Extended Data Fig. 3: Single-qubit gate Randomised Benchmarking.

We characterise the single-qubit gate fidelity for four nuclear spins N₁ ~ N₄ by performing a Randomised Benchmarking (RB) experiment. First, nuclear spins are initialised to the \(| {\Downarrow \Downarrow \Downarrow \Uparrow \Uparrow \Uparrow \rangle}\) state. For each qubit we apply a sequence of n Clifford gates which are randomly chosen from the single-qubit Clifford group, followed by a final recovery gate to return the target qubit to its initial state. Each sequence of length n is repeated 100 times, and the results are averaged over 9 randomised sequences. Data are presented as mean ± s.d. We measure the recovery probability as a function of the number of Clifford gates, n, following the decay model \({P}_{\Downarrow }(n)=A{p}_\mathrm{C}^{n}+B\), where A and B are constants that account for the state preparation and measurement (SPAM) errors. The depolarizing parameter p_C is related to the average Clifford gate fidelity F_C = (1 + p_C)/2. RB measurements performed on the nuclear spin qubits N₁ ~ N₄ within their respective single-qubit subspaces yield Clifford gate fidelities of 99.37 ± 0.03%, 99.73 ± 0.02%, 99.84 ± 0.01%, and 99.33 ± 0.04%, respectively. The fidelity uncertainties are derived by the bootstrap resampling and denoted at the 1σ confidence level. a, The experimental circuit for single-qubit randomised benchmarking. All 24 single-qubit Clifford gates are generated using X_π/2 and virtual Z_π/2 gates. b, Single-qubit randomised benchmarking measurement results for four nuclear spins N₁ ~ N₄.

Source data