Average-Case Quantum Query Complexity

Abstract. We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be at most polynomial 3]. We show that for average-case complexity under the uniform distribution, quantum algorithms can be exponentially faster than classical algorithms. Under non-uniform distributions the gap can even be super-exponential. We also prove some general bounds for average-case complexity and show that the average-case quantum complexity of MAJORITY under the uniform distribution is nearly quadratically better than the classical complexity.

• Type: Conference
• Year: 2000
• Where: STACS
• Authors: Andris Ambainis, Ronald de Wolf
• Keywords: Average-case Complexity, Average-case Quantum Complexity, Quantum, STACS 2000, Theoretical Computer Science