Synthesis of single-qutrit circuits from Clifford+R gates

We present two deterministic compilation algorithms for single-qutrit unitaries with O(log1/ε) gate depth. Each algorithm selects a nearby approximation to the target unitary and then exactly synthesizes the approxima tion over the Clifford + R basis. The first algorithm exhaustively searches over the group; while the second algorithm searches only for Householder reflections. The exhaustive search algorithm yields an average R count of 2.193(11) + 8.621(7)log10(1/ε), albeit with a time complexity of O(ε^−4.4). The Householder search algorithm results in a larger average R count of 3.20(13) + 10.77(3)log10(1/ε) at a reduced time complexity of O(ε^−0.42), greatly extending the reach in ε. These costs correspond asymptotically to 35% and 69% more non-Clifford gates compared with synthesizing the same unitary with two qubits. Such initial results are encouraging for using the R gate as the nontransversal gate for qutrit-based computation.

Duke Scholars

Author Shuchen Zhu Mathematics