Estimate of Minimal Noise in a Quantum Conductor

We study zero temperature fluctuations of charge flow in a metallic loop induced by time dependent magnetic flux, and solve for the optimal way of varying flux in order to minimize noise. Optimal time dependence of the flux is a sum of ``solitons,'' each corresponding to quantized flux change. Minimal noise coincides with that for the binomial distribution with the number of attempts equal to the number of solitons and with the probabilies defined by the scattering matrix of the system.