Effects of imperfections for Shor's factorization algorithm

Abstract

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 ${\epsilon }_c$ which drops only polynomially with ${\log }_{2}N$. The numerical dependence of ${\epsilon }_c$ on ${\log }_{2}N$ is explained by analytical estimates that allows to obtain the scaling for functionality of Shor's algorithm on realistic quantum computers with a large number of qubits.

10 pages, 10 figures, 1 table. Added references and new data. Erratum added as appendix. 1 Figure and 1 Table added. Research is available at http://www.quantware.ups-tlse.fr/

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• Fast Quantum Modular Exponentiation
• Quantum chaos and random matrix theoryfor fidelity decay in quantum computationswith static imperfections
• Scalability of Shor's algorithm with a limited set of rotation gates
• Quantum Computing of Quantum Chaos in the Kicked Rotator Model
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Cited by in corpus (1)

• Shor's factorization algorithm with a single control qubit and imperfections