Extended Data Figure 3: Experimental pulse sequence.

This laser pulse sequence implements the evolution described in Fig. 2f, g. The pulses are listed in the order in which they are applied, as indicated by the arrows. The pulses in the first box prepare the initial state, those in the second box implement one step of the time evolution, and those in the third box recouple the ions to the computational subspace, that is, bring back their populations to the qubit transition 4S_1/2(m = −1/2) to 3D_5/2(m = −1/2). The operations shown in the middle box are repeated once per evolution step, resulting in a total number of 12 + 51 × 4 + 6 = 222 pulses for 4 evolution steps. The pulses are labelled in the form Pulse(θ, ϕ, target qubit), where θ is the rotation angle (length) of the pulse, ϕ its phase, and the target qubit is an integer from 1 to 4 for addressed operations or ‘all’ for global operations. ‘R’ denotes a pulse on the qubit transition 4S_1/2(m = −1/2) to 3D_5/2(m = −1/2). ‘MS’ corresponds to an MS gate on the same transition. The hiding pulses ‘HidingA,B,C’ are applied on the transitions as follows: A, 4S_1/2(m = −1/2) to 3D_5/2(m = −5/2); B, 4S_1/2(m = +1/2) to 3D_5/2(m = −1/2); C, 4S_1/2(m = +1/2) to 3D_5/2(m = −3/2). These transitions are shown in the level scheme at the bottom right. The pulses shown in italics serve the purpose of correcting addressing crosstalk.