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Academician O.B. Lupanov International Scientific Seminar "Discrete Mathematics and Its Applications"

Quantum simulator experiment for binary classification prognostication via ensemble methods

Kamil Ravilevich Khadiev, Liliya Safina

Published Jan 1, 2022• 0 citations
Publisher

Abstract

In this work, we conducted an experiment on a quantum simulator for tasks of binary classification by the random forest method, estimated the time the complexity of the classical and quantum versions of the algorithms, as well as memory complexity of the algorithm for the quantum version. Previously we received temporal acceleration of the algorithm for prediction by using quantum amplitude amplification algorithm, and now tested the algorithm proposed by us on our quantum simulator and analyzed the predictive results.

DOI
10.20948/dms-2022-26

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In this work, we conducted an experiment on a quantum simulator for tasks of binary classification by the random forest method, estimated the time the complexity of the classical and quantum versions of the algorithms, as well as memory complexity of the algorithm for the quantum version. Previously we received temporal acceleration of the algorithm for prediction by using quantum amplitude amplification algorithm, and now tested the algorithm proposed by us on our quantum simulator and analyzed the predictive results.
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.
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 present a quantum circuit for a binary classification prediction algorithm using a random forest model. The quantum prediction algorithm is presented in our previous works. We construct a circuit and implement it using qiskit tools (python module for quantum programming). One of our goals is reducing the number of basic quantum gates (elementary gates). The set of basic quantum gates which we use in this work consists of single-qubit gates and a controlled NOT gate. The number of CNOT gates in our circuit is estimated by O(2n+2h+1)O{\text{(}}{{2}^{{n{\kern 1pt} + {\kern 1pt} 2h{\kern 1pt} + {\kern 1pt} 1}}}{\text{)}}O(2n+2h+1) , when trivial circuit decomposition techniques give O(4∣X∣+n+h+2)O({{4}^{{\left| X \right|{\kern 1pt} + {\kern 1pt} n{\kern 1pt} + {\kern 1pt} h{\kern 1pt} + {\kern 1pt} 2}}})O(4∣X∣+n+h+2) CNOT gates, where nnn is the number of trees in a random forest model, hhh is a tree height and ∣X∣\left| X \right|∣X∣ is the length of attributes of an input object XXX . The prediction process returns an index of the corresponding class for the input XXX .
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 BBB transformations of the quantum state which encodes the training set in only log(B)log\left(B\right)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 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.
In this work, we studied the use of Quantum Machine Learning (QML) algorithms for binary classification and compared their performance with classical Machine Learning (ML) methods. QML merges principles of Quantum Computing (QC) and ML, offering improved efficiency and potential quantum advantage in data-driven tasks and when solving complex problems. In binary classification, where the goal is to assign data to one of two categories, QML uses quantum algorithms to process large datasets efficiently. Quantum algorithms like Quantum Support Vector Machines (QSVM) and Quantum Neural Networks (QNN) exploit quantum parallelism and entanglement to enhance performance over classical methods. This study focuses on two common QML algorithms, Quantum Support Vector Classifier (QSVC) and QNN. We used the Qiskit software and conducted the experiments with three different datasets. Data preprocessing included dimensionality reduction using Principal Component Analysis (PCA) and standardization using scalers. The results showed that quantum algorithms demonstrated competitive performance against their classical counterparts in terms of accuracy, while QSVC performed better than QNN. These findings suggest that QML holds potential for improving computational efficiency in binary classification tasks. This opens the way for more efficient and scalable solutions in complex classification challenges and shows the complementary role of quantum computing.