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1. Compiling Conditional Quantum Gates without Using Helper Qubits

   https://doi.org/10.1145/3656436  

   Huang, Keli; Palsberg, Jens (June 2024, Proceedings of the ACM on Programming Languages)

   We present a compilation scheme for conditional quantum gates. Our scheme compiles a multi-qubit conditional to a linear number of two-qubit conditionals. This can be done straightforwardly with helper qubits, but we show how to do it without using helper qubits and with much fewer gates than in previous work. Specifically, our scheme requires 1/3 as many gates as the previous best scheme without using helper qubits, which is essential for practical use. Our experiments show that several quantum-circuit optimizers have little impact on the compiled code from the previous best scheme, confirming the need for our new scheme. Our experiments with Grover's algorithm and quantum walk also show that our scheme has a major impact on the reliability of the compiled code. 

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2. Does the Loop Quantum μo Scheme Permit Black Hole Formation?

   https://doi.org/10.3390/universe7110406  

   Li, Bao-Fei; Singh, Parampreet (November 2021, Universe)

   We explore the way different loop quantization prescriptions affect the formation of trapped surfaces in the gravitational collapse of a homogeneous dust cloud, with particular emphasis on the so-called μo scheme in which loop quantum cosmology was initially formulated. Its undesirable features in cosmological models led to the so-called improved dynamics or the μ¯ scheme. While the jury is still out on the right scheme for black hole spacetimes, we show that as far as black hole formation is concerned, the μo scheme has another, so far unknown, serious problem. We found that in the μo scheme, no trapped surfaces would form for a nonsingular collapse of a homogeneous dust cloud in the marginally bound case unless the minimum nonzero area of the loops over which holonomies are computed or the Barbero–Immirzi parameter decreases almost four times from its standard value. It turns out that the trapped surfaces in the μo scheme for the marginally bound case are also forbidden for an arbitrary matter content as long as the collapsing interior is isometric to a spatially flat Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. We found that in contrast to the situation in the μo scheme, black holes can form in the μ¯ scheme, as well as other lattice refinements with a mass gap determined by quantum geometry. 

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3. Optimum Resource Allocation for Full-Duplex Vehicular Communication Networks

   https://doi.org/10.1109/ACCESS.2020.3015539  

   Siddig, Ali A.; Ibrahim, Ahmed S.; Ismail, Mahmoud H. (August 2020, IEEE Access)

   In this article, we propose a resource allocation (RA) scheme for vehicular communication networks (VCNs). The proposed scheme exploits the spectral efficiency of full-duplex (FD) communications to fulfill the reliability constraints of vehicle-to-vehicle (V2V) links and the high capacity requirements of vehicle-to-infrastructure (V2I) links. Also, it is capable of coping with the fast variations of the channels due to the high mobility. Based on the links requirements, the RA problem is formulated as a non-convex problem, which is solved in two steps. First, the optimal power allocation (PA) is obtained by solving a system of linear equations. Second, the channel assignment (CA), which turns out to be a maximum weight bipartite matching problem, is solved using the Hungarian method. Also, a heuristic hybrid scheme, which combines the proposed FD scheme and the half-duplex (HD) scheme that optimally finds the RA, is proposed. Compared to the optimal HD-based scheme, simulation results show that the proposed FD scheme always offers higher sum of the V2I links’ capacities except for the case in which V2V links require low transmission rates, while the hybrid scheme ensures higher performance for all potential cases. 

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4. Lagrange Coded Computing with Sparsity Constraints

   https://doi.org/10.1109/ALLERTON.2019.8919966  

   Fahim, Mohammad; Cadambe, Viveck R. (September 2019, 2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton))

   In this paper, we propose a distributed coding scheme that allows for lower computation cost per computing node than the standard Lagrange Coded Computing scheme. The proposed coding scheme is useful for cases where the elements of the input data set are of large dimensions and the computing nodes have limited computation power. This coding scheme provides a trade-off between the computation cost per worker and the recovery threshold in a distributed coded computing framework. The proposed scheme is also extended to provide data privacy against at most t colluding worker nodes in the system. 

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5. Birational geometry of Beauville–Mukai systems III: Asymptotic behavior

   https://doi.org/10.1112/blms.13158  

   Qin, Xuqiang; Sawon, Justin (December 2024, Bulletin of the London Mathematical Society)

   Abstract Suppose that a Hilbert scheme of points on a K3 surface of Picard rank one admits a rational Lagrangian fibration. We show that if the degree of the surface is sufficiently large compared to the number of points, then the Hilbert scheme is the unique hyperkähler manifold in its birational class. In particular, the Hilbert scheme is a Lagrangian fibration itself, which we realize as coming from a (twisted) Beauville–Mukai system on a Fourier–Mukai partner of . We also show that when the degree of the surface is small our method can be used to find all birational models of the Hilbert scheme. 

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