  According to the laws of thermodynamics, no heat engine can beat the
efficiency of a Carnot cycle. This efficiency traditionally comes with
vanishing power output and practical designs, optimized for power, generally
achieve far less. Recently, various strategies to obtain Carnot's efficiency at
large power were proposed. However, a thermodynamic uncertainty relation
implies that steady-state heat engines can operate in this regime only at the
cost of large fluctuations that render them immensely unreliable. Here, we
demonstrate that this unfortunate trade-off can be overcome by designs
operating cyclically under quasi-static conditions. The experimentally relevant
yet exactly solvable model of an overdamped Brownian heat engine is used to
illustrate the formal result. Our study highlights that work in cyclic heat
engines and that in quasi-static ones are different stochastic processes.
