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/

References in corpus (24)

• Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance
• Quantum Networks for Elementary Arithmetic Operations
• Efficient Networks for Quantum Factoring
• Fast Quantum Modular Exponentiation
• Quantum Chaos Border for Quantum Computing
• Efficient factorization with a single pure qubit and $logN$ mixed qubits
• Emergence of Quantum Chaos in Quantum Computer Core and How to Manage It
• Efficient Quantum Computing of Complex Dynamics
• Shor's Factoring Algorithm and Modern Cryptography. An Illustration of the Capabilities Inherent in Quantum Computers
• Breit-Wigner width and participation ratio in finite interacting Fermi systems
• Factoring in a Dissipative Quantum Computer
• 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 computation with phase drift errors
• Quantum computing of quantum chaos and imperfection effects
• Quantum Computing of Quantum Chaos in the Kicked Rotator Model
• Simulating noisy quantum protocols with quantum trajectories
• Quantum computation of the Anderson transition in presence of imperfections
• Eigenstates of Operating Quantum Computer: Hypersensitivity to Static Imperfections
• Dissipative decoherence in the Grover algorithm
• Quantum chaos in the spectrum of operators used in Shor's algorithm
• Quantum chaos algorithms and dissipative decoherence with quantum trajectories
• Effects of dynamical phases in Shor's factoring algorithm with operational delays
• Phase diagram for the Grover algorithm with static imperfections

Cited by in corpus (4)

• Scaling laws for Shor's algorithm with a banded quantum Fourier transform
• Shor's factorization algorithm with a single control qubit and imperfections
• The modular multiplication operator and the quantized bakers maps
• Quantum Algorithms in Cybernetics