Linear-depth quantum oracles for clique problems from edge colorings and graph states, with linear non-Clifford cost and a provably bounded-error k-clique search
The episode discusses a paper introducing quantum oracles for k-clique and triangle finding problems with linear depth, achieved by using graph structures like one-factorization. Hosts discuss how this reduces circuit depth, making algorithms more feasible for real hardware. They highlight practical improvements to the search strategies, suggesting a path toward more robust and efficient solutions.