Canonical forms for single-qutrit Clifford+T operators

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.

Journal version with minor typographical errors fixed

References in corpus (3)

• Performance and structure of single-mode bosonic codes
• Qudit versions of the qubit "pi-over-eight" gate
• Hardware-Efficient Bosonic Quantum Error-Correcting Codes Based on Symmetry Operators

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• Constructing all qutrit controlled Clifford+T gates in Clifford+T
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• Transversal AND in Quantum Codes