Two Classical Queries versus One Quantum Query

TL;DR

This paper demonstrates that a quantum computer can solve certain decision problems with one query that would require two classical queries, highlighting the potential computational advantage of quantum over classical systems.

Contribution

It shows that quantum computers can simulate two classical SAT-queries with a single quantum query, revealing a fundamental difference in query complexity.

Findings

Quantum computer solves problems with one query that classical needs two.

Simulation holds for SAT-oracle but not for general black-box.

Highlights potential quantum advantage in structured query problems.

Abstract

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.