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 ).
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 ).
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(B) 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.
Abstract In this work, we present our experiment’s results where we simulate the quantum amplitude amplification algorithm for a prediction problem. The problem is to calculate the total probability of a good class by an ensemble model. Theoretically, the quantum prediction will be quadratically faster than a classical prediction. We need to get outputs (probabilities of the good class) of all classifiers. After that, by summation the probabilities the ensemble model returns the total probability of the good class for an input object. Let us demonstrate how the quantum amplitude amplification algorithm allows us to estimate the total probability. In this experiment, we count an iterations number of quantum search running to estimate the total probability.
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 Machine learning can make predictions on unseen data by extracting information and constructing algorithms and statistical models from the training data, which is highly desirable for speech recognition and computer vision. Quantum computing harnesses the phenomena of quantum mechanics realizing parallel computing, which could solve certain computational problems, such as RSA encryption significantly faster than classical computers. Quantum machine learning is reasonable to enable machine learning faster than that of classical computers by utilizing quantum operations. Binary classification is a typical quantum machine learning task applied to single qubits. Here we present a binary classifier for regions. Firstly, we sample two sets of quantum data points located in the X-Z plane of the Bloch sphere randomly. Then we utilize a single parameterized rotation gate and measure the qubits along the Z axis. We train the hybrid model combined by quantum mdoel and classical Neutral network and regard the corss entropy the predictions of the classical Netural network and labels as the loss function. Based on the above, we present the results of the trained hybrid model to classify new quantum qubits.
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.
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.