  One of the main challenges for quantum computation is that while the number
of gates required to perform a non-trivial quantum computation may be very
large, decoherence and errors in realistic quantum architectures limit the
number of physical gate operations that can be performed coherently. Therefore,
an optimal mapping of the quantum algorithm into the physically available set
of operations is of crucial importance. We examine this problem for a
measurement-only topological quantum computer based on Majorana zero modes,
where gates are performed through sequences of measurements. Such a scheme has
been proposed as a practical, scalable approach to process quantum information
in an array of topological qubits built using Majorana zero modes. Building on
previous work that has shown that multi-qubit Clifford gates can be enacted in
a topologically protected fashion in such qubit networks, we discuss methods to
obtain the optimal measurement sequence for a given Clifford gate under the
constraints imposed by the physical architecture, such as layout and the
relative difficulty of implementing different types of measurements. Our
methods also provide tools for comparative analysis of different architectures
and strategies, given experimental characterizations of particular aspects of
the systems under consideration. As a further non-trivial demonstration, we
discuss an implementation of the surface code in Majorana-based topological
qubits. We use the techniques developed here to obtain an optimized measurement
sequence that implements the stabilizer measurements using only fermionic
parity measurements on nearest-neighbor topological qubit islands.
