Efficient Quantum Algorithms for (Gapped) Group Testing and Junta Testing

Andris Ambainis, Aleksandrs Belovs, Oded Regev, Ronald de Wolf
2015 Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms  
In the k-junta testing problem, a tester has to efficiently decide whether a given function f : {0, 1} n → {0, 1} is a kjunta (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
more » ... 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(k 1/3 ) queries for junta-testing (for constant ε).
doi:10.1137/1.9781611974331.ch65 dblp:conf/soda/AmbainisBRW16 fatcat:4wplim2ppfdsjagxjlcc6i7z6q