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.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.

Jan 1, 200410 citations

\\epsilon

. The critical border

\\epsilon_c

between two phases drops polynomially with the number of qubits

n_q

\\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.