Work

Average-Case Quantum Query Complexity

Year: 1999

Type: article

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. 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.

Source: UvA-DARE (University of Amsterdam)

DOI: 10.48550/arxiv.quant-ph/9904079

Authors: Ambainis, Andris, de Wolf, Ronald

Institutions: University of California, Berkeley, Centrum Wiskunde & Informatica, University of Amsterdam

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Microsoft Research, Universiteit van Amsterdam

Award: A Proposal for Research on Quantum Computation and Clustering Algorithms