  Quantum error correction is capable of digitizing quantum noise and
increasing the robustness of qubits. Typically, error correction is designed
with the target of eliminating all errors - making an error so unlikely it can
be assumed that none occur. In this work, we use statistical quantum fault
injection on the quantum phase estimation algorithm to test the sensitivity to
quantum noise events. Our work suggests that quantum programs can tolerate
non-trivial errors and still produce usable output. We show that it may be
possible to reduce error correction overhead by relaxing tolerable error rate
requirements. In addition, we propose using variable strength (distance) error
correction, where overhead can be reduced by only protecting more sensitive
parts of the quantum program with high distance codes.
