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.
[BV97] Ethan Bernstein and Umesh Vazirani
2 Pith papers cite this work, alongside 3 external citations. Polarity classification is still indexing.
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k-juntas, low-degree Fourier functions, and sparse polynomials are testable with O(1/ε) queries independent of n for small ε.
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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.
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Classes Testable with $O(1/\epsilon)$ Queries for Small $\epsilon$ Independent of the Number of Variables
k-juntas, low-degree Fourier functions, and sparse polynomials are testable with O(1/ε) queries independent of n for small ε.