Fig. 5: Trade-off between T-count and synthesis accuracy for Pauli rotation gates.
The red, yellow, and blue regions indicate the achievable accuracy without any sampling overhead when we employ unitary, mixed, and error-crafted synthesis. The blue circles indicate the error solely from crafted synthesis for Rz(θ) with \(\theta \in {\{\frac{m\pi }{32}\}}_{m\ne 0{\rm{mod4}}}\) under various synthesis accuracy. Note that the total error, combined with hardware noise, is bounded by the chained black line, which indicates the contribution from noise in T gates. Here we choose error rate of 10−11 per T gate. The dotted red, yellow, and green lines are given by the empirical T-count of \(3{\log }_{2}(1/\varepsilon )\), \(1.5{\log }_{2}(1/\varepsilon )\), and \({\log }_{2}(1/\varepsilon )\), respectively, and the real lines indicate the total error.
