Methods, systems, and apparatus for determining frequencies at which to operate interacting qubits arranged as a two dimensional grid in a quantum device. In one aspect, a method includes the actions of defining a first cost function that characterizes technical operating characteristics of the system. The cost function maps qubit operation frequency values to a cost corresponding to an operating state of the quantum device; applying one or more constraints to the defined first cost function to define an adjusted cost function; and adjusting qubit operation frequency values to vary the cost according to the adjusted cost function such that the operating state of the quantum device is improved.