Two classical queries versus one quantum query

Scott Aaronson, Andris Ambainis, Andrej Bogdanov +2 more

Niel de Beaudrap, Not Available Not Available, Not Available Not Available

Alina Vasilieva, Elena Shishova, Taisia Mischenko-Slatenkova

Quantum computing aims to use quantum mechanical effects for the efficient performance of computational tasks. A popular research direction is enlarging the gap between classical and quantum algorithm complexity of the same computational problem. We present new results in quantum query algorithm design for multivalued functions that allow to achieve a large quantum versus classical complexity separation. To compute a basic finite multifunction in a quantum model only one query is enough while classically three queries are required. Then, we present two generalizations and a modification of the original algorithm, and obtain the following complexity gaps: QUD(M') ≤ N versus CUD(M') ≥ 3N, and QRD(M'') = 1 versus N/2 + 1 ≤ CRD(M'') ≤ N.

Kazuo Iwama

Wim van Dam

In this note we study the power of so called query-limited computers. We compare the strength of a classical computer that is allowed to ask two questions to an NP-oracle with the strength of a quantum computer that is allowed only one such query. It is shown that any decision problem that requires two parallel (non-adaptive) SAT-queries on a classical computer can also be solved exactly by a quantum computer using only one SAT-oracle call, where both computations have polynomial time-complexity. Such a simulation is generally believed to be impossible for a one-query classical computer. The reduction also does not hold if we replace the SAT-oracle by a general black-box. This result gives therefore an example of how a quantum computer is probably more powerful than a classical computer. It also highlights the potential differences between quantum complexity results for general oracles when compared to results for more structured tasks like the SAT-problem.

Can H. Bostanci