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

I. GARCÍA-MATA; K.M. FRAHM; D.L. SHEPELYANSKY

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

Año: 2008 vol. 78 p. 62323 - 62331

1050-2947

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 nq=18 computational qubits allowing to factor numbers up to N=205 193. We confirm that the algorithm remains operational up to a critical coupling strength ϵc which drops only polynomially with log2 N. The obtained numerical dependence of ϵc on log2 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.