Neural network approach to mitigating intra-gate crosstalk in superconducting CZ gates

Abstract

The potential of quantum computing is fundamentally constrained by the inherent susceptibility of qubits to noise and crosstalk, particularly during multi-qubit gate operations. Existing strategies, such as hardware isolation and dynamical decoupling, face limitations in scalability, experimental feasibility, and robustness against complex noise sources. In this manuscript, we propose a physics-guided neural control (PGNC) framework to generate robust control pulses for superconducting transmon qubit systems, specifically targeting crosstalk mitigation. By combining a hardware aware parameterization with a Hamiltonian-informed objective that accounts for condition-dependent crosstalk distortions, PGNC steers the search toward smooth and physically realizable pulses while efficiently exploring high dimensional control landscapes. Numerical simulations for the CZ gate demonstrate superior fidelity and pulse smoothness compared to a Krotov baseline under matched constraints. Taken together, the results show consistent and practically meaningful improvements in both nominal and perturbed conditions, with pronounced gains in worst-case fidelity, supporting PGNC as a viable route to robust control on near-term transmon devices.

Figures (5)

• Figure 1: (a) Conceptual illustration of coherent and crosstalk in a two-transmon system. Each transmon qubit $Q_q$ is controlled by local microwave I/Q envelopes $\Omega_q$ together with an instantaneous detuning term $\delta_q$, while coupled through an effective interaction $J_{zz}$, $q\in\{1,2\}$. Solid arrows denote the intended drives applied directly to the qubits, whereas dashed arrows denote corsstalk-induced perturbations to the effective control parameters. Classical cross-drive leakage is captured by the mixing coefficients $r_{12}$ and $r_{21}$. A normalized crosstalk-condition vector $c$ summarizes concurrent-drive settings and induces condition-dependent biases in the effective parameters, e.g., $J_{zz}^{\mathrm{eff}}(t;c)$ and $r_{\mathrm{eff}}(c)$ (Eqs. \ref{['eq:b_def']} and \ref{['eq:G_def']}). The coefficients $\varepsilon_{1,2}$ denote parasitic $Z$-shifts correlated with activating $J_{zz}(t)$ (Eq. \ref{['eq:coupler_zshift']}). (b) Conditioned neural-network training loop for quantum control. Given $(t,c)$, the neural network outputs hardware-constrained waveforms $u_{\theta}(t;c)$, which define the condition-augmented Hamiltonian $H(t;c)$. The open-system dynamics are simulated via Lindblad evolution, from which we compute $\overline{F}(c)$, $\mathrm{Leak}(c)$, and $\mathrm{Smooth}(c)$ and form the aggregated training objective $\mathcal{J}_{\mathrm{tot}}$. Gradients are obtained by automatic differentiation and used by an optimizer to update $\theta$ until convergence; after training, fidelities are reported on a held-out evaluation set.
• Figure 2: Training dynamics and learned control waveforms for a two-qubit gate comparing PGNC, Krotov, and GRAPE algorithms. (a) Trace of the infidelity ($1 - \mathcal{F}$) versus training iteration on a logarithmic scale. (b-h) Learned hardware-feasible waveforms for the two qubits, plotted over the full gate window $T = 50$ ns: dynamic ZZ coupling ($J_{zz}$) (b), in-phase drives $\Omega_{x1}$ (c) and $\Omega_{x2}$ (e), quadrature drives $\Omega_{y1}$ (d) and $\Omega_{y2}$ (f), and detunings $\delta_{1}$ (g) and $\delta_{2}$ (h). Amplitudes and couplings are reported in rad/ns.
• Figure 3: Discrete-condition comparison and off-grid generalization scan. (a) Fidelity distributions (violin plots) for four representative conditions $c_0$--$c_3$ (annotated in each panel), evaluated on an ensemble of 128 Haar-random two-qubit input states, comparing PGNC, Krotov, and GRAPE. PGNC generates conditioned pulses by taking $c$ as an input at inference time, whereas Krotov and GRAPE are used as static baseline methods that output fixed waveforms under the chosen optimization setup and are then evaluated across different $c$. (b) Off-grid scan over $(c_I,c_Q)$ for three fixed carrier-offset tags $c_f\in\{0,-0.1,-0.25\}$. Each square panel contains two heatmaps: the left half shows the average-fidelity difference $\Delta\mathrm{avgF}=\mathrm{avgF}_{\mathrm{PGNC}}-\mathrm{avgF}_{\mathrm{Krotov}}$, and the right half shows $\Delta\mathrm{avgF}=\mathrm{avgF}_{\mathrm{PGNC}}-\mathrm{avgF}_{\mathrm{GRAPE}}$ (see color bar). Grey squares mark the locations of the four discrete conditions used in (a) on the corresponding scan planes.
• Figure 4: Per-condition optimized CZ-gate fidelity distributions under representative crosstalk conditions. (a--d) Violin plots of the final gate fidelity obtained by independently optimizing PGNC, Krotov, and GRAPE for four fixed conditions $c0$--$c3$. All methods are evaluated under matched amplitude and smoothness constraints and the same optimization budget. The violin width indicates the distribution over repeated runs on an ensemble of 128 Haar-random two-qubit input states
• Figure 5: Robustness to two-qubit detuning drifts. Contour maps of the average gate fidelity $\overline{F}$ as a function of static detuning offsets $(\delta_1,\delta_2)$ applied to the two qubits during the gate. The top panel shows PGNC, while the bottom panels show GRAPE and Krotov under the same physical model, constraints, and evaluation protocol. For each grid point $(\delta_1,\delta_2)$, we shift the detuning controls as $\delta_q(t)\mapsto \delta_q(t)+\delta_q$ ($q\in\{1,2\}$) and re-evaluate the gate fidelity on an ensemble of input states (the same evaluation set used throughout the paper), reporting the resulting average $\overline{F}$. The white central region indicates parameter pairs for which $\overline{F}>0.99$ (values above the color scale).