  The surface code is a prominent topological error-correcting code exhibiting
high fault-tolerance accuracy thresholds. Conventional schemes for error
correction with the surface code place qubits on a planar grid and assume
native CNOT gates between the data qubits with nearest-neighbor ancilla qubits.
  Here, we present surface code error-correction schemes using $\textit{only}$
Pauli measurements on single qubits and on pairs of nearest-neighbor qubits. In
particular, we provide several qubit layouts that offer favorable trade-offs
between qubit overhead, circuit depth and connectivity degree. We also develop
minimized measurement sequences for syndrome extraction, enabling reduced
logical error rates and improved fault-tolerance thresholds.
  Our work applies to topologically protected qubits realized with Majorana
zero modes and to similar systems in which multi-qubit Pauli measurements
rather than CNOT gates are the native operations.
