  Measurements and feedback are essential in the control of any device
operating at the quantum scale and exploiting the features of quantum physics.
As the number of quantum components grows, it becomes imperative to consider
the energetic expense of such elementary operations. Here, we derive energy
requirements for general quantum measurement, extending previous models and
obtaining stronger bounds in relevant situations, and then study two important
classes of measurements in detail. One is the projective measurement, where we
obtain the exact cost rather than a lower bound, and the other is the so-called
inefficient measurement, in which we explicitly show that energy extraction is
possible. As applications, we derive the energy-precision trade-off in quantum
Zeno stabilisation schemes and the exact energy expense for quantum error
correction. Our results constitute fundamental energetic limitations against
which to benchmark implementations of future quantum devices as they grow in
complexity.
