Methods, systems and apparatus for determining operating parameters for a quantum processor including multiple interacting qubits. In one aspect, a method includes generating a graph of nodes and edges, wherein each node represents a respective qubit and is associated with an operating parameter of the respective qubit, and wherein each edge represents a respective interaction between two qubits and is associated with an operating parameter of the respective interaction; selecting an algorithm that traverses the graph based on a traversal rule; identifying one or multiple disjoint subsets of nodes or one or multiple disjoint subsets of edges, wherein nodes in a subset of nodes and edges in a subset of edges are related via the traversal rule; and determining calibrated values for the nodes or edges in each subset using a stepwise constrained optimization process where constraints are determined using previously calibrated operating parameters.