Noise effect on Grover algorithm |
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Authors: | P J Salas |
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Institution: | (1) Depto. Tecnologías Especiales Aplicadas a la Telecomunicación, ETSI Telecomunicación, UPM, Ciudad Universitaria s/n, 28040 Madrid, Spain |
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Abstract: | 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. |
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Keywords: | 03 67 Lx Quantum computation 03 67 Pp Quantum error correction and other methods for protection against decoherence |
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