Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are implementations of quantum classifiers, or models for the classification of data inputs with a quantum computer. Following the success of collective decision making with ensembles in classical machine learning, this paper introduces the concept of quantum ensembles of quantum classifiers. Creating the ensemble corresponds to a state preparation routine, after which the quantum classifiers are evaluated in parallel and their combined decision is accessed by a single-qubit measurement. This framework naturally allows for exponentially large ensembles in which - similar to Bayesian learning - the individual classifiers do not have to be trained. As an example, we analyse an exponentially large quantum ensemble in which each classifier is weighed according to its performance in classifying the training data, leading to new results for quantum as well as classical machine learning.Quantum machine learning witnesses an increasing amount of quantum algorithms for data-driven decision making, a problem with potential applications ranging from automated image recognition to medical diagnosis. Many of those algorithms are implementations of quantum classifiers, or models for the classification of data inputs with a quantum computer. Following the success of collective decision making with ensembles in classical machine learning, this paper introduces the concept of quantum ensembles of quantum classifiers. Creating the ensemble corresponds to a state preparation routine, after which the quantum classifiers are evaluated in parallel and their combined decision is accessed by a single-qubit measurement. This framework naturally allows for exponentially large ensembles in which - similar to Bayesian learning - the individual classifiers do not have to be trained. As an example, we analyse an exponentially large quantum ensemble in which each classifier is weighed according to its performance in classifying the training data, leading to new results for quantum as well as classical machine learning.

Scientific ReportsFeb 5, 201883 citations

Quantum Ensemble for Classification

Antonio Macaluso, L. Clissa, Stefano Lodi +1 more

A powerful way to improve performance in machine learning is to construct an ensemble that combines the predictions of multiple models. Ensemble methods are often much more accurate and lower variance than the individual classifiers that make them up but have high requirements in terms of memory and computational time. In fact, a large number of alternative algorithms is usually adopted, each requiring to query all available data. We propose a new quantum algorithm that exploits quantum superposition, entanglement and interference to build an ensemble of classification models. Thanks to the generation of the several quantum trajectories in superposition, we obtain $B$ transformations of the quantum state which encodes the training set in only $log\left(B\right)$ operations. This implies exponential growth of the ensemble size while increasing linearly the depth of the correspondent circuit. Furthermore, when considering the overall cost of the algorithm, we show that the training of a single weak classifier impacts additively the overall time complexity rather than multiplicatively, as it usually happens in classical ensemble methods. We also present small-scale experiments on real-world datasets, defining a quantum version of the cosine classifier and using the IBM qiskit environment to show how the algorithms work.A powerful way to improve performance in machine learning is to construct an ensemble that combines the predictions of multiple models. Ensemble methods are often much more accurate and lower variance than the individual classifiers that make them up but have high requirements in terms of memory and computational time. In fact, a large number of alternative algorithms is usually adopted, each requiring to query all available data. We propose a new quantum algorithm that exploits quantum superposition, entanglement and interference to build an ensemble of classification models. Thanks to the generation of the several quantum trajectories in superposition, we obtain $B$ transformations of the quantum state which encodes the training set in only $log\left(B\right)$ operations. This implies exponential growth of the ensemble size while increasing linearly the depth of the correspondent circuit. Furthermore, when considering the overall cost of the algorithm, we show that the training of a single weak classifier impacts additively the overall time complexity rather than multiplicatively, as it usually happens in classical ensemble methods. We also present small-scale experiments on real-world datasets, defining a quantum version of the cosine classifier and using the IBM qiskit environment to show how the algorithms work.

arXiv:2007.01028Jul 2, 20209 citations

Quantum Ensemble for Classification

Antonio Macaluso, L. Clissa, Stefano Lodi +1 more

Abstract A powerful way to improve performance in machine learning is to construct an ensemble that combines the predictions of multiple models. Ensemble methods are often much more accurate and have a lower variance than the individual classifiers that make them up, but have high requirements in terms of memory and computational time. In fact, a large number of alternative algorithms is usually adopted, each requiring to query all available data. We propose a new quantum algorithm that exploits quantum superposition, entanglement and interference to build an ensemble of classification models. Thanks to the generation of the several quantum trajectories in superposition, we obtain B transformations of the quantum state which encodes the training set in only log ( B ) operations. This implies an exponential growth of the ensemble size while increasing linearly the depth of the correspondent circuit. Furthermore, when considering the overall cost of the algorithm, we show that the training of a single weak classifier impacts additively to the overall time complexity rather than multiplicatively, as it usually happens in classical ensemble methods. We also present small-scale experiments on real-world datasets, defining a quantum version of the cosine classifier and using the IBM qiskit environment to show how the algorithms work.Abstract A powerful way to improve performance in machine learning is to construct an ensemble that combines the predictions of multiple models. Ensemble methods are often much more accurate and have a lower variance than the individual classifiers that make them up, but have high requirements in terms of memory and computational time. In fact, a large number of alternative algorithms is usually adopted, each requiring to query all available data. We propose a new quantum algorithm that exploits quantum superposition, entanglement and interference to build an ensemble of classification models. Thanks to the generation of the several quantum trajectories in superposition, we obtain B transformations of the quantum state which encodes the training set in only log ( B ) operations. This implies an exponential growth of the ensemble size while increasing linearly the depth of the correspondent circuit. Furthermore, when considering the overall cost of the algorithm, we show that the training of a single weak classifier impacts additively to the overall time complexity rather than multiplicatively, as it usually happens in classical ensemble methods. We also present small-scale experiments on real-world datasets, defining a quantum version of the cosine classifier and using the IBM qiskit environment to show how the algorithms work.

Aug 1, 20222 citations

Ensembles of quantum classifiers

Emiliano Tolotti, Enrico Zardini, Enrico Blanzieri +1 more

In the current era, known as Noisy Intermediate-Scale Quantum (NISQ), encoding large amounts of data in the quantum devices is challenging and the impact of noise significantly affects the quality of the obtained results. A viable approach for the execution of quantum classification algorithms is the introduction of a well-known machine learning paradigm, namely, the ensemble methods. Indeed, the ensembles combine multiple internal classifiers, which are characterized by compact sizes due to the smaller data subsets used for training, to achieve more accurate and robust prediction performance. In this way, it is possible to reduce the qubit requirements with respect to a single larger classifier while achieving comparable or improved performance. In this work, we present an implementation and an extensive empirical evaluation of ensembles of quantum instance-based classifiers for binary classification, with the purpose of providing insights into their effectiveness, limitations, and potential for enhancing the performance of basic quantum models. In particular, three classical ensemble methods and three quantum instance-based classifiers have been taken into account here. Hence, the scheme that has been implemented (in Python) has a hybrid nature. The results (obtained on real-world datasets) have shown an accuracy advantage for the ensemble techniques with respect to the single quantum classifiers, and also an improvement in robustness. In fact, ensembles have proven effective not only in mitigating unsuitable data normalizations but also in reducing the impact of noise on quantum classifiers, enhancing their stability.In the current era, known as Noisy Intermediate-Scale Quantum (NISQ), encoding large amounts of data in the quantum devices is challenging and the impact of noise significantly affects the quality of the obtained results. A viable approach for the execution of quantum classification algorithms is the introduction of a well-known machine learning paradigm, namely, the ensemble methods. Indeed, the ensembles combine multiple internal classifiers, which are characterized by compact sizes due to the smaller data subsets used for training, to achieve more accurate and robust prediction performance. In this way, it is possible to reduce the qubit requirements with respect to a single larger classifier while achieving comparable or improved performance. In this work, we present an implementation and an extensive empirical evaluation of ensembles of quantum instance-based classifiers for binary classification, with the purpose of providing insights into their effectiveness, limitations, and potential for enhancing the performance of basic quantum models. In particular, three classical ensemble methods and three quantum instance-based classifiers have been taken into account here. Hence, the scheme that has been implemented (in Python) has a hybrid nature. The results (obtained on real-world datasets) have shown an accuracy advantage for the ensemble techniques with respect to the single quantum classifiers, and also an improvement in robustness. In fact, ensembles have proven effective not only in mitigating unsuitable data normalizations but also in reducing the impact of noise on quantum classifiers, enhancing their stability.

arXiv:2311.09750Quantum Information and ComputationMar 1, 20241 citation

Quantum ensemble of trained classifiers

Ismael C. S. Araújo, Adenilton José da Silva

Through superposition, a quantum computer is capable of representing an exponentially large set of states, according to the number of qubits available. Quantum machine learning is a subfield of quantum computing that explores the potential of quantum computing to enhance machine learning algorithms. An approach of quantum machine learning named quantum ensembles of quantum classifiers consists of using superposition to build an exponentially large ensemble of classifiers to be trained with an optimization-free learning algorithm. In this work, we investigate how the quantum ensemble works with the addition of an optimization method. Experiments using benchmark datasets show the improvements obtained with the addition of the optimization step.Through superposition, a quantum computer is capable of representing an exponentially large set of states, according to the number of qubits available. Quantum machine learning is a subfield of quantum computing that explores the potential of quantum computing to enhance machine learning algorithms. An approach of quantum machine learning named quantum ensembles of quantum classifiers consists of using superposition to build an exponentially large ensemble of classifiers to be trained with an optimization-free learning algorithm. In this work, we investigate how the quantum ensemble works with the addition of an optimization method. Experiments using benchmark datasets show the improvements obtained with the addition of the optimization step.

arXiv:2007.09293International Joint Conference on Neural Networks (IJCNN)Jul 1, 202013 citations

On quantum ensembles of quantum classifiers

Abbas, Amira, Maria Schuld, Francesco Petruccione

Quantum machine learning seeks to exploit the underlying nature of a quantum computer to enhance machine learning techniques. A particular framework uses the quantum property of superposition to store sets of parameters, thereby creating an ensemble of quantum classifiers that may be computed in parallel. The idea stems from classical ensemble methods where one attempts to build a stronger model by averaging the results from many different models. In this work, we demonstrate that a specific implementation of the quantum ensemble of quantum classifiers, called the accuracy-weighted quantum ensemble, can be fully dequantised. On the other hand, the general quantum ensemble framework is shown to contain the well-known Deutsch-Jozsa algorithm that notably provides a quantum speedup and creates the potential for a useful quantum ensemble to harness this computational advantage.Quantum machine learning seeks to exploit the underlying nature of a quantum computer to enhance machine learning techniques. A particular framework uses the quantum property of superposition to store sets of parameters, thereby creating an ensemble of quantum classifiers that may be computed in parallel. The idea stems from classical ensemble methods where one attempts to build a stronger model by averaging the results from many different models. In this work, we demonstrate that a specific implementation of the quantum ensemble of quantum classifiers, called the accuracy-weighted quantum ensemble, can be fully dequantised. On the other hand, the general quantum ensemble framework is shown to contain the well-known Deutsch-Jozsa algorithm that notably provides a quantum speedup and creates the potential for a useful quantum ensemble to harness this computational advantage.

arXiv:2001.10833Jan 29, 20201 citation

B

transformations of the quantum state which encodes the training set in only

log\left(B\right)

operations. This implies exponential growth of the ensemble size while increasing linearly the depth of the correspondent circuit. Furthermore, when considering the overall cost of the algorithm, we show that the training of a single weak classifier impacts additively the overall time complexity rather than multiplicatively, as it usually happens in classical ensemble methods. We also present small-scale experiments on real-world datasets, defining a quantum version of the cosine classifier and using the IBM qiskit environment to show how the algorithms work.