A new quantum approach to binary classification

Abstract

This paper proposes a new quantum-like method for the binary classification applied to classical datasets. Inspired by the quantum Helstrom measurement, this innovative approach has enabled us to define a new classifier, called Helstrom Quantum Centroid (HQC). This binary classifier (inspired by the concept of distinguishability between quantum states) acts on density matrices—called density patterns —that are the quantum encoding of classical patterns of a dataset. In this paper we compare the performance of HQC with respect to twelve standard (linear and non-linear) classifiers over fourteen different datasets. The experimental results show that HQC outperforms the other classifiers when compared to the Balanced Accuracy and other statistical measures. Finally, we show that the performance of our classifier is positively correlated to the increase in the number of “quantum copies” of a pattern and the resulting tensor product thereof.

A quantum-inspired classifier for clonogenic assay evaluations

“…The idea for this procedure originates from quantum information theory where—unlike in the classical case—taking copies of a given state provides additional information with respect to the initial state. In particular, considering more copies of the states can increase the probability of providing a correct discrimination between two quantum states 6 . Let us remark how this is relevant because it suggests that the performance of the HQC could be, in principle, improved by increasing the number of the copies for each density pattern obtained from the initial dataset.…”

“…The last hyperparameter was represented by two types of class weights assigned to the two quantum centroids in the HQC. The first type, called equiprobable, assigns equal weights of 1/2 to both of the two quantum centroids; the second type, called weighted, assigns to each centroid a weight which is proportional to the cardinality of the respective classes 6 . The pre-processing and hypertuning steps are outlined in Fig.…”

“…Moreover, recent progress made in the direction of producing real quantum computers suggested the combination between machine learning and quantum computing as a natural connection. However, the discussion involving real quantum computers is not the only way to exploit the properties of quantum theory at the service of machine learning; recent works showed that quantum information can inspire new ways to design machine learning algorithms without requiring the use of quantum computers 6 , 7 . In other words, it is possible to develop classical algorithms that are inspired by quantum information.…”

“…Recently, promising results from QiML have shown to efficiently solve different kinds of classification problems, i.e., the problem of assigning each object of a given dataset to a membership class 9 . In particular, the work 6 proposed a QiML technique for binary classification inspired by the theory of quantum state discrimination 10 , whereby the idea was in that discrimination between quantum states produces a very efficient classification process. The authors compared the QiML algorithm—called the Helstrom Quantum Classifier (HQC)—with other commonly used classifiers, by applying these classifiers to several conventional machine learning repository datasets, and they had obtained results which showed an average supremacy of the HQC compared to the other classifiers.…”

Real-time calibration of coherent-state receivers: Learning by trial and error

“…Quantum state discrimination (QSD) is the problem of determining the state of a quantum system among a set of possible candidates. It constitutes a fundamental primitive in quantum information processing, with applications ranging from long-distance communication [1][2][3][4][5][6][7][8][9], cryptography [10][11][12][13][14][15][16][17], and, recently, quantum machine learning [18][19][20][21][22][23][24][25][26].…”