Yerassyl Balkybek | Searcharxiv

arXiv2026

Parametrized-circuit-free quantum regression with variance regularization

Quantum regression tasks for predicting properties of quantum states are commonly addressed using variational quantum algorithms. While variational quantum circuits are highly expressive and allow to achieve reasonable accuracy, training these circuits may demand a considerable amount of time and resources. In this work, we propose an approach of constructing problem-specific quantum regression models with encoding relevant symmetries and regularizing the variance. The proposed method is based on finding the coefficients of the linear combination of suitably chosen observables. Although it requires the knowledge of the symmetries of the problem in question, the method does not involve parameterized quantum circuits, and the training is done efficiently once the observables are measured. We demonstrate this method on two examples: Prediction of the transverse field strength in the Ising model, and quantification of entanglement in bipartite qubit systems. Our approach is accurate and less resource-intensive than conventional variational methods.

quant-ph↗

arXiv2025

Predicting properties of quantum systems by regression on a quantum computer

Quantum computers can be considered as a natural means for performing machine learning tasks for inherently quantum labeled data. Many quantum machine learning techniques have been developed for solving classification problems, such as distinguishing between phases of matter or quantum processes. Similarly, one can consider a more general problem of regression, when the aim is to predict continuous labels quantifying properties of quantum states, such as purity or entanglement. In this work, we propose a method for predicting such properties. The method is based on the notion of parametrized quantum circuits, and it seeks to find an observable the expectation of which gives the prediction of the property of interest with a low variance. We numerically test our approach in learning to predict (i) the parameter of a parametrized channel given its output state, (ii) entanglement of two-qubit states, and (iii) the parameter of a parametrized Hamiltonian given its ground state. The results show that the proposed method is able to find observables such that they provide highly accurate predictions of the considered properties, and in some cases even saturate the Cramer-Rao bound, which characterizes the prediction error. We also compare our method with the Bayesian approach, and find that the latter prefers to minimize the prediction variance, having therefore a larger bias.

quant-ph↗