We present a theoretical framework for solving the inverse problem in one-dimensional Angular Correlation of Positron Annihilation Radiation (ACAR) using large, position-insensitive detectors and Hadamard-matrix grating sequences. A forward model is developed linking coincidence count rates to the underlying angular emission probability distribution, and a grating-selection strategy is introduced that maximizes orthogonality in the system response matrix. Reconstruction is demonstrated using pseudoinverse methods and evaluated through null-space analysis; null fractions epsilon less than or similar to 5% yield stable, accurate recovery. Ray-tracing simulations based on representative geometries produce count-rate vectors that reconstruct the original emission distributions with good fidelity. While the present treatment is one-dimensional, the approach naturally extends to two-dimensional coded apertures. These results support reduced detector baselines and improved angular and energy resolution in future ACAR instrumentation.
Variational Quantum Algorithms (VQAs) provide a promising framework for tackling complex optimization problems on near-term quantum hardware. Here, we demonstrate that hybrid qubit-qumode quantum devices offer an efficient route to solving Quadratic Unconstrained Binary Optimization (QUBO) problems using the Echoed Conditional Displacement Variational Quantum Eigensolver (ECD-VQE). Leveraging circuit quantum electrodynamics (cQED) architectures, we encode QUBO instances across multiple qumodes weakly coupled to a single qubit and extract binary solutions directly from photon-number measurements. We apply ECD-VQE to the Binary Knapsack Problem and show that it outperforms the Quantum Approximate Optimization Algorithm (QAOA) implemented on conventional qubit circuits, achieving higher-quality solutions with dramatically fewer resources. We also demonstrate that ECD-VQE can be extended to chemically motivated tasks such as active-space selection for multireference electronic structure methods. These results highlight the utility of hybrid qubit-qumode platforms for a broad class of NP-hard and chemistry-related optimization problems and demonstrate that variational ECD ansatz can realize expressive state preparation with significantly shallower circuits than qubit-only architectures, positioning qubit-qumode gates as compelling candidates for constrained optimization in early fault-tolerant quantum computing.
Headwater streams play critical roles in hydrologic and biogeochemical processes and functions, yet their spatial distribution and land cover context remain poorly understood at continental scales, and no dedicated geospatial dataset exists. Building from a high-resolution conterminous United States (CONUS) hydrography network dataset, we quantified the spatial extent, density, and upstream catchment characteristics of headwater stream segments across the CONUS. We identified approximately 8.4 million kilometers of headwater streams, finding that 77
Previously published thermal expansion data for almandine and spessartine garnets are sparse and inconsistent. We have therefore measured the thermal expansion of two garnets of compositions Alm90 Grs2.7 Py2.3 Ski4.5 (sample Alm90) and Sps81 Alm15 Grs3 And1 (sample Sps81) from ca. 90 K to ca. 780 K by synchrotron X-ray powder diffraction using quartz as an internal calibrant for temperature. The adiabatic elastic tensors of these two samples have been determined by single-crystal Brillouin scattering at room conditions; for the Alm90 sample c11 = 302.0(5), c12 = 111.3(4), c44 = 93.3(1), giving KS = 174.9(4) GPa, and for the Sps81 sample c11 = 303.1(4), c12 = 109.5(4), c44 = 93.6(2), giving KS = 174.0(4) GPa. These new data have been used in combination with P-V, P-T-V and P-T-Ks data from the literature to determine the equations of state (EoS) of end-member almandine and spessartine. The parameters of q-compromise Mie-Grüneisen-Debye thermal pressure EoS with a third-order Birch-Murnaghan EoS to describe the compressional properties at room temperature are: The parameters are available in .eos files for the EosFit suite of programs in the supplementary data, and from www.rossangel.com and www.mineralogylab.com . The most significant changes from the previous EoS are the lower Debye temperatures because our data show higher thermal expansion above room temperature. The biggest consequence for host-inclusion piezobarometry is that these new EoS lead to lower entrapment temperatures for zircon inclusions in garnet. We also show that there is no significant difference in the P-V/V0 behaviour of almandine and spessartine and that the available experimental data for intermediate compositions does not indicate any significant non-ideality in the compressional or thermal expansion behaviour of almandine-spessartine garnets.
