Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2402.12356 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914177779499008 |
|---|---|
| author | Zindorf, Ben Bose, Sougato |
| author_facet | Zindorf, Ben Bose, Sougato |
| contents | Universal gate sets for quantum computation, when single and two qubit operations are accessible, include both Hermitian and non-Hermitian gates. Here we utilize the fact that any single-qubit operator may be implemented as two Hermitian gates, and thus a purely Hermitian universal set is possible. This implementation can be used to prepare high fidelity single-qubit states in the presence of amplitude errors, and helps to achieve a high fidelity single-qubit gate decomposition using four Hermitian gates. An implementational convenience can be that non-identity single-qubit Hermitian gates are equivalent to $π$ rotations up to a global phase. We show that a gate set comprised of $π$ rotations about two fixed axes, along with the CNOT gate, is universal for quantum computation. Moreover, we show that two $π$ rotations can transform the axis of any multi-controlled unitary, a special case being a single CNOT sufficing for any controlled $π$ rotation. These gates simplify the process of circuit compilation in view of their Hermitian nature. We exemplify by designing efficient circuits for a variety of controlled gates, and achieving a CNOT count reduction for the four-controlled Toffoli gate in LNN-restricted qubit connectivity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12356 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | All You Need is pi: Quantum Computing with Hermitian Gates Zindorf, Ben Bose, Sougato Quantum Physics Universal gate sets for quantum computation, when single and two qubit operations are accessible, include both Hermitian and non-Hermitian gates. Here we utilize the fact that any single-qubit operator may be implemented as two Hermitian gates, and thus a purely Hermitian universal set is possible. This implementation can be used to prepare high fidelity single-qubit states in the presence of amplitude errors, and helps to achieve a high fidelity single-qubit gate decomposition using four Hermitian gates. An implementational convenience can be that non-identity single-qubit Hermitian gates are equivalent to $π$ rotations up to a global phase. We show that a gate set comprised of $π$ rotations about two fixed axes, along with the CNOT gate, is universal for quantum computation. Moreover, we show that two $π$ rotations can transform the axis of any multi-controlled unitary, a special case being a single CNOT sufficing for any controlled $π$ rotation. These gates simplify the process of circuit compilation in view of their Hermitian nature. We exemplify by designing efficient circuits for a variety of controlled gates, and achieving a CNOT count reduction for the four-controlled Toffoli gate in LNN-restricted qubit connectivity. |
| title | All You Need is pi: Quantum Computing with Hermitian Gates |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2402.12356 |