Phase diagram for the Grover algorithm with static imperfections

Pomeransky, A. A.; Zhirov, O. V.; Shepelyansky, D. L.

Phase diagram for the Grover algorithm with static imperfections

Authors

Pomeransky, A. A.

Zhirov, O. V.

Shepelyansky, D. L.

Description

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 $ε$. The critical border $ε_c$ between two phases drops polynomially with the number of qubits $n_q$ as $ε_c \sim n_q^{-3/2}$. In the regular phase $(ε< ε_c)$ the algorithm remains robust against imperfections showing the efficiency gain $ε_c / ε$ for $ε\gtrsim 2^{-n_q/2}$. In the chaotic phase $(ε> ε_c)$ the algorithm is completely destroyed.
4 pages, 4 figs, research at http://www.quantware.ups-tlse.fr