Wim van Dam, Hieu D. Nguyen
Searching for a marked target in a list of $N$ items requires $\Omega(N)$ oracle queries when using a classical computer, while a quantum computer can accomplish the same task in $\bigO{\sqrt{N}}$ queries using Grover's quantum search algorithm. Although this quadratic speed-up has been indisputable, the Copenhagen interpretation of quantum mechanics does not make understanding how this enhancement over classical occurs intuitive. At the same time, cosmologists have proposed the theory of decoherent histories as an alternative to the Copenhagen school in order to explain how classical physics arises from the more fundamental quantum laws. This article applies theory of decoherent histories to Grover's algorithm. It finds a quasi-classical domain within the search evolution and compares it to classical searching. Moreover, under the theory of decoherent histories, the quantum process can be described in a language very much similar to a stochastic process. Thus, quantum searching, which has been of primal importance in quantum computing, also gives an exactly solvable toy model for the theory of decoherent histories.
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http://arxiv.org/abs/1206.1946
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