Noise effect on Grover algorithm
Depto. Tecnologías Especiales Aplicadas a la Telecomunicación, ETSI Telecomunicación, UPM, Ciudad Universitaria s/n, 28040 Madrid, Spain
Corresponding author: a firstname.lastname@example.org
Revised: 21 September 2007
Published online: 19 October 2007
The decoherence effect on Grover algorithm has been studied numerically through a noise modelled by a depolarizing channel. Two types of error are introduced characterizing the qubit time evolution and gate application, so the noise is directly related to the quantum network construction. The numerical simulation concludes an exponential damping law for the successive probability of the maxima as time increases. We have obtained an allowed-error law for the algorithm: the error threshold for the allowed noise behaves as εth(N) ∼1/N1.1 (N being the size of the data set). As the power of N is almost one, we consider the Grover algorithm as robust to a certain extent against decoherence. This law also provides an absolute threshold: if the free evolution error is greater than 0.043, Grover algorithm does not work for any number of qubits affected by the present error model. The improvement in the probability of success, in the case of two qubits has been illustrated by using a fault-tolerant encoding of the initial state by means of the [[7,1,3]] quantum code.
PACS: 03.67.Lx – Quantum computation / 03.67.Pp – Quantum error correction and other methods for protection against decoherence
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007