  We introduce canonical forms for single qutrit Clifford+T circuits and prove
that every single-qutrit Clifford+T operator admits a unique such canonical
form. We show that our canonical forms are T-optimal in the sense that among
all the single-qutrit Clifford+T circuits implementing a given operator our
canonical form uses the least number of T gates. Finally, we provide an
algorithm which inputs the description of an operator (as a matrix or a
circuit) and constructs the canonical form for this operator. The algorithm
runs in time linear in the number of T gates. Our results provide a
higher-dimensional generalization of prior work by Matsumoto and Amano who
introduced similar canonical forms for single-qubit Clifford+T circuits.
