Entanglement Simulations of Shor's Algorithm

Details Entanglement Simulations of Shor's Algorithm Entanglement Simulations of Shor's Algorithm

2001-02-27

arxiv.org/abs/quant-ph/0102136v2

Physics

Quantum Physics

17 pages including 16 figures. Typos corrected and more efficient simulation methods outlined

Scientific paper

10.1080/09500340110107207

We demonstrate that, in the case of Shor's algorithm for factoring, highly mixed states will allow efficient quantum computation, indeed factorization can be achieved efficiently with just one initial pure qubit and a supply of initally maximally mixed qubits (S. Parker and M. B. Plenio, Phys. Rev. Lett. 85, 3049 (2000)) . This leads us to ask how this affects the entanglement in the algorithm. We thus investigate the behaviour of entanglement in Shor's algorithm for small numbers of qubits by classical computer simulation of the quantum computer at different stages of the algorithm. We find that entanglement is an intrinsic part of the algorithm and that the entanglement through the algorithm appears to be closely related to the amount of mixing. Furthermore, if the computer is in a highly mixed state any attempt to remove entanglement by further mixing of the algorithm results in a significant decrease in its efficiency.

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