Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0809.0444

Quantum classification

Sébastien Gambs

Published Sep 2, 2008• 20 citations
arXivHTMLPDF

Abstract

Quantum classification is defined as the task of predicting the associated class of an unknown quantum state drawn from an ensemble of pure states given a finite number of copies of this state. By recasting the state discrimination problem within the framework of Machine Learning (ML), we can use the notion of learning reduction coming from classical ML to solve different variants of the classification task, such as the weighted binary and the multiclass versions.

DOI
10.48550/arxiv.0809.0444

Related papers

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

The quantum version of prediction for binary classification problem by ensemble methods

Kamil Ravilevich Khadiev, Liliya Safina

In this work, we consider the performance of using a quantum algorithm to predict the result of a binary classification problem when a machine learning model is an ensemble of any simple classifiers. This approach is faster than classical prediction and uses quantum and classical computing, but it is based on a probabilistic algorithm. Let N be the number of classifiers from an ensemble model and O(T) be the running time of prediction of one classifier. In classical case, the final result is obtained by ”averaging” outcomes of all ensemble model’s classifiers. The running time in classical case is O (N · T). We propose an algorithm that works in O (√N · T ).

arXiv:2112.13346•International Conference on Micro- and Nano-Electronics (ICMNE)•Jan 31, 2022•10 citations

Sampling-based learning control for quantum discrimination and ensemble classification

Chunlin Chen, Daoyi Dong, Bo Qi +2 more

Quantum ensemble classification has significant applications in discrimination of atoms (or molecules), separation of isotopic molecules and quantum information extraction. In this paper, we recast quantum ensemble classification as a supervised quantum learning problem. A systematic classification methodology is presented by using a sampling-based learning control (SLC) approach for quantum discrimination. The classification task is accomplished via simultaneously steering members belonging to different classes to their corresponding target states (e.g., mutually orthogonal states). Numerical results demonstrate the effectiveness of the proposed approach for the discrimination of two quantum systems and the binary classification of two-level quantum ensembles.

International Joint Conference on Neural Networks (IJCNN)•Jul 1, 2014•1 citation

Quantum Inspired Classification Algorithms

Zambrini Cruzeiro, Emmanuel, De Mol, Christine, Massar, Serge +1 more

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.

•Jan 1, 2025•0 citations

Investigating Classification with Quantum Computing

Muhammad Hamid, Bashir Alam, Om Pal +1 more

In the last two decades machine learning and quantum computing have seen massive growth in terms of application and implementation. Quantum computers can provide the solution to certain classes of problem that classical computers fail to solve. Hence a greater number of optimized quantum algorithms are being developed. Today quantum computers are used in various fields to solve difficult problems like optimization and critical prediction problems in finance, artificial intelligence, and medicine. Quantum computing is based on the laws of quantum mechanics and uses superposition and entanglement properties to solve computation complexities in analyzing large data. Quantum machine learning is a new discipline for machine learning. In this survey, we will explore algorithms for quantum machine learning tasks. We will study parametrized quantum circuits for multi-class classification. This chapter also shows that quantum machine learning and near-term quantum devices open new doors for fast learning and enhanced classification.

Auerbach Publications eBooks•Sep 8, 2023•1 citation

Quantum Ensemble Classification: A Sampling-Based Learning Control Approach

Chunlin Chen, Daoyi Dong, Bo Qi +2 more

Quantum ensemble classification (QEC) has significant applications in discrimination of atoms (or molecules), separation of isotopes, and quantum information extraction. However, quantum mechanics forbids deterministic discrimination among nonorthogonal states. The classification of inhomogeneous quantum ensembles is very challenging, since there exist variations in the parameters characterizing the members within different classes. In this paper, we recast QEC as a supervised quantum learning problem. A systematic classification methodology is presented by using a sampling-based learning control (SLC) approach for quantum discrimination. The classification task is accomplished via simultaneously steering members belonging to different classes to their corresponding target states (e.g., mutually orthogonal states). First, a new discrimination method is proposed for two similar quantum systems. Then, an SLC method is presented for QEC. Numerical results demonstrate the effectiveness of the proposed approach for the binary classification of two-level quantum ensembles and the multiclass classification of multilevel quantum ensembles.

arXiv:1312.6945•IEEE Transactions on Neural Networks and Learning Systems•Mar 23, 2016•31 citations
Quantum classification is defined as the task of predicting the associated class of an unknown quantum state drawn from an ensemble of pure states given a finite number of copies of this state. By recasting the state discrimination problem within the framework of Machine Learning (ML), we can use the notion of learning reduction coming from classical ML to solve different variants of the classification task, such as the weighted binary and the multiclass versions.
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.
In this work, we consider the performance of using a quantum algorithm to predict the result of a binary classification problem when a machine learning model is an ensemble of any simple classifiers. This approach is faster than classical prediction and uses quantum and classical computing, but it is based on a probabilistic algorithm. Let N be the number of classifiers from an ensemble model and O(T) be the running time of prediction of one classifier. In classical case, the final result is obtained by ”averaging” outcomes of all ensemble model’s classifiers. The running time in classical case is O (N · T). We propose an algorithm that works in O (√N · T ).
Quantum ensemble classification has significant applications in discrimination of atoms (or molecules), separation of isotopic molecules and quantum information extraction. In this paper, we recast quantum ensemble classification as a supervised quantum learning problem. A systematic classification methodology is presented by using a sampling-based learning control (SLC) approach for quantum discrimination. The classification task is accomplished via simultaneously steering members belonging to different classes to their corresponding target states (e.g., mutually orthogonal states). Numerical results demonstrate the effectiveness of the proposed approach for the discrimination of two quantum systems and the binary classification of two-level quantum ensembles.
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.
In the last two decades machine learning and quantum computing have seen massive growth in terms of application and implementation. Quantum computers can provide the solution to certain classes of problem that classical computers fail to solve. Hence a greater number of optimized quantum algorithms are being developed. Today quantum computers are used in various fields to solve difficult problems like optimization and critical prediction problems in finance, artificial intelligence, and medicine. Quantum computing is based on the laws of quantum mechanics and uses superposition and entanglement properties to solve computation complexities in analyzing large data. Quantum machine learning is a new discipline for machine learning. In this survey, we will explore algorithms for quantum machine learning tasks. We will study parametrized quantum circuits for multi-class classification. This chapter also shows that quantum machine learning and near-term quantum devices open new doors for fast learning and enhanced classification.
Quantum ensemble classification (QEC) has significant applications in discrimination of atoms (or molecules), separation of isotopes, and quantum information extraction. However, quantum mechanics forbids deterministic discrimination among nonorthogonal states. The classification of inhomogeneous quantum ensembles is very challenging, since there exist variations in the parameters characterizing the members within different classes. In this paper, we recast QEC as a supervised quantum learning problem. A systematic classification methodology is presented by using a sampling-based learning control (SLC) approach for quantum discrimination. The classification task is accomplished via simultaneously steering members belonging to different classes to their corresponding target states (e.g., mutually orthogonal states). First, a new discrimination method is proposed for two similar quantum systems. Then, an SLC method is presented for QEC. Numerical results demonstrate the effectiveness of the proposed approach for the binary classification of two-level quantum ensembles and the multiclass classification of multilevel quantum ensembles.