Multi-qutrit exact synthesis
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916244361314304 |
|---|---|
| author | Kalra, Amolak Ratan Saikia, Manimugdha Valluri, Dinesh Winnick, Sam Yard, Jon |
| author_facet | Kalra, Amolak Ratan Saikia, Manimugdha Valluri, Dinesh Winnick, Sam Yard, Jon |
| contents | We present an exact synthesis algorithm for qutrit unitaries in $\mathcal{U}_{3^n}(\mathbb{Z}[1/3,e^{2πi/3}])$ 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 $\mathcal{U}_{3^n}(\mathbb{Z}[1/3,e^{2πi/9}])$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08147 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multi-qutrit exact synthesis Kalra, Amolak Ratan Saikia, Manimugdha Valluri, Dinesh Winnick, Sam Yard, Jon Quantum Physics We present an exact synthesis algorithm for qutrit unitaries in $\mathcal{U}_{3^n}(\mathbb{Z}[1/3,e^{2πi/3}])$ 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 $\mathcal{U}_{3^n}(\mathbb{Z}[1/3,e^{2πi/9}])$ 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. |
| title | Multi-qutrit exact synthesis |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2405.08147 |