Uniqueness of imaginarity-assisted transformation from computationally universal to strictly universal quantum computation
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910050478456832 |
|---|---|
| author | Nakayama, Yasuaki Takeuchi, Yuki Akibue, Seiseki |
| author_facet | Nakayama, Yasuaki Takeuchi, Yuki Akibue, Seiseki |
| contents | The computational universality with an elementary gate set $\{H,CCZ\}$ can be transformed to the strict universality by using a maximally imaginary state $|+i\rangle$ and some non-imaginary ancillary qubits. From the viewpoint of operational resource theory, it would be intriguing to elucidate a resource for the universality transformation. In this paper, we explore a necessary and sufficient condition for resource states to realize the universality transformation under free real operations. We show that $|+i\rangle$ is a unique resource state up to the free operations. Moreover, we obtain a stronger conclusion. If a given resource state cannot be used for the universality transformation, then realizable quantum gates are restricted to real orthogonal matrices. Therefore, we can tell that $|+i\rangle$ is unique (up to the free operations) not only as a state whose resource measure of imaginarity is maximal, but also as a state which empowers real operations with the ability to apply at least one non-real quantum gate (regardless of the magnitudes of its imaginary parts). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11812 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uniqueness of imaginarity-assisted transformation from computationally universal to strictly universal quantum computation Nakayama, Yasuaki Takeuchi, Yuki Akibue, Seiseki Quantum Physics The computational universality with an elementary gate set $\{H,CCZ\}$ can be transformed to the strict universality by using a maximally imaginary state $|+i\rangle$ and some non-imaginary ancillary qubits. From the viewpoint of operational resource theory, it would be intriguing to elucidate a resource for the universality transformation. In this paper, we explore a necessary and sufficient condition for resource states to realize the universality transformation under free real operations. We show that $|+i\rangle$ is a unique resource state up to the free operations. Moreover, we obtain a stronger conclusion. If a given resource state cannot be used for the universality transformation, then realizable quantum gates are restricted to real orthogonal matrices. Therefore, we can tell that $|+i\rangle$ is unique (up to the free operations) not only as a state whose resource measure of imaginarity is maximal, but also as a state which empowers real operations with the ability to apply at least one non-real quantum gate (regardless of the magnitudes of its imaginary parts). |
| title | Uniqueness of imaginarity-assisted transformation from computationally universal to strictly universal quantum computation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.11812 |