Canonical forms for single-qutrit Clifford+T operators

Andrew N. Glaudell; Neil J. Ross; Jacob M. Taylor

doi:10.1016/j.aop.2019.04.001

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arXiv · 1803.05047

Canonical forms for single-qutrit Clifford+T operators

Andrew N. Glaudell·Neil J. Ross·Jacob M. Taylor

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Abstract

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.

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Andrew N. Glaudell, Neil J. Ross, Jacob M. Taylor. 2019-08-19. Canonical forms for single-qutrit Clifford+T operators. https://doi.org/10.1016/j.aop.2019.04.001

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