# Shor&#x27;s factorization algorithm with a single control qubit and imperfections - Quantum Physics

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Abstract: We formulate and numerically simulate the single control qubit Shor algorithmfor the case of static imperfections induced by residual couplings betweenqubits. This allows us to study the accuracy of Shor-s algorithm with respectto these imperfections using numerical simulations of realistic quantumcomputations with up to $n q=18$ computational qubits allowing to factornumbers up to N=205193. We confirm that the algorithm remains operational up toa critical coupling strength $\epsilon c$ which drops only polynomially with$\log 2 N$. The obtained numerical dependence of $\epsilon c$ on $\log 2 N$ isin a good agreement with the analytical estimates that allows to obtain thescaling for functionality of Shor-s algorithm on realistic quantum computerswith a large number of qubits.

Autor: Ignacio Garcia-Mata, Klaus M. Frahm, Dima L. Shepelyansky

Fuente: https://arxiv.org/