Fig. 3
From: Two-axis quantum control of a fast valley qubit in silicon
Quantum control of the valley qubit. a, b Measured and simulated oscillations with a dynamical projection axis determined by tθ, demonstrating a complete map of the Bloch sphere surface. Independent oscillations as functions of pulse widths are visible with frequencies of 4.6 GHz and 2.5 GHz. A linear background is subtracted from the data. c Pulse form used for two-axis state rotations. Pulse heights are fixed at \({\it{\epsilon }}_x\) and \({\it{\epsilon }}_z\) and the pulse widths tθ and tϕ are varied. d Theoretical prediction of the measured probability |−z〉|U(θ, ϕ)|z〉|2 with U(θ, ϕ) given by the product of Eqs (1–3). See Supplementary Note 2 and Supplementary Fig. 2 for more details. e A schematic of the three pulse stages. In stage 1 (blue), the state is rotated about x by angle θ. In stage 2 (red), the state is rotated about z by angle ϕ, and in stage 3 (cyan) the state is rotated about a tilted axis by angle θ', where θ' = θ by design
