I am looking for the T-depth (or Toffoli-depth) of the smallest T-depth known quantum multiplier of 2 registers (specifically, I am into $x*x=x^2$), I will be happy for a reference and/or formula. I guess it will be one that is implemented with Toffoli and not with QFT.
So far what I found:
- Optimizing Quantum Circuits for Arithmetic and Quantum schoolbook multiplication with fewer Toffoli gates- shows only Toffoli count and not depth
- A Logarithmic-Depth Quantum Carry-Lookahead Adder - only adder
- A Comprehensive Study of Quantum Arithmetic Circuits - too wide analysis
