2015/07/11 by Andris Ambainis, Aleksandrs Belovs, Ambainis, Andris +5 · 2 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · #Advanced biosensing and bioanalysis techniques #Computational Complexity (cs.CC) #Cryptography and Data Security #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning and Algorithms #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1507.03126
openalex publication_date 2015/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the k-junta testing problem, a tester has to efficiently decide whether a given function f:\0,1\n→ \0,1\ is a k-junta (i.e., depends on at most k of its input bits) or is ε-far from any k-junta. Our main result is a quantum algorithm for this problem with query complexity O(√(k/ε)) and time complexity O(n√(k/ε)). This quadratically improves over the query complexity of the previous best quantum junta tester, due to Atıcı and Servedio. Our tester is based on a new quantum algorithm for a gapped version of the combinatorial group testing problem, with an up to quartic improvement over the query complexity of the best classical algorithm. For our upper bound on the time complexity we give a near-linear time implementation of a shallow variant of the quantum Fourier transform over the symmetric group, similar to the Schur-Weyl transform. We also prove a lower bound of Ω(k1/3) queries for junta-testing (for constant ε).