  We show that space- and time-correlated single-qubit rotation errors can lead
to high-weight errors in a quantum circuit when the rotation angles are drawn
from heavy-tailed distributions. This leads to a breakdown of quantum error
correction, yielding reduced or in some cases no protection of the encoded
logical qubits. While heavy-tailed phenomena are prevalent in the natural
world, there is very little research as to whether noise with these statistics
exist in current quantum processing devices. Furthermore, it is an open problem
to develop tomographic or noise spectroscopy protocols that could test for the
existence of noise with such statistics. These results suggest the need for
quantum characterization methods that can reliably detect or reject the
presence of such errors together with continued first-principles studies of the
origins of space- and time-correlated noise in quantum processors. If such
noise does exist, physical or control-based mitigation protocols must be
developed to mitigate this noise as it would severely hinder the performance of
fault-tolerant quantum computers.

Quantum Physics