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We investigate the influence of random errors in external control parameterson the stability of holonomic quantum computation in the case of arbitraryloops and adiabatic connections. A simple expression is obtained for the caseof small random uncorrelated errors. Due to universality of mathematicaldescription our results are valid for any physical system which can bedescribed in terms of holonomies. Theoretical results are confirmed bynumerical simulations.Comment: 7 pages, 3 figure

Fidelity of holonomic quantum computations in the case of random errors in the values of control parameters