019

Commercialization and Human Settlement of the Moon and Cislunar Space – A Look Ahead at the Possibilities over the Next 50 Years

Over 50 years have passed since the movie 2001: A Space Odyssey debuted in April 1968. In the film, Dr. Heywood Floyd flies to a large artificial gravity space station orbiting Earth aboard a commercial space plane. He then embarks on a commuter flight to the Moon arriving there 25hours later. Today, on the 50th anniversary of the Apollo 11 lunar landing, the images portrayed in 2001 still remain well beyond our capabilities. This paper examines key technologies and systems (in-situ resource utilization, fission power, advanced chemical and nuclear propulsion),and orbiting infrastructure elements (providing a propellant depot and cargo transfer function),that could be developed by NASA and the private sector in future decades allowing the operational capabilities presented in 2001 to be achieved, albeit on a more spartan scale. Lunar derived propellants (LDPs) will be essential to reducing the launch mass requirements from Earth and developing a reusable lunar transportation system (LTS) that can allow initial outposts to evolve into settlements supporting a variety of commercial activities like in-situ propellant production. Deposits of icy regolith found within permanently shadowed craters at the lunar pole scan supply the feedstock material to produce liquid oxygen (LO2) and hydrogen (LH2) propellan tneeded by surface-based lunar landing vehicles (LLVs) using chemical rocket engines. Along the Moon's nearside equatorial corridor, iron oxide-rich volcanic glass beads from vast pyroclasticdeposits, together with mare regolith, can provide the materials to produce lunar-derived LO2plus other important solar wind implanted (SWI) volatiles, including H2 and helium-3. Mega watt classfission power systems will be essential for providing continuous "24/7" power to LLVs will provide cargo and passenger "orbit-to-surface" access and willalso be used to transport LDP to Space Transportation Nodes (STNs) located in lunar polar(LPO) and equatorial orbits (LLO). Spaced-based, reusable lunar transfer vehicles (LTVs),operating between STNs in low Earth orbit (LEO), LLO, and LPO, and able to refuel with LDPs,can offer unique mission capabilities including short transit time crewed cargo transports. Even acommuter shuttle service similar to that portrayed in 2001 appears possible, allowing 1-way trip times to and from the Moon as short as 24 hours. The performance of LTVs using both RL10B-2chemical rockets, and a variant of the nuclear thermal rocket (NTR), the LO2-Augmented NTR(LANTR), are examined and compared. The bipropellant LANTR engine utilizes its divergent nozzle section as an afterburner into which oxygen is injected and supersonically combusted with reactor-heated hydrogen emerging from the engine's sonic throat. If only 1% of the LDP obtained from icy regolith, volcanic glass, and SWI volatile deposits were available for use in lunar orbit,such a supply could support routine commuter flights to the Moon for many thousands of years!This paper provides a look ahead at what might be possible in the not too distant future,quantifies the operational characteristics of key in-space and surface technologies and systems,and provides conceptual designs for the various architectural elements discussed.

Borowski, Stanley K.↗
NASA NTRSDate not supplied

Air Mobility Data & Reasoning Fabric

Throughout the world, especially in dense urban environments, the quality of life is being negatively impacted by ever growing commute time. Travel, beyond commuting, is increasingly driven by door-to-door challenges ? not just gate-to-gate considerations. Air Mobility may be an approach to address these challenges, as it can effectively convert our 2D mobility system to a 3D mobility system, vastly increasing mobility options.

Air mobility↗
DOE OSTI2025

Efficient Simulation of Open Quantum Systems on NISQ Trapped‐Ion Hardware

Abstract Simulating open quantum systems, which interact with external environments, presents significant challenges on noisy intermediate‐scale quantum (NISQ) devices due to limited qubit resources and noise. In this study, an efficient framework is proposed for simulating open quantum systems on NISQ hardware by leveraging a time‐perturbative Kraus operator representation of the system's dynamics. This approach avoids the computationally expensive Trotterization method and exploits the Lindblad master equation to represent time evolution in a compact form, particularly for systems satisfying specific commutation relations. The efficiency of this method is demonstrated by simulating quantum channels, such as the continuous‐time Pauli channel and damped harmonic oscillators, on NISQ trapped‐ion hardware, including IonQ Harmony and Quantinuum H1‐1. Additionally, hardware‐agnostic error mitigation techniques are introduced, including Pauli channel fitting and quantum depolarizing channel inversion, to enhance the fidelity of quantum simulations. These results show strong agreement between the simulations on real quantum hardware and exact solutions, highlighting the potential of Kraus‐based methods for scalable and accurate simulation of open quantum systems on NISQ devices. This framework opens pathways for simulating more complex systems under realistic conditions in the near term.

Burdine, Colin [Department of Electrical and Compu↗
DOE OSTI2025

Geometry of soft scalars at one loop

We extend the soft theorems for scattering amplitudes of scalar effective field theories to one-loop order. Our analysis requires carefully accounting for the fact that the soft limit is not guaranteed to commute with evaluating IR-divergent loop integrals; new results for the soft limit of general scalar one-loop integrals are presented. The geometric soft theorem remains unmodified for any derivatively-coupled scalar effective field theory, and we conjecture that this statement holds to all orders. In contrast, the soft theorem receives nontrivial corrections in the presence of potential interactions, analogous to the case of non-Abelian gauge theories. We derive the universal leading-order correction to the scalar soft theorem arising from potential interactions at one loop. Explicit examples are provided that illustrate the general results.

differential and algebraic geometry↗
DOE OSTI2025

Quantum area fluctuations from gravitational phase space

We study the gravitational phase space associated to a stretched horizon within a finite-sized causal diamond in (d + 2)-dimensional spacetimes. By imposing the Raychaudhuri equation, we obtain its constrained symplectic form using the covariant phase space formalism and derive the relevant quantum commutators by inverting the symplectic form and quantizing. Finally, we compute the area fluctuations of the causal diamond by taking a Carrollian limit of the stretched horizon in pure Minkowski spacetime, and derive the relationship $\left\langle {\left(\Delta A\right)}^2\right\rangle \ge \frac{2\pi G}{d}\left\langle A\right\rangle$, showing that the variance of the area fluctuations is proportional to the area itself.

classical theories of gravity↗
DOE OSTI2024

Small circle expansion for adjoint QCD 2 with periodic boundary conditions

We study 1 + 1-dimensional SU(N) gauge theory coupled to one adjoint multiplet of Majorana fermions on a small spatial circle of circumference L. Using periodic boundary conditions, we derive the effective action for the quantum mechanics of the holonomy and the fermion zero modes in perturbation theory up to order (gL) 3 . When the adjoint fermion mass-squared is tuned to g 2 N/(2π), the effective action is found to be an example of supersymmetric quantum mechanics with a nontrivial superpotential. We separate the states into the ℤN center symmetry sectors (universes) labeled by p = 0, . . . , N – 1 and show that in one of the sectors the supersymmetry is unbroken, while in the others it is broken spontaneously. These results give us new insights into the (1, 1) supersymmetry of adjoint QCD 2 , which has previously been established using light-cone quantization. When the adjoint mass is set to zero, our effective Hamiltonian does not depend on the fermions at all, so that there are 2 N−1 degenerate sectors of the Hilbert space. This construction appears to provide an explicit realization of the extended symmetry of the massless model, where there are 2 2N−2 operators that commute with the Hamiltonian. We also generalize our results to other gauge groups G, for which supersymmetry is found at the adjoint mass-squared g 2 h ∨ /(2π), where h ∨ is the dual Coxeter number of G.

effective field theories↗
DOE OSTI2025

Efficient Quantum Gibbs Samplers with Kubo–Martin–Schwinger Detailed Balance Condition

Lindblad dynamics and other open-system dynamics provide a promising path towards efficient Gibbs sampling on quantum computers. In these proposals, the Lindbladian is obtained via an algorithmic construction akin to designing an artificial thermostat in classical Monte Carlo or molecular dynamics methods, rather than being treated as an approximation to weakly coupled system-bath unitary dynamics. Recently, Chen, Kastoryano, and Gilyén (arXiv:2311.09207) introduced the first efficiently implementable Lindbladian satisfying the Kubo–Martin–Schwinger (KMS) detailed balance condition, which ensures that the Gibbs state is a fixed point of the dynamics and is applicable to non-commuting Hamiltonians. This Gibbs sampler uses a continuously parameterized set of jump operators, and the energy resolution required for implementing each jump operator depends only logarithmically on the precision and the mixing time. In this work, we build upon the structural characterization of KMS detailed balanced Lindbladians by Fagnola and Umanità, and develop a family of efficient quantum Gibbs samplers using a finite set of jump operators (the number can be as few as one), akin to the classical Markov chain-based sampling algorithm. Compared to the existing works, our quantum Gibbs samplers have a comparable quantum simulation cost but with greater design flexibility and a much simpler implementation and error analysis. Moreover, it encompasses the construction of Chen, Kastoryano, and Gilyén as a special instance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Discrete Superconvergence Analysis for Quantum Magnus Algorithms of Unbounded Hamiltonian Simulation

Motivated by various applications, unbounded Hamiltonian simulation has recently garnered great attention. Quantum Magnus algorithms, designed to achieve commutator scaling for time-dependent Hamiltonian simulation, have been found to be particularly efficient for such applications. When applied to unbounded Hamiltonian simulation in the interaction picture, they exhibit an unexpected superconvergence phenomenon. However, existing proofs are limited to the spatially continuous setting and do not extend to discrete spatial discretizations. Here, in this work, we provide the first superconvergence estimate in the fully discrete setting with a finite number of spatial discretization points N, and show that it holds with an error constant uniform in N. The proof is based on the two-parameter symbol class, which, to our knowledge, is applied for the first time in algorithm analysis. The key idea is to establish a semiclassical framework by identifying two parameters through the discretization number and the time step size rescaled by the operator norm, such that the semiclassical uniformity guarantees the uniformity of both. This approach may have broader applications in numerical analysis beyond the specific context of this work.

Borns-Weil, Yonah [University of California, Berke↗