  Color-code quantum computation seamlessly combines Majorana-based hardware
with topological error correction. Specifically, as Clifford gates are
transversal in two-dimensional color codes, they enable the use of the
Majoranas' nonabelian statistics for gate operations at the code level. Here,
we discuss the implementation of color codes in arrays of Majorana nanowires
that avoid branched networks such as T-junctions, thereby simplifying their
realization. We show that, in such implementations, nonabelian statistics can
be exploited without ever performing physical braiding operations. Physical
braiding operations are replaced by Majorana tracking, an entirely
software-based protocol which appropriately updates the Majoranas involved in
the color-code stabilizer measurements. This approach minimizes the required
hardware operations for single-qubit Clifford gates. For Clifford completeness,
we combine color codes with surface codes, and use color-to-surface-code
lattice surgery for long-range multi-target CNOT gates which have a time
overhead that grows only logarithmically with the physical distance separating
control and target qubits. With the addition of magic state distillation, our
architecture describes a fault-tolerant universal quantum computer in systems
such as networks of tetrons, hexons, or Majorana box qubits, but can also be
applied to non-topological qubit platforms.
