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Phase diagram for the Grover algorithm with static imperfections

A. A. Pomeransky·O. V. Zhirov·D. L. Shepelyansky
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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 $ε$. 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.

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A. A. Pomeransky, O. V. Zhirov, D. L. Shepelyansky. 2004-03-19. Phase diagram for the Grover algorithm with static imperfections. https://doi.org/10.1140/epjd%2Fe2004-00113-4

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