Gustafson, Erik | Engineering Papers

DOE OSTI2024

Highly-efficient quantum Fourier transformations for certain non-Abelian groups

Quantum Fourier transformations are an essential component of many quantum algorithms, from prime factoring to quantum simulation. While the standard Abelian QFrT is well studied, important variants corresponding to non-Abelian groups of interest have seen less development. In particular, fast non-Abelian Fourier transformations are important components for both quantum simulations of field theories as well as approaches to the non-Abelian hidden subgroup problem. In this work, we present fast quantum Fourier transformations for a number of non-Abelian groups of interest for high energy physics, B T , B O , 6 Δ ( 27 ) , Δ ( 54 ) , and Σ ( 36 × 3 ) . For each group, we derive explicit quantum circuits and estimate resource scaling for fault-tolerant implementations. Our work shows that the development of a fast Fourier transformation can substantively reduce simulation costs by an up to three orders of magnitude for the finite groups that we have investigated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2019

Modular Active Self-Assembling Space Telescope Swarms

The Phase I study included a detailed exploration of a specific mission concept based on this architecture - a 31-meter diameter version of the LUVOIR (Large Ultraviolet Optical Infrared Surveyor) mission concept with the same wavelength coverage and wave-front quality requirements. The study focused on establishing the feasibility of the proposed concept with respect to what were identified as the most challenging aspects of the mission: the ability to find orbital solutions using solar sail propulsion for both the initial transfers and subsequent rendezvous trajectories; and the ability to generate the required final primary mirror surface out of uniformly polished individual module mirrors using deformation via mechanical degrees of freedom. As a result of the Phase I work it was shown that both orbital and optical solutions are feasible, but will require technology advancement in multiple key areas. In particular, improvements to solar sail areal densities and loading factors will allow us to more easily find fully general solutions for the transfer trajectories, while lower mass, ultra-precise cryogenic linear actuators will likely be needed to form the final mirror shape. However, it was found that current state of the art in solar sails was sufficient for rendezvous trajectories once on-orbit, that the requisite wave-front quality could be achieved with actuation requirements not more stringent than those being carried by LUVOIR, and that there exists a well-defined design space in which the module spacecraft designs can be optimized. The technology development required to progress this work overlaps significantly with numerous NASA technology roadmaps, as well as the Exoplanet Exploration Program's technologies gap list, meaning that continued development of this concept would directly benefit a variety of NASA programs, as well as enabling the completely unique capabilities provided by a 31-meter optical space telescope...Our architecture requires only a single module type allowing us to directly leverage the cost and efficiency benefits of true mass production, in direct contrast to previously explored self-assembling swarm concepts, which typically include multiple module types.

Astronomy↗