Chronological feed of everything captured from Sean Cairncross.
This paper investigates three distinct extremal problems related to subgraph densities. It corrects a prior result on k-edge star maximization, determines the extrema for k-edge stars in ordered graphs, and presents novel complete results for the maximum density of a specific 3-edge-colored complete graph, representing a significant advancement in colored graph analysis.
This paper proves that the inducibility of a rainbow k-clique (R) is k!/(k^k-k) for k ≥ 11. This addresses a generalization of a problem by Erdős and Sós, posed by Huang. The extremal construction is a balanced recursive blow-up of R. The authors also establish a broader result, showing that k-vertex connected rainbow graphs with a minimum degree of at least C log(k) (for some constant C > 0) also have inducibility k!/(k^k-k).
Researchers have successfully demonstrated a universal, high-fidelity gate set using arrays of optically trapped $^{171}$Yb atoms. This system utilizes the long coherence times of nuclear spin qubits to achieve robust entanglement, with measured two-qubit gate fidelities exceeding 99%. The work represents a significant step towards scalable neutral atom quantum computing by enabling complex algorithm execution with high precision.
This research demonstrates a method for mid-circuit measurement, re-initialization, and replacement of lost atoms within optical tweezer arrays without compromising the coherence of remaining qubits. This capability enables repeated syndrome extraction and real-time conditional branching, essential for fault-tolerant logical computation beyond the natural lifetime of individual atoms.