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95 records · Page 6

Classification of dynamical Lie algebras generated by spin interactions on undirected graphs

Dynamical Lie algebras (DLAs) are a versatile tool for various topics that span from the expressibility-trainability of variational quantum algorithms (VQAs), to simulation of many body Hamiltonians. Quantum gates and most of the Hamiltonians of interest consist of local interactions; therefore, the analysis of all possible DLAs generated by 1- and 2-local operators is crucial for quantum simulation and VQAs on current hardware. Previously in [R. Wiersema et al ., npj Quantum Inf. 10 , 110 (2024)], we analyzed the DLAs on linear, circular and all-to-all topologies, and obtained results about their dimensions and algebraic structure. Here, in this work, we extend our analysis into any possible hardware topology and provide a classification of all DLAs generated by Pauli strings on any undirected interaction graph. Our results indicate that the DLAs depend solely on whether the connectivity or interaction graph is bipartite or not. In addition, we find that the non-trivial polynomially scaling DLAs appear only on 1D line or circle topologies, and all other DLAs have dimensions scaling exponentially with the system size. Together with the current VQA literature, our results imply that either the majority of VQAs are non-trainable, or we are yet to understand the role of DLAs on the trainability of VQAs.

Algebraic structures

Coupling and recoupling coefficients for Wigner’s U(4) supermultiplet symmetry

A novel procedure for evaluating Wigner coupling coefficients and Racah recoupling coefficients for U(4) in two group–subgroup chains is presented. The canonical U(4) > U(3) > U(2) > U(1) coupling and recoupling coefficients are applicable to any system that possesses U(4) symmetry, while the physical U(4) coupling coefficients are more specific to nuclear structure studies that utilize Wigner’s supermultiplet symmetry concept. The procedure that is proposed sidesteps the use of binomial coefficients and alternating sum series and consequently enables fast and accurate computation of any and all U(4)-underpinned features. The inner multiplicity of a (S, T) pair within a single U(4) > SU S (2) Ⓧ SU T (2) irreducible representation is obtained from the dimension of the null space of the SU(2) raising generators, while the resolution for the outer multiplicity follows from the work of Alex et al. on U(N) . It is anticipated that a C++ library will ultimately be available for determining generic coupling and recoupling coefficients associated with both the canonical and the physical group–subgroup chains of U(4).

Cross-Coupling Reaction

SCF Framework, HF Stability, and RPA Correlation for Jordan–Wigner-Transformed Spin Hamiltonians on Arbitrary Coupling Topologies

Mapping spins to fermions via the Jordan–Wigner (JW) transformation can render mean-field (Hartree–Fock, HF) descriptions effective for strongly correlated spin systems. As established in recent work, the application of such approaches is not limited by the nonlocal structure of JW strings or by site ordering because string operators can be absorbed into Thouless rotations of a Slater determinant, and the variational optimization of a unitary Lie-algebraic similarity transformation removes any ordering dependence. Leveraging these ideas, we develop a self-consistent field (SCF) scheme that expresses the mean-field energy as a functional of the single-particle density matrix, providing an alternative to gradient-based optimization of Thouless parameters. We derive the analytical orbital Hessian to diagnose HF stability and compute the ground-state correlation energy through the random-phase approximation (RPA). Benchmark results for the XXZ and J 1 –J 2 model on one- and two-dimensional lattices demonstrate that RPA significantly improves mean-field accuracy.

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Some Aeronautical Communications Experiments

Classically there has existed an asymmetry between the computing and communicating sides of aerospace systems. Over the past few decades, this asymmetry has shifted to favoring communication link technologies, meaning that advancements in available central processing units (CPUs), storage devices, and internal data buses have stagnated. Indeed, the increased emphasis placed on refining subsystem performance such as with antenna bandwidth in phased arrays, amplifier power efficiency, software defined radio (SDR) flexibility and encoding for data compression and error correction has given rise to successful debuts of multi-gigabit-per-second data return from long space-link distances. These accomplishments are easily quantifiable through link budgets and illustrate what is possible, but also reveal the deficiencies in overall communications capabilities. In particular, the ever-accelerating presence of aerospace vehicles gives rise to newer and larger classes of challenges to address the needs of 21st century systems. Furthermore remote sensing and imaging capabilities have far outpaced our ability to transmit their products to the ground, so we are increasingly dependent on pre-processing and downselection to contend with the communications bottleneck. No longer may we depend upon the constrained logistics in delivering end-to-end data delivery through manual reconfigurations, static event scheduling and execution on a per-vehicle basis, for these methods do not scale and therefore must give way to dynamic, networked approaches with an overall systems view in mind. Emerging mission requirements exhibit a trend toward multiple smaller-scale vehicles working together to perform dissimilar observations. Such operations necessitate sensor fusion across a constellation, and where data processing may be distributed throughout a fairly disconnected network whose topology changes over time in non-deterministic manners. Individual communications link performance is still very relevant to deploying an effective communications system, but now must be embedded within a greater architecture of capability to optimally utilize the bandwidth available from each link to generate an ultimate end-to-end quality of service. The deleterious effects of timing uncertainty across the arrangement presents a challenge to measurement synchronization and delivery, so a successful deployed system needs to be tolerant to the delays inherent in time-of-light between elements and digital processing latencies existing at each node. In this presentation we share the flight test results from a high performance Gbps laser communications terminal evaluated with a suite of store and forward capabilities called High-rate Delay Tolerant Networking (HDTN). The communications payload is operated over Lake Erie across a range of configurations including several convergence layers, and is evaluated to determine recovery time after link disruptions, information loss, efficiency and speed. The effectiveness of utilizing a flying laboratory to increase the Technology Readiness Level (TRL) of an integrated system in relevant environments is discussed, as well as the value of conducting aeronautics experiments to retire risk for technology infusion into space missions. Upcoming flight campaigns will be presented, including opportunities to demonstrate secure command and control, data intensive hyperspectral imaging, quantum link characterization, 4k High Definition (HD) video streaming and internetworked space-ground-aero relay operations. These experiments will pave the way for future missions which will depend upon interoperability across disparate government and privately owned networks, involve contention with uncertain and dynamic timing, and require agility to autonomously configure optimal parameters across networks of ever-increasing size and complexity to ensure data delivery. https://www1.grc.nasa.gov/space/scan/acs/tech-studies/dtn/

Daniel Raible

Ligand‐Mediated Quantum Yield Enhancement in 1‐D Silver Organothiolate Metal–Organic Chalcogenolates

X-ray free electron laser (XFEL) microcrystallography and synchrotron single-crystal crystallography are used to evaluate the role of organic substituent position on the optoelectronic properties of metal–organic chalcogenolates (MOChas). MOChas are crystalline 1D and 2D semiconducting hybrid materials that have varying optoelectronic properties depending on composition, topology, and structure. While MOChas have attracted much interest, small crystal sizes impede routine crystal structure determination. A series of constitutional isomers where the aryl thiol is functionalized by either methoxy or methyl ester are solved by small molecule serial femtosecond X-ray crystallography (smSFX) and single crystal rotational crystallography. While all the methoxy examples have a low quantum yield (0-1%), the methyl ester in the ortho position yields a high quantum yield of 22%. Here, the proximity of the oxygen atoms to the silver inorganic core correlates to a considerable enhancement of quantum yield. Four crystal structures are solved at a resolution range of 0.8–1.0 Å revealing a collapse of the 2D topology for functional groups in the 2- and 3- positions, resulting in needle-like crystals. Further analysis using density functional theory (DFT) and many-body perturbation theory (MBPT) enables the exploration of complex excitonic phenomena within easily prepared material systems.

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