Multi-qutrit exact synthesis

• URL: http://arxiv.org/abs/2405.08147v1
• Date: Mon, 13 May 2024 19:48:10 GMT
• Title: Multi-qutrit exact synthesis
• Authors: Amolak Ratan Kalra, Manimugdha Saikia, Dinesh Valluri, Sam Winnick, Jon Yard,
• Abstract summary: We present an exact synthesis algorithm for qutrit unitaries in $mathcalU_3n(mathbbZ[/3,e2pi i/3])$ over the Clifford$+T$ gate set with at most one ancilla. This, in particular, gives an exact synthesis algorithm of single-qutrit Clifford$+mathcalD$ over the multi-qutrit Clifford$+T$ gate set with at most two ancillas.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present an exact synthesis algorithm for qutrit unitaries in $\mathcal{U}_{3^n}(\mathbb{Z}[1/3,e^{2\pi i/3}])$ over the Clifford$+T$ gate set with at most one ancilla. This extends the already known result of qutrit metaplectic gates being a subset of Clifford$+T$ gate set with one ancilla. As an intermediary step, we construct an algorithm to convert 3-level unitaries into multiply-controlled gates, analogous to Gray codes converting 2-level unitaries into multiply-controlled gates. Finally, using catalytic embeddings, we present an algorithm to exactly synthesize unitaries $\mathcal{U}_{3^n}(\mathbb{Z}[1/3,e^{2\pi i/9}])$ over the Clifford$+T$ gate set with at most 2 ancillas. This, in particular, gives an exact synthesis algorithm of single-qutrit Clifford$+\mathcal{D}$ over the multi-qutrit Clifford$+T$ gate set with at most two ancillas.

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