In quantum computers, each logical qubit must be encoded in several physical
qubits to protect against noise in physical qubits. The tetrahedral color code is such
an encoding. In the primal lattice, the three-dimensional tetrahedral color code is
a bitruncated octahedral lattice, and in the dual lattice, the tetrahedral color code
is a four-colorable body-centered cubic lattice. This color code can be utilized for
measurement-based quantum computing, for which all entanglement is present in a
cluster state at the beginning of the computation and gate operations are performed
by local measurements and classical operations. Moreover, this color code admits a
gate set that is both transversal, i.e., realized by qubit-wise operations, and universal when supplemented by measurement and classical computing. During cluster state
preparation and computation, errors may occur on the physical qubits. Therefore,
it is necessary to have a decoder that, using the syndrome of these errors, finds a
set of qubits to correct and performs the operations needed to correct those qubits.
The decoder is considered successful if and only if the correction does not cause a
logical error on the logical qubit. In this thesis, I present a decoder for Pauli Z, or
phase-flip, errors on the three-dimensional tetrahedral color code with nonperiodic
boundaries. This decoder for Z-errors includes as a subroutine a decoder for Pauli X
errors. The decoder uses a restriction procedure to map the tetrahedral color code
to a toric code. The toric code is another quantum error correcting code. Then,
an existing toric code decoder interprets the error syndrome. This research on the
bounded color code builds upon previous work on the unbounded color code and
the two-dimensional color code. Under independently identically distributed noise,
evidence indicates an error probability threshold for Z-errors between 0.01% and
0.02% and for X-errors between 2.5% and 3.3%. I also present example errors and
illustrate how the decoder attempts to correct those errors.Physic
