Speaker
Description
There are two classes of universal quantum computation: strict and computational universalities. The former is sufficient to generate any unitary matrix, while the latter can generate any probability distribution but not all unitary matrices. An example of a strictly universal gate set is $\{H, \Lambda(S)\}$, and an example of a computationally universal one is $\{H, CCZ\}$. Since $\{H, CCZ\}$ consists of only real components, it cannot generate unitary matrices containing imaginary numbers. Recently, Takeuchi [PRL 133, 050601 (2024)] showed that $\{H, CCZ\}$ can be transformed into $\{H, \Lambda(S)\}$ by using $|+i\rangle$, an eigenstate of the Pauli-$Y$ matrix. This implies that maximally imaginary states—the most resourceful states in the resource theory of imaginarity—are sufficient for this universality transformation. In this presentation, we show that maximally imaginary states are also necessary for the universality transformation. Furthermore, we demonstrate that unitary operators implemented with non-maximally imaginary states are strictly restricted to real orthogonal matrices. While resource states exist continuously from maximal to zero, the resource for the universality transformation exhibits a strict dichotomy: universal resource, which can be used for generating all unitaries, or zero resource, which cannot be used for implementing any imaginary components except for global phases. Finally, we investigate the circuit optimization of this transformation and present a circuit that generates $\Lambda(S)$ without using non-imaginary ancillary qubits, using fewer $CCZ$ gates than the previous work. This presentation is based on arXiv:2603.11812 and arXiv:2603.13169.