Noise effect on Grover algorithm

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 Eth(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.Comment: Accepted to be published in Eur. Phys. J. D (2008

Noise in Grover's Quantum Search Algorithm

Grover's quantum algorithm improves any classical search algorithm. We show how random Gaussian noise at each step of the algorithm can be modelled easily because of the exact recursion formulas available for computing the quantum amplitude in Grover's algorithm. We study the algorithm's intrinsic robustness when no quantum correction codes are used, and evaluate how much noise the algorithm can bear with, in terms of the size of the phone book and a desired probability of finding the correct result. The algorithm loses efficiency when noise is added, but does not slow down. We also study the maximal noise under which the iterated quantum algorithm is just as slow as the classical algorithm. In all cases, the width of the allowed noise scales with the size of the phone book as N^-2/3.Comment: 17 pages, 2 eps figures. Revised version. To be published in PRA, December 199

Reduced Susceptibility to Two-Stage Skin Carcinogenesis in Mice with Epidermis-Specific Deletion of Cd151

Altered expression of the tetraspanin CD151 is associated with skin tumorigenesis; however, whether CD151 is causally involved in the tumorigenic process is not known. To evaluate its role in tumor formation, we subjected epidermis-specific Cd151 knockout mice to chemical skin carcinogenesis. Mice lacking epidermal Cd151 developed fewer and smaller tumors than wild-type mice after treatment with 7,12-dimethylbenzanthracene (DMBA)/12-O-tetradecanoylphorbol-13-acetate (TPA). Furthermore, Cd151-null epidermis showed a reduced hyperproliferative response to short-term treatment with TPA as compared with wild-type skin, whereas epidermal turnover was increased. Tumors were formed in equal numbers after DMBA-only treatment. We suggest that DMBA-initiated keratinocytes lacking Cd151 leave their niches in the epidermis and hair follicles in response to TPA treatment and subsequently are lost by differentiation. Because genetic ablation of Itga3 also reduced skin tumor formation, we tested whether reduced expression of α3 could further suppress tumor formation in epidermis-specific Cd151 knockout mice. Although DMBA/TPA-induced formation of skin tumors was similar in compound heterozygotes for Cd151 and Itga3 to that in wild-type mice, heterozygosity for Itga3 on a Cd151-null background diminished tumorigenesis, suggesting genetic interaction between the two genes. We thus identify CD151 as a critical factor in TPA-dependent skin carcinogenesis