Effects of imperfections for Shor?s factorization algorithm

IGNACIO GARCIA MATA; D.L. SHEPELYANSKY

ASPET

Workshop; GDR-Information et Communication Quantique: Aspects théoriques de l?information quan- tique; 2007

We study effects of imperfections induced by residual couplings between qubits on the accuracy of Shor?s algorithm using numerical simulations of realistic quantum computations with up to 30 qubits. The factoring of numbers up to N=943 show that the width of peaks, which frequencies allow to determine the factors, grow exponentially with the number of qubits. However, the algorithm remains operational up to a critical coupling strength ϵc which drops only polynomially with log2N. The numerical dependence of ϵc on log2N is explained by analytical estimates that allows one to obtain the scaling for functionality of Shor?s algorithm on realistic quantum computers with a large number of qubits.