© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Quantum Inspired Classification Algorithms

Zambrini Cruzeiro, Emmanuel, De Mol, Christine, Massar, Serge, Pironio, Stefano

Published Jan 1, 2025• 0 citations

Abstract

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.

Related papers

Quantum-inspired classifiers

Roberto Leporini, Cesarino Bertini

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.

Computer Science Research Notes•Jan 1, 2025•0 citations

Classification of quantum correlations via quantum-inspired machine learning

Giuseppe Sergioli, Andrés Camilo Granda Arango, Carlo Cuccu +3 more

Abstract Quantum information theory, and in particular, the theory of quantum state discrimination, has enabled the development of a supervised multi-class classification algorithm. Inspired by the Pretty Good Measurement (PGM), a quantum-inspired classifier named the PGM Classifier has been designed, capable of classifying among multiple classes without resorting to the One versus One or One versus Rest strategy. In the recent past, several approaches of quantum machine learning have been introduced to classify entangled and separable states. In this article, we apply the PGM Classifier to discriminate among factorized states, separable states, and entangled states. We analyze from the simplest case ( 2 qubits) up to a system of ( 5 qubits) and offer a comparison between our quantum-inspired classifier and other classical classifiers. Finally, we propose a refined classification of non-locality based on the violation of the Mermin and Svetlichny inequalities.

Quantum Machine Intelligence•Nov 25, 2025•2 citations

Quantum-Inspired Classification Based on Voronoi Tessellation and Pretty-Good Measurements

Roberto Leporini, Davide Pastorello

In quantum machine learning, feature vectors are encoded into quantum states. Measurements for the discrimination of states are useful tools for classification problems. Classification algorithms inspired by quantum state discrimination have recently been implemented on classical computers. We present a local approach combining Vonoroi-type tessellation of a training set with pretty-good measurements for quantum state discrimination.

Quantum Reports•Oct 17, 2022•1 citation

Quantum State Discrimination for Supervised Classification

Roberto Giuntini, Héctor Freytes, Daniel K. Park +4 more

In this paper we investigate the connection between quantum information theory and machine learning. In particular, we show how quantum state discrimination can represent a useful tool to address the standard classification problem in machine learning. Previous studies have shown that the optimal quantum measurement theory developed in the context of quantum information theory and quantum communication can inspire a new binary classification algorithm that can achieve higher inference accuracy for various datasets. Here we propose a model for arbitrary multiclass classification inspired by quantum state discrimination, which is enabled by encoding the data in the space of linear operators on a Hilbert space. While our algorithm is quantum-inspired, it can be implemented on classical hardware, thereby permitting immediate applications.

arXiv:2104.00971•Apr 2, 2021•6 citations

Quantum-Inspired Applications for Classification Problems

Cesarino Bertini, Roberto Leporini

In the context of quantum-inspired machine learning, quantum state discrimination is a useful tool for classification problems. We implement a local approach combining the k-nearest neighbors algorithm with some quantum-inspired classifiers. We compare the performance with respect to well-known classifiers applied to benchmark datasets.

Entropy•Feb 23, 2023•3 citations

Towards a Quantum-Inspired Binary Classifier

Prayag Tiwari, Massimo Melucci

Machine Learning classification models learn the relation between input as features and output as a class in order to predict the class for the new given input. Several research works have demonstrated the effectiveness of machine learning algorithms but the state-of-the-art algorithms are based on the classical theories of probability and logic. Quantum Mechanics (QM) has already shown its effectiveness in many fields and researchers have proposed several interesting results which cannot be obtained through classical theory. In recent years, researchers have been trying to investigate whether the QM can help to improve the classical machine learning algorithms. It is believed that the theory of QM may also inspire an effective algorithm if it is implemented properly. From this inspiration, we propose the quantum-inspired binary classifier, which is based on quantum detection theory. We used text corpora and image corpora to explore the effect of our proposed model. Our proposed model outperforms the state-of-the-art models in terms of precision, recall, and F-measure for several topics (categories) in the 20 newsgroup text corpora. Our proposed model outperformed all the baselines in terms of recall when the MNIST handwritten image dataset was used; F-measure is also higher for most of the categories and precision is also higher for some categories. Our proposed model suggests that binary classification effectiveness can be achieved by using quantum detection theory. In particular, we found that our Quantum-Inspired Binary Classifier can increase the precision, recall, and F-measure of classification where the state-of-the-art methods cannot.

IEEE Access•Jan 1, 2019•58 citations

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 Quantum information theory, and in particular, the theory of quantum state discrimination, has enabled the development of a supervised multi-class classification algorithm. Inspired by the Pretty Good Measurement (PGM), a quantum-inspired classifier named the PGM Classifier has been designed, capable of classifying among multiple classes without resorting to the One versus One or One versus Rest strategy. In the recent past, several approaches of quantum machine learning have been introduced to classify entangled and separable states. In this article, we apply the PGM Classifier to discriminate among factorized states, separable states, and entangled states. We analyze from the simplest case ( 2 qubits) up to a system of ( 5 qubits) and offer a comparison between our quantum-inspired classifier and other classical classifiers. Finally, we propose a refined classification of non-locality based on the violation of the Mermin and Svetlichny inequalities.

In this paper we investigate the connection between quantum information theory and machine learning. In particular, we show how quantum state discrimination can represent a useful tool to address the standard classification problem in machine learning. Previous studies have shown that the optimal quantum measurement theory developed in the context of quantum information theory and quantum communication can inspire a new binary classification algorithm that can achieve higher inference accuracy for various datasets. Here we propose a model for arbitrary multiclass classification inspired by quantum state discrimination, which is enabled by encoding the data in the space of linear operators on a Hilbert space. While our algorithm is quantum-inspired, it can be implemented on classical hardware, thereby permitting immediate applications.

Machine Learning classification models learn the relation between input as features and output as a class in order to predict the class for the new given input. Several research works have demonstrated the effectiveness of machine learning algorithms but the state-of-the-art algorithms are based on the classical theories of probability and logic. Quantum Mechanics (QM) has already shown its effectiveness in many fields and researchers have proposed several interesting results which cannot be obtained through classical theory. In recent years, researchers have been trying to investigate whether the QM can help to improve the classical machine learning algorithms. It is believed that the theory of QM may also inspire an effective algorithm if it is implemented properly. From this inspiration, we propose the quantum-inspired binary classifier, which is based on quantum detection theory. We used text corpora and image corpora to explore the effect of our proposed model. Our proposed model outperforms the state-of-the-art models in terms of precision, recall, and F-measure for several topics (categories) in the 20 newsgroup text corpora. Our proposed model outperformed all the baselines in terms of recall when the MNIST handwritten image dataset was used; F-measure is also higher for most of the categories and precision is also higher for some categories. Our proposed model suggests that binary classification effectiveness can be achieved by using quantum detection theory. In particular, we found that our Quantum-Inspired Binary Classifier can increase the precision, recall, and F-measure of classification where the state-of-the-art methods cannot.