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arXiv · 2603.13169

Circuit Optimization for Universality Transformation

Yasuaki Nakayama·Yuki Takeuchi·Seiseki Akibue
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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 $|0 \rangle |+i \rangle$.

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Yasuaki Nakayama, Yuki Takeuchi, Seiseki Akibue. 2026-03-13. Circuit Optimization for Universality Transformation. https://arxiv.org/abs/2603.13169

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