DISQ: Dynamic Iteration Skipping for Variational Quantum Algorithms

TL;DR

DISQ tackles noise drift in variational quantum algorithms by introducing a drift detector that reuses reference outputs from prior iterations and augments them with multiple references. It combines this with Pauli-term subsetting to drastically reduce overhead, enabling drift detection to run efficiently while preserving a drift-free gradient for optimization. The framework demonstrates 1.51–2.24× fidelity improvements over baselines and 1.1–1.9× gains over leading dynamic-noise approaches, along with roughly 2.07× faster drift detection on diverse QPUs. This approach offers a practical path to more reliable VQA training on NISQ devices with reduced resource consumption.

Abstract

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 1.51-2.24x fidelity improvement over the traditional baseline. DISQ's benefit is 1.1-1.9x over the best alternative approach while boosting average noise detection speed by 2.07x

Figures (18)

• Figure 1: Computing resource-efficient iteration skipping approach to filter out the noise drift impact. Previous iterations act as optimal reference circuits to detect the noise drift on the current VQA iteration. Pauli-term subsetting is utilized to proactively minimize computation during noise drift detection.
• Figure 2: Noise drift errors on circuits. Circuit data are collected by 100 continuous runs of a circuit batch from an experiment on IBMQ Belem. Each data point is the average expectation value of the circuit batch (25 identical circuits). The mean value is -0.62, but the range value is concerning 0.22.
• Figure 3: VQA landscape navigation. Contour levels correspond to different objective function values, with darker colors indicating smaller values. The orange dot marks the objective function value for each parameter configuration chosen by the optimizer. The tuning process is represented by an arrow trace. a) represents the drift-free (ideal) scenario; b) and d) depict scenarios with out-of-range noise drift; c) illustrates a scenario where noise drift is acceptable.
• Figure 4: Overview of DISQ: a VQA iteration execution is partitioned into two stages ($S_1$, $S_2$); Prime subset corresponding to the current iteration $i$ (blue circuit in $S_1$) and its references (gray circuits) are executed in $S_1$ to detect the noise drift; If noise drift is present, DISQ skips the results of the current job and reschedules all the circuits in $S_1$ via the next job (orange line). Otherwise, minor subset corresponding to the current iteration $i$ (blue circuits in $S_2$) are executed to proceed with VQA (green line).
• Figure 5: The benefits of averaging in reducing deviations. Expectation value data over 50 executions of two circuit batches (blue line: three different circuits; gray line: one circuit) is compared in two different circuit features on IBMQ Lagos.