The quantum query complexity of certification

Authors:
Andris Ambainis;Andrew M. Childs;François Le Gall;Seiichiro Tani
Affiliations:
Faculty of Computing, University of Latvia, Riga, Latvia;Department of Combinatorics & Optimization and Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada;Quantum Computation and Information Project, Solution Oriented Research for Science and Technology, Japan Science and Technology Agency, Tokyo, Japan;NTT Communication Science Laboratories, NTT Corporation, Atsugi, Japan and Quantum Computation and Information Project, Solution Oriented Research for Science and Technology, Japan Science and Tec ...
Venue:
Quantum Information & Computation
Year:
2010

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Abstract

We study the quantum query complexity of finding a certificate for a d-regular, k-levelbalanced NANDformula. We show that the query complexity is Θ(d(k+1)/2) forO-certificates, and Θ(dk/2) for 1-certificates. In particular, this shows that the zero-errorquantum query complexity of evaluating such formulas is Õ(d(k+1)/2). Our lower boundrelies on the fact that the quantum adversary method obeys a direct sum theorem.