Practical implementation of a single-qubit rotation algorithm

Abstract: The Toffoli is an important universal quantum gate, and will alongside the Clifford gates be available in future Fault-Tolerant Quantum Computing hardware. Many quantum algorithms rely on performing arbitrarily small single-qubit rotations for their function, and these rotations may also be used to construct any unitary from a limited (but universal) gate set; it is then of significant interest how to carry out such rotations. In this work, we evaluate the performance of a recently proposed single-qubit rotation algorithm using the Clifford+Toffoli gate set by implementation on both a real and simulated quantum computer. We test the algorithm under various simulated noise levels utilizing a per-qubit depolarizing error noise model, finding that the errors are seemingly explained by a binomial distribution wherein these errors change controlling ancilla measurements from $0$ into $1$. Similar observations appear to hold when conducting live runs; noise levels here make further meaningful conclusions difficult, although for the smallest possible number of ancillary controls we do note that error mitigation is helpful. Our results suggest that the algorithm will perform well under up to $1\%$ noise, under the noise model we chose. Our results also suggest the algorithm could be used as a benchmark for Quantum Processing Units, given its linear increase in total number of qubits and Toffoli gates required.