Any n-qubit unitary can be implemented approximately with Õ(2^{n/2}) oracle queries or exactly with Õ(2^{n/2}) circuit depth via Grover search reductions, with matching lower bounds for certain implementations.
Asymp- totically optimal circuit depth for quantum state preparation and general unitary synthesis
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Query and Depth Upper Bounds for Quantum Unitaries via Grover Search
Any n-qubit unitary can be implemented approximately with Õ(2^{n/2}) oracle queries or exactly with Õ(2^{n/2}) circuit depth via Grover search reductions, with matching lower bounds for certain implementations.