Figure 1: Diagrams of device and measurement sequence.

(a) A false-colour device image highlighting the circuit elements such as the qubits (dark squares) and the half-wavelength coplanar waveguide resonator (the sinusoidal line in the middle). Four superconducting qubits Q_k (k=1, 2, 3 and 4) are individually coupled to the resonator (R). The microwave drive to the resonator is applied through the transmission line between Q₁ and Q₂ as indicated. (b) Simplified circuit schematic. (c) Illustration of the pulse sequence, where the x axis indexes the qubits and the resonator, the y axis represents the sequence time and the z axis represents the frequency (Supplementary Note 5 for designing the sequence). The four qubits, originally sitting at their idling frequencies, are simultaneously tuned to the same frequency ω_q(t₀) such that λ/λ_c=0.5 (at this point all qubits and the resonator are individually in their own ground state), following which ω_q(t) is swept for a time t up to τ, such that λ/λ_c increases uniformly from 0.5 to 2.5 over the full period of τ (see the asymptotic curves and their shades). During the ramping, a microwave drive (the blue sinusoidal line) to the resonator R with a fixed frequency ω_d and a fixed drive strength Ω is always on (Methods for determining Ω). We record the four-qubit occupation probabilities as functions of the sweep time t, by simultaneously tuning all four qubits to their measurement points at lower frequencies for joint qubit-state readout after sweeping ω_q(t) (see the sharp trapezoids and their shades): in each sequence we record each qubit’s state by ‘0’ or ‘1’ in a single-shot manner, and repeating the same sequences many times ∼10³–10⁴), we count the 16 probabilities P₀₀₀₀, P₀₀₀₁, P₀₀₁₀, ⋯ and P₁₁₁₁, where ‘0’ and ‘1’ denote, respectively, the ground and excited states of each qubit. These probabilities are used to calculate the collective spin operator 〈J_z〉 (Methods).