Fig. 1: Illustration of the CAB procedure for assessing the fidelity of an n-qubit gate, U.

a shows the circuit, beginning with the preparation of the state \({\left\vert 0\right\rangle }^{\otimes n}\), followed by a random local Clifford gate \({\bigotimes }_{i = 1}^{n}{C}_{i}\). Subsequently, 2m layers of random Pauli gates \({\bigotimes }_{j = 1}^{n}{P}_{j}^{(i)}\) are interleaved with alternate sequences of U and U⁻¹. The inverse gate \({U}_{inv}={({\Pi }_{i = 1}^{m}({U}^{-1}{\bigotimes }_{j = 1}^{n}{P}_{j}^{(2i)}U{\bigotimes }_{j = 1}^{n}{P}_{j}^{(2i-1)}))}^{-1}\) and the inverse of the local Clifford gate \({\bigotimes }_{i = 1}^{n}{C}_{i}^{-1}\) are applied thereafter. Finally, one applies computational-basis measurements and records the outcome. One needs to sample K_r random sequences, and for each sequence, one measures K_s times. The outcome statistics are counted for each sequence, as in (b). After that, one randomly chooses K_q observables \({Z}_{w}\in {\{{\mathbb{I}},Z\}}^{\otimes n}\), where w ∈ {0, 1}ⁿ and pt(Z_w) = w, with probability 2⁻²ⁿ3^∣w∣. One estimates the expectation values of these chosen observables, and the expectation values need to be averaged across K_r random sequences. The above procedure is repeated for different m from a circuit depth set, {m₁, m₂, ⋯, m_M}. For all m, the chosen observables have to be the same. c demonstrates the expectation values of different observables for different sequence lengths. The expectation value O_w(m) is approximately proportional to \({\lambda }_{w}^{2m}\), which can be fit to Aλ^2m to determine quality parameter λ_w like (d). e shows the last step. The final fidelity estimation is the average of the fitting values, and subsequently, one can further evaluate the gate correlation and employ gate optimization. Practical experimental settings choose constant values for K_r, K_s, and K_q independent of the qubit count.