Results for “COMMUTATION RELATIONS” — Page 8

DOE OSTI2024

Phase diagram of the three-dimensional subsystem toric code

Subsystem quantum error-correcting codes typically involve measuring a sequence of noncommuting parity check operators. They can sometimes exhibit greater fault tolerance than conventional codes, which use commuting checks. However, unlike subspace codes, it is unclear if subsystem codes—in particular their advantages—can be understood in terms of ground-state properties of a physical Hamiltonian. In this paper, we address this question for the three-dimensional subsystem toric code (3D STC), as recently constructed by Kubica and Vasmer [], which exhibits single-shot error correction. Motivated by a conjectured relation between single-shot properties and thermal stability, we study the zero- and finite-temperature phases of an associated noncommuting Hamiltonian. By mapping the Hamiltonian model to a pair of 3D Z 2 gauge theories coupled by a kinetic constraint, we find various phases at zero temperature, all separated by first-order transitions: There are 3D toric code-like phases with deconfined point-like excitations in the bulk, and there are phases with a confined bulk supporting a 2D toric code on the surface when appropriate boundary conditions are chosen. The latter is similar to the surface topological order present in 3D STC. However, the similarities between the single-shot correction in 3D STC and the confined phases are only partial: they share the same sets of degrees of freedom, but they are governed by different dynamical rules. Instead, we argue that the process of single-shot error correction can more suitably be associated with a path (rather than a point) in the zero-temperature phase diagram, a perspective, which inspires alternative measurement sequences enabling single-shot error correction. Moreover, since none of the above-mentioned phases survives at nonzero temperature, the single-shot error-correction property of the code does not imply thermal stability of the associated Hamiltonian phase. Published by the American Physical Society 2024

Li, Yaodong (ORCID:0000000337421944)↗

DOE OSTI2019

On a Question About Generalized Congruence Subgroups. I

A set of additive subgroups σ = (σ{sub ij}), 1 ≤ i, j ≤ n, of a field (or ring) K is called a net of order n over K if σ{sub ir}σ{sub rj} ⊆ σ{sub ij} for all values of the indices i, r, j. The same system, but without diagonal, is called an elementary net. A full or elementary net σ = (σ{sub ij}) is said to be irreducible if all the additive subgroups σ{sub ij} are different from zero. An elementary net σ is closed if the subgroup E(σ) does not contain new elementary transvections. The present paper is related to a question posed by Y. N. Nuzhin in connection with V. M. Levchuk’s question No. 15.46 from the Kourovka notebook about the admissibility (closure) of elementary net (carpet) σ = (σ{sub ij}) over a field K. Let J be an arbitrary subset of {1, . . . , n}, n ≥ 3, and the cardinality m of J satisfies the condition 2 ≤ m ≤ n − 1. Let R be a commutative integral domain (non-field) with identity, and let K be the quotient field of R. An example of a net σ = (σ{sub ij}) of order n over K, for which the group E(σ) ∩ 〈t{sub ij}(K) : i, j ∈ J〉 is not contained in the group 〈t{sub ij}(σ{sub ij}) : i, j ∈ J〉, is constructed.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1974

Small V/STOL aircraft analysis, volume 1

A study has been made of the economic viability of advanced V/STOL aircraft concepts in performing general aviation missions. A survey of general aviation aircraft users, operators, and manufacturers indicated that personnel transport missions formulated around business executive needs, commuter air service, and offshore oil supply are the leading potential areas of application using VTOL aircraft. Advanced VTOL concepts potentially available in the late 1970 time period were evaluated as alternatives to privately owned contemporary aircraft and commercial airline service in satisfying these personnel transport needs. Economic analysis incorporating the traveler's value of time as the principle figure of merit were used to identify the relative merits of alternative VTOL air transportation concepts.

Smith, K. R., Jr.↗

NASA NTRS1963

THE ECONOMIC EFFECTS OF THE SPACE PROGRAM

The purpose of this paper is to discuss the economic impact of the amazing space program presented in the preceding papers. My function is to view the space program objectively as an economist so as to assess its impact upon the Nation's economy as a whole and upon certain regions in particular. In order to be objective, I will not take the extreme view that our entire lives will be changed by this program overnight-we will not all be wearing air-conditioned Moonsuits in 2 years and commuting to work by individual miniaturized Rocketpacks. An attempt will be made to avoid the other extreme of thinking that the space program is the greatest boondoggle since the Pyramids; it is not merely a form of scientific leaf-raking on a gigantic scale. My definition of the space program includes the program of the National Aeronautics and Space Administration (NASA) and some work of other agencies doing related space exploration, particularly the Department of Defense. In essence, I hope to answer the question: What will NASA's program mean to the participants in the Nation's economy?

ECONOMICS↗

NASA NTRS1983

Multi-Fuel Rotary Engine for General Aviation Aircraft

Design studies, conducted for NASA, of Advanced Multi-fuel General Aviation and Commuter Aircraft Rotary Stratified Charge Engines are summarized. Conceptual design studies of an advanced engine sized to provide 186/250 shaft KW/HP under cruise conditions at 7620/25,000 m/ft. altitude were performed. Relevant engine development background covering both prior and recent engine test results of the direct injected unthrottled rotary engine technology, including the capability to interchangeably operate on gasoline, diesel fuel, kerosene, or aviation jet fuel, are presented and related to growth predictions. Aircraft studies, using these resultant growth engines, define anticipated system effects of the performance and power density improvements for both single engine and twin engine airplanes. The calculated results indicate superior system performance and 30 to 35% fuel economy improvement for the Rotary-engine airplanes as compared to equivalent airframe concept designs with current baseline engines. The research and technology activities required to attain the projected engine performance levels are also discussed.

Jones, C.↗

DOE OSTI2025

2009 Interstate 95 Express Phase 1A Survey

# 2009 Interstate 95 Express Phase 1A Survey The 2009 Phase 1A Survey focused on commuters using Interstate 95 express lanes between downtown Miami and the Golden Glades Interchange in Florida. Survey participants answered questions about their trip's purpose, frequency, and mode as well as demographics such as their age, race/ethnicity, and income. It also asked if and why or why not they had used Interstate 95 before and/or after the installation of two high-occupancy toll lanes, if they were satisfied with the upgrade, and about their related perceptions of safety. ## Data Collection Agency The survey was conducted by and for the Florida Department of Transportation. ## Survey Methodology The survey was conducted online in May 2009. ## Survey Records, Data, and Documentation Survey records include 9,156 participants.