|Title||Canonical forms for single-qutrit Clifford plus T operators|
|Publication Type||Journal Article|
|Year of Publication||2019|
|Authors||A. N. Glaudell, N. J. Ross, and J. M. Taylor|
|Type of Article||Article|
|Keywords||Quantum circuits, quantum computation, Qutrits, Universal gate sets|
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. (C) 2019 Elsevier Inc. All rights reserved.