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A simpler, Hamiltonian-based quantum algorithm prepares $S_n$ character states with up to $O(n)$ gates, drastically improving on prior $\widetilde O(n^3)$ QFT methods.
A single quantum query can solve a non-convex optimization problem previously requiring superpolynomial classical time, and CV-QAOA offers a path to efficient quantum advantage on problems intractable for classical gradient descent.
Quantum interferometry shatters the topological barriers that trap classical algorithms in the disordered phase of spin glasses, enabling sampling at temperatures far below the dynamical transition.