The authors construct relative-phase n-qubit Toffoli gates without ancillas and O(log n)-depth multi-controlled SU(2)/U(2) decompositions, improving on earlier methods.
Polylogarithmic-depth controlled-not gates without ancilla qubits,
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Logarithmic Depth Decomposition of Approximate Multi-Controlled Single-Qubit Gates Without Ancilla Qubits
The authors construct relative-phase n-qubit Toffoli gates without ancillas and O(log n)-depth multi-controlled SU(2)/U(2) decompositions, improving on earlier methods.