Robust Parametric Quantum Gate Against Stochastic Time-Varying Noise

Abstract

The performance of quantum processors in the noisy intermediate-scale quantum (NISQ) era is severely constrained by environmental noise and other uncertainties. While the recently proposed quantum control robustness landscape (QCRL) offers a powerful framework for generating robust control pulses for parametric gate families, its application has been practically restricted to quasi-static noise. To address the spectrally complex, time-varying noise prevalent in reality, we propose filter function-enhanced QCRL (FF-QCRL), which integrates filter function formalism into the QCRL framework. The resulting FF-QCRL algorithm minimizes a generalized robustness metric that faithfully encodes the impact of stochastic processes, enabling robust pulse-family generation for parametric gates under realistic time-varying noise. Numerical validation in a representative single-qubit setting confirms the effectiveness of the proposed method.

The paper addresses how to generate continuous families of parametric gates with approximately constant robustness against stochastic, time-varying noise, extending quantum control robustness landscape (QCRL) methods beyond quasi-static noise. Its filter-function-enhanced framework, FF-QCRL, uses a noise-spectrum-weighted filter-function integral as an approximate infidelity metric. It first optimizes a seed pulse for fidelity, robustness, power and smoothness, then applies robustness-invariant pulse variation (RIPV), projecting parameter updates orthogonally to the robustness gradient while changing the target gate parameter. Numerical validation considers $R_x(\theta)$ gates driven by a single control field under multiband stochastic detuning noise. Pulses have duration $50\,\mathrm{ns}$ and seven Fourier parameters. For an initial $R_x(\pi)$ pulse, optimization targets low-frequency noise and a second band near six times $2\pi/T$. Monte Carlo simulations with 500 noise realizations report approximately $30\%$ lower infidelity than a quasi-static-noise-optimized baseline. RIPV generates pulses over $\theta\in[\pi,2\pi]$; tests at 11 angles report average fidelities above $98.5\%$ across the tested noise range, with approximately quadratic noise-strength scaling. An auxiliary six-qubit variational-circuit surrogate approximates the robustness metric and supplies gradients for RIPV. It tracks exact RIPV approximately through $1.5\pi$ but degrades at larger angles. At $1.5\pi$ and the largest tested noise strength, fidelities are $0.98728$ for exact RIPV and $0.98137$ for the surrogate. No computational speedup is demonstrated. Validation remains limited to one qubit and one noise channel; multiple channels, two-qubit gates, fuller surrogate benchmarking and experimental tests are left for future work.