2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/97284Strong, fast pulses, called ``bang-bang'' controls can be used to eliminate the effects of system-environment interactions. This method for preventing errors in quantum information processors is treated here in a geometric setting which leads to an intuitive perspective. Using this geometric description, we clarify the notion of group symmetrization as an averaging technique, and provide a geometric picture for evaluating errors due to imperfect bang-bang controls. This will provide additional support for the usefulness of such controls as a means for providing more reliable quantum information processing.7 pages, 5 figures, Changes in new version: added references and a comment on the subgroup conditionQuantum Physicstext