Quantum algorithms achieve poly(k) query complexity for tolerant k-junta testing with ε1 = 1/2-1/k and ε2 = 1/2-1/(2k²), while classical algorithms require k^Ω(log k) queries.
[FKR+04] Eldar Fischer, Guy Kindler, Dana Ron, Shmuel Safra, and Alex Samorodnitsky
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Quantum Advantage in Tolerant Junta Testing
Quantum algorithms achieve poly(k) query complexity for tolerant k-junta testing with ε1 = 1/2-1/k and ε2 = 1/2-1/(2k²), while classical algorithms require k^Ω(log k) queries.