Work

Efficient quantum algorithms for (Gapped) group testing and junta testing

Year: 2016

Type: conference-paper

Abstract: 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 ∈).

Source: Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands

Authors: Ambainis, Andris, Belovs, Aleksandr, Regev, Oded, Wolf, Ronald

Institutions: University of Latvia, Centrum Wiskunde & Informatica, New York University, University of Amsterdam

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: AF: Small: Computational Foundations of Lattices

OpenAlex ID: W1465613978