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Quantum-classical correspondence in the oracle model of computation

Antoni Wojcik Ravindra W. Chhajlany
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Abstract

The oracle model of computation is believed to allow a rigorous proof of quantum over classical computational superiority. Since quantum and classical oracles are essentially different, a correspondence principle is commonly implicitly used as a platform for comparison of oracle complexity. Here, we question the grounds on which this correspondence is based. Obviously, results on quantum speed-up depend on the chosen correspondence. So, we introduce the notion of genuine quantum speed-up which can serve as a tool for reliable comparison of quantum vs classical complexity, independently of the chosen correspondence principle.

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Antoni Wojcik Ravindra W. Chhajlany. 2005-06-29. Quantum-classical correspondence in the oracle model of computation. https://arxiv.org/abs/quant-ph/0506248

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