preprint · arXiv (Cornell University) · 1999

Quantum Bounded Query Complexity

Buhrman, Harry, van Dam, Wim

Cited by 0Open access

Abstract

We combine the classical notions and techniques for bounded query classes with those developed in quantum computing. We give strong evidence that quantum queries to an oracle in the class NP does indeed reduce the query complexity of decision problems. Under traditional complexity assumptions, we obtain an exponential speedup between the quantum and the classical query complexity of function classes. For decision problems and function classes we obtain the following results: o P_||^NP[2k] is included in EQP_||^NP[k] o P_||^NP[2^(k+1)-2] is included in EQP^NP[k] o FP_||^NP[2^(k+1)-2] is included in FEQP^NP[2k] o FP_||^NP is included in FEQP^NP[O(log n)] For sets A that are many-one complete for PSPACE or EXP we show that FP^A is included in FEQP^A[1]. Sets A that are many-one complete for PP have the property that FP_||^A is included in FEQP^A[1]. In general we prove that for any set A there is a set X such that FP^A is included in FEQP^X[1], establishing that no set is superterse in the quantum setting.

Cite this paper

APA 7

Buhrman, H., & van Dam, W. (1999). Quantum Bounded Query Complexity. arXiv (Cornell University). https://doi.org/10.48550/arxiv.quant-ph/9903035

MLA 9

Buhrman, Harry, and Wim van Dam. “Quantum Bounded Query Complexity.” arXiv (Cornell University), 1999, https://doi.org/10.48550/arxiv.quant-ph/9903035.

Chicago

Buhrman, Harry, and Wim van Dam. 1999. “Quantum Bounded Query Complexity.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.quant-ph/9903035.

Harvard

Buhrman, H. and van Dam, W. (1999) ‘Quantum Bounded Query Complexity’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.quant-ph/9903035.

BibTeX

@misc{buhrman1999quantum,
  title = {{Quantum Bounded Query Complexity}},
  author = {Buhrman, Harry and van Dam, Wim},
  journal = {arXiv (Cornell University)},
  year = {1999},
  doi = {10.48550/arxiv.quant-ph/9903035}
}

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