  We introduce a technique for recovering noise-free observables in noisy
quantum systems by combining the results of many slightly different
experiments. Our approach is applicable to a variety of quantum systems but we
illustrate it with applications to quantum computing and quantum sensing. The
approach corresponds to repeating the same quantum evolution many times with
known variations on the underlying systems' error properties, e.g. the
spontaneous emission and dephasing times, $T_1$ and $T_2$. As opposed to
standard quantum error correction methods, which have an overhead in the number
of qubits (many physical qubits must be added for each logical qubit) our
method has only an overhead in number of evaluations, allowing the overhead to,
in principle, be hidden via parallelization. We show that the effective
spontaneous emission, $T_1$, and dephasing, $T_2$, times can be increased using
this method in both simulation and experiments on an actual quantum computer.
We also show how to correct more complicated entangled states and how Ramsey
fringes relevant to quantum sensing can be significantly extended in time.
