Optimal two-qubit quantum circuits using exchange interactions
Heng Fan, Vwani Roychowdhury, Thomas Szkopek · Physical Review A · 2005
We give the optimal decomposition of a universal two-qubit circuit using Heisenberg exchange interactions and single qubit rotations. Tuning the strength and duration of the Heisenberg exchange allows one to implement ${(\mathrm{SWAP})}^{\ensuremath{\alpha}}$ gates. Our optimal circuit is constructed from only three ${(\mathrm{SWAP})}^{\ensuremath{\alpha}}$ gates and six single qubit gates. We show that three ${(\mathrm{SWAP})}^{\ensuremath{\alpha}}$ gates are not only sufficient, but necessary. Since six single-qubit gates are already known to be necessary, our implementation is optimal in gate count.