Phase diagram for the Grover algorithm with static imperfections

Abstract

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.

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

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