Phase diagram for the Grover algorithm with static imperfections

Details Phase diagram for the Grover algorithm with static imperfections Phase diagram for the Grover algorithm with static imperfections

2004-03-19

arxiv.org/abs/quant-ph/0403138v1

Eur. Phys. J. D 31, 131-135 (2004)

Physics

Quantum Physics

4 pages, 4 figs, research at http://www.quantware.ups-tlse.fr

Scientific paper

10.1140/epjd/e2004-00113-4

We study effects of static inter-qubit interactions on the stability of the Grover quantum search algorithm. Our numerical and analytical results show existence of regular and chaotic phases depending on the imperfection strength $\epsilon$. The critical border $\epsilon_c$ between two phases drops polynomially with the number of qubits $n_q$ as $\epsilon_c \sim n_q^{-3/2}$. In the regular phase $(\epsilon < \epsilon_c)$ the algorithm remains robust against imperfections showing the efficiency gain $\epsilon_c / \epsilon$ for $\epsilon \gtrsim 2^{-n_q/2}$. In the chaotic phase $(\epsilon > \epsilon_c)$ the algorithm is completely destroyed.

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