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Quantum Gibbs states for complex, non-commuting Hamiltonians can now be prepared efficiently by transferring guarantees from simpler sources, overcoming the limitations of prior Hamiltonian families.
Quantum interferometric algorithms are no longer bottlenecked by rigid pilot-state preparation: moving from ordinary to relative algebraic decoding elevates effective code distances from $O(1)$ to $\Theta(n)$, unlocking verifiable quantum advantages in non-commuting optimization tasks.
