Fig. 2: Stabilizing noise in gate layers.
From: Error mitigation with stabilized noise in superconducting quantum processors
a Graphical representation of the coefficients of the sparse Pauli–Lindblad noise models of two layers. The layers consist of \({\mathsf{CZ}}\) gates covering different qubit pairs (shaded box): {(1, 2), (3, 4), (5, 6)} for layer 1 and {(2, 3), (4, 5)} for layer 2. The model parameters apply to Pauli terms on each of the six qubits, as well as weight-two Pauli terms on connected qubits. The model parameters \({\{{\lambda }_{k}\}}_{k\in {{\mathcal{K}}}}\) are determined by applying the learning protocol separately to each of the two layers. The inset on the right depicts the position of the Pauli coefficients and the color bars for the one- and two-qubit terms. b–d Provides a more detailed picture of model parameter instability by computing the model coefficient fluctuation δλk(t) = λk(t) − median[λk(t)], where median[ ⋅ ] computes a median value of the time-varying model coefficient. The plot shows δλk(t) at a specific time t (x-axis) for various Pauli jump terms Pk (y-axis). We show the first 20 parameters sorted by maximum fluctuation. e Shows the total sampling overhead, γ, monitored over time for three different scenarios: (i) a baseline control experiment with kTLS = κ held at a constant neutral point κ for all qubits; (ii) an averaged experiment where kTLS is set to κ plus a slowly varying triangular wave with 1 Hz frequency and amplitude of ±0.2; and (iii) an optimized experiment carried out by periodically update kTLS to a value that maximizes \({{{\mathcal{P}}}}_{e}\). Optimization is performed just prior to each learning experiment for the optimized noise channel. The right inset illustrates the median value and the first and third quartiles of each experiment. f For the optimized experiment, the qubit–TLS interaction landscape of Q2 is probed using TLS control parameter kTLS. The plot displays the resulting \({{{\mathcal{P}}}}_{e}\) over time, along with the optimized control parameters, indicated by the red crosses. Strong qubit–TLS interactions appear as dark green boxes, and can be seen to drift close to the neutral point κ (horizontal black line) at an elapsed time of ~13 h. This coincides with the elevated noise level γ and noticeably larger fluctuations over time in plot (e). The data used for this plot is the same as that used for plot (b–d). Error bars in e are determined using 100 bootstrapped instances of the experimental data. Likewise, error bars for λk are obtained from 100 bootstrapped instances, and the maximum fluctuation of each row in (b–d) is all larger than the error bar. Further details on experiment conditions are described in the “Methods” section.
