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Scientific Reports

A quantum-inspired classification for random mixed states

Giuseppe Sergioli, Carlo Cuccu, Carla Rieger, Andrés Camilo Granda Arango, Bikash K. Behera, Riccardo Era, Roberto Giuntini

Published Mar 30, 2026• 0 citations
Publisher

Abstract

We present a quantum-inspired classification framework designed to identify correlation structures: product, separable, and entangled, in random mixed quantum states. Building on previous work where the Pretty-Good-Measurement (PGM) classifier demonstrated a competitive performance on pure-state ensembles, we extend this method to the more challenging domain of mixed states. We apply our quantum-inspired classifier to randomly generated ensembles of two- and three-qubit mixed states, encompassing all possible varieties of subsystem correlations while ensuring statistical neutrality. The results indicate that learning architectures inspired by quantum state discrimination can offer scalable and physically grounded tools for the characterization of entanglement and separability even in the mixed-state regime.

DOI
10.1038/s41598-026-44068-5

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We present algorithms for supervised classification tasks in machine learning that are inspired by quantum mechanics. They rely on the so-called problem of quantum state discrimination, which consists in identifying which one of a known set of quantum states has been prepared based on the outcome of a quantum measurement on the state. After building the quantum states associated with the training data, which are encoded as density matrices, we explore various quantum measurement strategies suited for the classification task, including those based on semi-definite programming and on the so-called Pretty GoodMeasurement.We also consider how the measurement performs on multiple copies of the quantum state, since this in principle improves quantum state discrimination at the price of a higher computational cost. For the Pretty Good Measurement classifier, an analogue of the well-known Kernel Trick in learning theory can be devised, so that the cost scales only with the number of examples in the training dataset. This allows to study the performance of this classifier on tensor products of the quantum state. Finally, thedifferent classifiers are benchmarked on the MNIST and MNIST-1D datasets.
Quantum-inspired machine learning is a new branch of machine learning based on the application of the mathematical formalism of quantum mechanics to devise novel algorithms for classical computers.We implement some quantum-inspired classification algorithms, based on quantum state discrimination, within a local approach in the feature space by taking into account elements close to the element to be classified.This local approach improves the accuracy in classification and motivates the integration with the classifiers.The quantum-inspired classifiers require the encoding of the feature vectors into density operators and methods for estimating the distinguishability of quantum states like the Helstrom state discrimination and the Pretty-Good measurement.We present a comparison of the performances of the local quantum-inspired classifiers against well-known classical algorithms in order to show that the local approach can be a valuable tool for increasing the performances of this kind of classifiers.
Abstract A classification of multipartite entanglement is introduced for pure and mixed states. The classification is based on the distribution of entanglement between the qubits of a given system, with a mathematical framework used to characterize fully entangled states. Then we use current machine learning and deep learning techniques to automatically classify a random state of two, three, and four qubits without the need to compute the amount of the different types of entanglement in each run; rather this is done only in the learning process. The technique shows high, near-perfect, accuracy in the case of pure states. As expected, this accuracy drops, more or less, when dealing with mixed states and when increasing the number of parties involved.
A classification of multipartite entanglement in qubit systems is introduced for pure and mixed states. The classification is based on the robustness of the said entanglement against partial trace operation. Then we use current machine learning and deep learning techniques to automatically classify a random state of two, three and four qubits without the need to compute the amount of the different types of entanglement in each run; rather this is done only in the learning process. The technique shows high, near perfect, accuracy in the case of pure states. As expected, this accuracy drops, more or less, when dealing with mixed states and when increasing the number of parties involved.