Uniqueness of imaginarity-assisted transformation from computationally universal to strictly universal quantum computation

Fuente: arXiv
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Autores principales: Nakayama, Yasuaki, Takeuchi, Yuki, Akibue, Seiseki
Formato: Preprint
Publicado: 2026
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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