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.
arXiv comments
5 pages including 2 figures. Final version submitted to PRL. Now includes additional comments on entanglement and mixedness as algorithm proceeds. Added references to work by Mosca
> Shor's algorithm requires not only the logical qubit to be stable (the superposition of 1 and 0, but also the phase [..] to be noise free to an extraordinary degree. There are rotations in very small angles many, many times in the computation. This is wrong. Those rotations…
> Shor's algorithm requires not only the logical qubit to be stable (the superposition of 1 and 0, but also the phase [..] to be noise free to an extraordinary degree. There are rotations in very small angles many, many times in the computation. This is wrong. Those rotations…
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