  The thermodynamic uncertainty relation posits that higher thermodynamic costs
are essential for a system to function with greater precision. Recent
discussions have expanded thermodynamic uncertainty relations beyond classical
non-equilibrium systems, investigating how quantum characteristics can be
utilized to improve precision. In this Letter, we explore how quantum feedback,
a control technique used to manipulate quantum systems, can enhance the
precision. Specifically, we derive a quantum thermodynamic uncertainty relation
for feedback control under jump measurement, which provides the lower bound to
the scaled variance of the number of jumps. We find that the presence of
feedback control can increase the accuracy of continuous measured systems,
which is verified with numerical simulations. Moreover, we derive a quantum
thermodynamic uncertainty relation for feedback control under homodyne
detection.
