Yasuaki Nakayama

There exist two types of universality in quantum computation: strict and computational universalities. The former is known to be stronger than the latter. In this presentation, we give a method of transforming from the computational universality with an elementary gate set {H,CCZ} to the strict universality by using a maximally imaginary state |+i>, which is an eigenstate of the Pauli-Y operator. From the viewpoint of resource theory, it would be intriguing whether the maximum imaginarity is necessary for the universality transformation. We show that |+i> is a unique resource state up to free operations. More precisely, we obtain the stronger conclusion that if a given resource state cannot be used for the universality transformation, then the realizable quantum gates are restricted to only orthogonal operators. This implies that by rotating a single-qubit state from the eigenstate |+> of the Pauli-X operator to |+i>, we can observe a kind of phase transition. The first half of our results has been published in PRL 133, 050601 (2024).