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Efficient factorization with a single pure qubit and $log N$ mixed qubits

S. Parker·M. B. Plenio
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Abstract

It is commonly assumed that Shor's quantum algorithm for the efficient factorization of a large number $N$ requires a pure initial state. Here we demonstrate that a single pure qubit together with a collection of $log_2 N$ qubits in an arbitrary mixed state is sufficient to implement Shor's factorization algorithm efficiently.

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S. Parker, M. B. Plenio. 2005-11-20. Efficient factorization with a single pure qubit and $log N$ mixed qubits. https://doi.org/10.1103/physrevlett.85.3049

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