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Testing quantum machine learning claims in practice: a classical benchmark from random circuits and a five-step test for variational regression

Satish G. Prajapati

Published Oct 29, 2026• 0 citations
Publisher
DOI
10.5281/zenodo.23755328

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Variational quantum circuits have recently gained popularity as quantum machine learning models. While considerable effort has been invested to train them in supervised and unsupervised learning settings, relatively little attention has been given to their potential use in reinforcement learning. In this work, we leverage the understanding of quantum policy gradient algorithms in a number of ways. First, we investigate how to construct and train reinforcement learning policies based on variational quantum circuits. We propose several designs for quantum policies, provide their learning algorithms, and test their performance on classical benchmarking environments. Second, we show the existence of task environments with a provable separation in performance between quantum learning agents and any polynomial-time classical learner, conditioned on the widely-believed classical hardness of the discrete logarithm problem. We also consider more natural settings, in which we show an empirical quantum advantage of our quantum policies over standard neural-network policies. Our results constitute a first step towards establishing a practical near-term quantum advantage in a reinforcement learning setting. Additionally, we believe that some of our design choices for variational quantum policies may also be beneficial to other models based on variational quantum circuits, such as quantum classifiers and quantum regression models.
AbstractThis study provides a comprehensive empirical benchmark of quantum, classical, and Bayesian machine learning approaches for regression under challenging small-sample conditions with multicollinear features and skew-normal innovations. We systematically compare nine algorithms—including three quantum methods (Quantum Circuit Learning, Quantum Error Regression, Quantum Kernel Methods),four classical machine learning techniques (Lasso, Ridge, Random Forest, Gradient Boosting, Support Vector Regression), and Bayesian Structural Time Series— across two sample size regimes (n=30 and n=80) with five features. Outcome of the study revealed robust sample-size-dependent performance hierarchies in regularized linear methods (Lasso, Ridge) and Bayesian paradigms which ordinarily subsist in small-sample regimes of (n=30), with RMSE values of 4.46-5.74, while non-linear ensemble methods (Random Forest) exhibited superiority with moderate samples (n=80, RMSE: 2.07). Quantum machine learning methods had overtimes underperform classical benchmarks when exhibiting 91% higher error rates at small sample size of n=30, this may be due to classical method learned the noise, though Quantum Circuit Learning exhibited substantial convergence toward classical performance at n=80 (only 25% worse than best model),thus higher sample sizes thresholds will be better off for quantum-classical parity.