2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119692We find expectation values of functions of time integrated two-level telegraph noise. Expectation values of this noise are evaluated under simple control pulses. Both the Gaussian limit and $1/f$ noise are considered. We apply the results to a specific superconducting quantum computing example, which illustrates the use of this technique for calculating error probabilities.10 pages, revtek4Quantum Physicstext