A Logarithmic-Depth Quantum Multiplier
The authors developed a quantum algorithm to multiply two n-bit integers with circuit depths and T-depths bounded by O(log2 n). This construction uses O(n^2) gates and ancillary qubits. It achieves this by generating partial products via indicator-controlled copying, summing them using a tree of reversible 3-to-2 adders, and employing a quantum carry-lookahead adder.