Synthesizing Toffoli-optimal quantum circuits for arbitrary multi-qubit unitaries
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916094583767040 |
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| author | Mukhopadhyay, Priyanka |
| author_facet | Mukhopadhyay, Priyanka |
| contents | In this paper we study the Clifford+Toffoli universal fault-tolerant gate set. We introduce a generating set in order to represent any unitary implementable by this gate set and with this we derive a bound on the Toffoli-count of arbitrary multi-qubit unitaries. We analyse the channel representation of the generating set elements, with the help of which we infer $|\mathcal{J}_n^{Tof}|<|\mathcal{J}_n^T|$, where $\mathcal{J}_n^{Tof}$ and $\mathcal{J}_n^T$ are the set of unitaries exactly implementable by the Clifford+Toffoli and Clifford+T gate set, respectively. We develop Toffoli-count optimal synthesis algorithms for both approximately and exactly implementable multi-qubit unitaries. With the help of these we prove $|\mathcal{J}_n^{Tof}|=|\mathcal{J}_n^{CS}|$, where $\mathcal{J}_n^{CS}$ is the set of unitaries exactly implementable by the Clifford+CS gate set. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08950 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Synthesizing Toffoli-optimal quantum circuits for arbitrary multi-qubit unitaries Mukhopadhyay, Priyanka Quantum Physics In this paper we study the Clifford+Toffoli universal fault-tolerant gate set. We introduce a generating set in order to represent any unitary implementable by this gate set and with this we derive a bound on the Toffoli-count of arbitrary multi-qubit unitaries. We analyse the channel representation of the generating set elements, with the help of which we infer $|\mathcal{J}_n^{Tof}|<|\mathcal{J}_n^T|$, where $\mathcal{J}_n^{Tof}$ and $\mathcal{J}_n^T$ are the set of unitaries exactly implementable by the Clifford+Toffoli and Clifford+T gate set, respectively. We develop Toffoli-count optimal synthesis algorithms for both approximately and exactly implementable multi-qubit unitaries. With the help of these we prove $|\mathcal{J}_n^{Tof}|=|\mathcal{J}_n^{CS}|$, where $\mathcal{J}_n^{CS}$ is the set of unitaries exactly implementable by the Clifford+CS gate set. |
| title | Synthesizing Toffoli-optimal quantum circuits for arbitrary multi-qubit unitaries |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2401.08950 |