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 ∈-far from any k-junta. Our main result is a quantum algorithm for this problem with query complexity Ō(√∈) and time complexity Ō(n√∈). This quadratically improves over the query complexity of the previous best quantum junta tester, due to Atici 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 ∈).

Additional Metadata
Conference Annual ACM-SIAM Symposium on Discrete Algorithms
Grant This work was funded by the European Commission 7th Framework Programme; grant id erc/615307 - Progress in quantum computing: Algorithms, communication, and applications (QPROGRESS)
Citation
Ambainis, A, Belovs, A, Regev, O, & de Wolf, R.M. (2016). Efficient quantum algorithms for (Gapped) group testing and junta testing. Presented at the Annual ACM-SIAM Symposium on Discrete Algorithms.

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25186.pdf Author Manuscript , 520kb