Extended Data Fig. 4: Coherence times.

All measurements are performed with all qubits initialized to spin-down and the exchange couplings turned off. All errors are 1σ from the mean. a, Schematic sequence of the T₁ measurement. The qubit state is measured after the preparation of a spin-up excited state and an idle time of t_w. b–d, T₁ measurement results. Each dataset is fit by an exponential decay to extract the T₁ relaxation time. e, Schematic sequence of the Ramsey interferometry. Instead of detuning the microwave frequency, we vary the phase of the second microwave pulse as θ = 2πt_evol × (2 MHz) such that we observe an oscillation at about 2 MHz. f–h, Ramsey interferometry measurement results. To extract the \({T}_{2}^{* }\) inhomogeneous dephasing time, each dataset is fitted with a Gaussian decay function \(P\left({t}_{{\rm{evol}}}\right)=A{\rm{\exp }}\left(-{\left(\frac{{t}_{{\rm{evol}}}}{{T}_{2}^{* }}\right)}^{2}\right){\rm{\cos }}(2\pi \left({\rm{\delta }}f\right){t}_{{\rm{evol}}}+\varphi )+B\), in which A and B are the constants to account for the readout fidelities, δf is the oscillation frequency and ϕ is the phase offset. The integration time is about 70 s for all traces. The larger scattering of the data points for Q₂ (g) is due to the longer pulse cycle and less averaging. i, Schematic sequence of the Hahn echo measurement. j–l, Hahn echo results. For each dataset, the echo time \({T}_{2}^{{\rm{H}}}\) is extracted by fitting with an exponential decay function \(P\left({t}_{{\rm{evol}}}\right)=V{\rm{\exp }}\left(-{\left(\frac{{t}_{{\rm{evol}}}}{{T}_{2}^{{\rm{H}}}}\right)}^{\gamma }\right)\), in which V is the visibility and γ is the exponent. The exponents are γ = 0.98 ± 0.09 (Q₁), 1.46 ± 0.05 (Q₂) and 1.83 ± 0.07 (Q₃).