DISQ: Dynamic Iteration Skipping for Variational Quantum Algorithms

In the noisy intermediate scale quantum (NISQ) era, the Variational Quantum Algorithm (VQA) has emerged as one of the most promising approaches to harness the power of quantum computers. In VQA, a classical optimizer iteratively updates the parameters of a variational quantum circuit to minimize a cost objective obtained by executing the quantum circuit on real quantum hardware. However, the deployment of VQA applications on NISQ devices encounters substantial noise, which degrades training stability. Moreover, the drift of noise is particularly intractable due to its dynamic nature in duration and magnitude. Noise drift leads to significant deviations in VQA iteration's objective function estimation and shapes a dynamic noisy landscape, which poses a considerable challenge for stable VQA parameter training, thereby hampering the accurate convergence of VQA optimizations. This paper proposes DISQ to craft a stable landscape for VQA training and tackle the noise drift challenge. DISQ adopts a “drift detector” with a reference circuit to identify and skip iterations that are severely affected by noise drift errors. Specifically, the circuits from the previous training iteration are re-executed as a reference circuit in the current iteration to estimate noise drift impacts. The iteration is deemed compromised by noise drift errors and thus skipped if noise drift flips the direction of the ideal optimization gradient. To enhance noise drift detection reliability, we further propose to leverage multiple reference circuits from previous iterations to provide a well-founded judge of current noise drift. Nevertheless, multiple reference circuits also introduce considerable execution overhead. To mitigate extra overhead, we propose Pauli-term subsetting (prime and minor subsets) to execute only observable circuits with large coefficient magnitudes (prime subset) during drift detection. Only this minor subset is executed when the current iteration is drift-free. Evaluations across various applications and QPUs demonstrate that DISQ can mitigate a significant portion of the noise drift impact on VQAs and achieve 1.51-2.24× fidelity improvement over the traditional baseline. DISQ's benefit is 1.1-1.9× over the best alternative approach while boosting average noise detection speed by 2.07×.