Quantum zero-error algorithms cannot be composed

Authors:
Harry Buhrman;Ronald de Wolf
Affiliations:
CWI and University of Amsterdam, Kruislaan 413, Amsterdam 1098 SJ, The Netherlands;CWI, Kruislaan 413, Amsterdam 1098 SJ, The Netherlands
Venue:
Information Processing Letters
Year:
2003

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Abstract

We exhibit two black-box problems, both of which have an efficient quantum algorithm with zero-error, yet whose composition does not have an efficient quantum algorithm with zero-error. This shows that quantum zero-error algorithms cannot be composed. In oracle terms, we give a relativized world where ZQPZQP ≠ ZQP, while classically we always have ZPPZPP = ZPP.