Canonical forms for single-qutrit Clifford+T operators
| Autor: | Glaudell, Andrew N., Ross, Neil J., Taylor, Jacob M. |
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| Rok vydání: | 2018 |
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| Zdroj: | Annals of Physics, Vol. 406, pp. 54-70, 2019 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.aop.2019.04.001 |
| Popis: | 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. Comment: Journal version with minor typographical errors fixed |
| Databáze: | arXiv |
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