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Accueil du site > Publications > Publications 2008 > Shor’s factorization algorithm with a single control qubit and imperfections

Shor’s factorization algorithm with a single control qubit and imperfections

Ignacio García-Mata, Klaus M. Frahm and Dima L. Shepelyansky

par Ignacio Garcia-Mata - 4 novembre 2008

We formulate and numerically simulate the single control qubit Shor algorithm for the case of static imperfections induced by residual couplings between qubits. This allows us to study the accuracy of Shor’s algorithm with respect to these imperfections using numerical simulations of realistic quantum computations with up to n_q=18 computational qubits allowing to factor numbers up to N=205193. We confirm that the algorithm remains operational up to a critical coupling strength \epsilon_c which drops only polynomially with \log_2 N. The obtained numerical dependence of \epsilon_c on \log_2 N is in a good agreement with the analytical estimates that allows to obtain the scaling for functionality of Shor’s algorithm on realistic quantum computers with a large number of qubits.