Quantum Zero-Error Algorithms Cannot be Composed
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.
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