Circuit Optimization for Universality Transformation

It is known that a computationally universal gate set $\{H,CCZ\}$ can be transformed to a strictly universal one $\{Λ(S), H\}$ 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 $|+i\rangle$.

Source: arXiv:2603.13169v1 - http://arxiv.org/abs/2603.13169v1 PDF: https://arxiv.org/pdf/2603.13169v1 Original Link: http://arxiv.org/abs/2603.13169v1