Circuit Optimization for Universality Transformation

Abstract:It is known that a computationally universal gate set $\{H,CCZ\}$ can be transformed to a strictly universal one $\{H, \Lambda(S)\}$ using one maximally imaginary state $|+i \rangle$ and non-imaginary ancillary qubits. We succeed this transformation with a shorter circuit that eliminates non-imaginary ancillary qubits. We further extend this to the continuous gate-set setting, showing that any multi-qubit unitary can be exactly generated by real single-qubit unitary gates, $CCZ$ gates and $|0 \rangle |+i \rangle$.

2 pages, 1 figure. Revised in response to referee comments

arXiv:2603.13169 [quant-ph]

(or arXiv:2603.13169v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2603.13169 Focus to learn more arXiv-issued DOI via DataCite

J. Phys. Soc. Jpn. 95, 085001 (2026)

https://doi.org/10.7566/JPSJ.95.085001 Focus to learn more DOI(s) linking to related resources

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