  The quantum dynamical activity constitutes a thermodynamic cost in trade-off
relations such as the quantum speed limit and the quantum thermodynamic
uncertainty relation. However, calculating the quantum dynamical activity has
been a challenge and its exact solution has not been hitherto derived. In this
Letter, we present the exact solution to the quantum dynamical activity,
deploying the continuous matrix product state method. Moreover, using the
derived exact solution, we find the upper bound to the dynamical activity,
which comprises the standard deviation of the system Hamiltonian and the jump
operators. We confirm the exact solution and the upper bound by performing
numerical simulations.

Quantum Physics;Statistical Mechanics