Methods, systems, and apparatus for implementing a quantum circuit that moves a surface code patch of qubits. In one aspect, a method includes performing a first surface code cycle in a system of measure and data qubits. A first CNOT gate is applied to a measure qubit and a first data qubit, where the first data qubit is coupled to the measure qubit in a first direction and the first CNOT gate targets one of the measure qubits and the first data qubit. A second CNOT gate is applied to the measure qubit and the first data qubit, where the second CNOT gate targets another of the measure qubit and the first data qubit. Performing the first surface code cycle transfers information stored by the measure qubit and information stored by the first data qubit to other qubits to logically move the measure qubit and the first data qubit.