Dissipative controller as a hidden source of errors in quantum gates

Quantum systems are typically controlled by classical devices that necessarily dissipate energy to the surrounding environment. By the fluctuation-dissipation theorem, this implies noise in the control field produced. We investigate the relationship between the resulting errors and the entropy produced by the macroscopic controller, working in the context of a concrete minimal model. In the most experimentally relevant regime of fast control and high fidelity, we find a tradeoff between dissipation and control errors. These findings are exemplified by perturbative calculations of the gate fidelity for simple gate implementations and of the fidelity of state transfer via shortcuts to adiabaticity in the Landau-Zener model. Our results quantitatively demonstrate that suppressing errors in quantum control typically comes at the cost of macroscopic dissipation, which is needed to tame fluctuations in the classical controller.