Quantum bounded query complexity

Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317) Pub Date : 1999-03-09 DOI:10.1109/CCC.1999.766273

H. Buhrman, W. V. Dam

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引用次数: 12

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: P/sub /spl par///sup NP[2k]//spl sube/EQP/sub /spl par///sup NP[k]/; P/sub /spl par///sup NP[2k+1-2]//spl sube/EQP/sup NP[k]/; FP/sub /spl par///sup NP[2k=1-2]//spl sube/FEQP/sup NP[2k]/; FP/sub /spl par///sup NP/spl sube/FEQP(NP[Olog n)]/. For sets A that are many-one complete for PSPACE or EXP we show that Fp/sup A//spl sube/FEQP/sup A[1]/. Sets A that are many-one complete for PP have the property that FP/sub /spl par///sup A//spl sube/FEQP/sup A[1]/. In general we prove that for any set A there is a set X such that FP/sup A//spl sube/FEQP/sup X[1]/, establishing that no set is superterse in the quantum setting.

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量子有界查询复杂度

我们将有界查询类的经典概念和技术与量子计算中开发的概念和技术相结合。我们给出了强有力的证据，证明对NP类的oracle的量子查询确实降低了决策问题的查询复杂性。在传统的复杂度假设下，我们得到了函数类的量子查询复杂度与经典查询复杂度之间的指数级加速。对于决策问题和函数类，我们得到了以下结果:P/sub /spl par///sup NP[2k]//spl sub /EQP/sub /spl par///sup NP[k]/;P/sub /spl par///sup NP[2k+1-2]//spl sub /EQP/sup NP[k]/;FP/sub /spl par///sup NP[2k=1-2]//spl sub /FEQP/sup NP[2k]/;FP/sub /spl par///sup NP/spl sub /FEQP(NP[Olog n)]/。对于PSPACE或EXP的多一完全集合A，我们证明了Fp/sup A//spl sub /FEQP/sup A[1]/。对于PP来说，多一完全集合A具有FP/sub /spl par///sup A//spl sub /FEQP/sup A[1]/的属性。一般地，我们证明了对于任意集合A，存在一个集合X使得FP/sup A//spl subbe /FEQP/sup X[1]/，建立了在量子集合中没有超简洁的集合。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)

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