Scientific Reports

An efficient geometric approach to quantum-inspired classifications

Roberto Leporini, Davide Pastorello

Published May 24, 2022• 7 citations

Abstract

Optimal measurements for the discrimination of quantum states are useful tools for classification problems. In order to exploit the potential of quantum computers, feature vectors have to be encoded into quantum states represented by density operators. However, quantum-inspired classifiers based on nearest mean and on Helstrom state discrimination are implemented on classical computers. We show a geometric approach that improves the efficiency of quantum-inspired classification in terms of space and time acting on quantum encoding and allows one to compare classifiers correctly in the presence of multiple preparations of the same quantum state as input. We also introduce the nearest mean classification based on Bures distance, Hellinger distance and Jensen-Shannon distance comparing the performance with respect to well-known classifiers applied to benchmark datasets.

DOI: 10.1038/s41598-022-12392-1

Related papers

Support Vector Machines with Quantum State Discrimination

Roberto Leporini, Davide Pastorello

We analyze possible connections between quantum-inspired classifications and support vector machines. Quantum state discrimination and optimal quantum measurement are useful tools for classification problems. In order to use these tools, feature vectors have to be encoded in quantum states represented by density operators. Classification algorithms inspired by quantum state discrimination and implemented on classic computers have been recently proposed. We focus on the implementation of a known quantum-inspired classifier based on Helstrom state discrimination showing its connection with support vector machines and how to make the classification more efficient in terms of space and time acting on quantum encoding. In some cases, traditional methods provide better results. Moreover, we discuss the quantum-inspired nearest mean classification.

Quantum ReportsAug 28, 20215 citations

Quantum-inspired classifiers

Roberto Leporini, Cesarino Bertini

Quantum-inspired machine learning is a new branch of machine learning based on the application of the mathematical formalism of quantum mechanics to devise novel algorithms for classical computers.We implement some quantum-inspired classification algorithms, based on quantum state discrimination, within a local approach in the feature space by taking into account elements close to the element to be classified.This local approach improves the accuracy in classification and motivates the integration with the classifiers.The quantum-inspired classifiers require the encoding of the feature vectors into density operators and methods for estimating the distinguishability of quantum states like the Helstrom state discrimination and the Pretty-Good measurement.We present a comparison of the performances of the local quantum-inspired classifiers against well-known classical algorithms in order to show that the local approach can be a valuable tool for increasing the performances of this kind of classifiers.

Computer Science Research NotesJan 1, 20250 citations

Quantum-Inspired Applications for Classification Problems

Cesarino Bertini, Roberto Leporini

In the context of quantum-inspired machine learning, quantum state discrimination is a useful tool for classification problems. We implement a local approach combining the k-nearest neighbors algorithm with some quantum-inspired classifiers. We compare the performance with respect to well-known classifiers applied to benchmark datasets.

EntropyFeb 23, 20233 citations

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, 20250 citations

A new quantum approach to binary classification

Giuseppe Sergioli, Roberto Giuntini, Héctor Freytes

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.

PLoS ONEMay 9, 201954 citations

Quantum-inspired classification via efficient simulation of Helstrom measurement

Wooseop Hwang, Daniel K. Park, Israel F. Araujo +1 more

The Helstrom measurement (HM) is known to be the optimal strategy for distinguishing non-orthogonal quantum states with minimum error. Previously, a binary classifier based on classical simulation of the HM has been proposed. It was observed that using multiple copies of the sample data reduced the classification error. Nevertheless, the exponential growth in simulation runtime hindered a comprehensive investigation of the relationship between the number of copies and classification performance. We present an efficient simulation method for an arbitrary number of copies by utilizing the relationship between HM and state fidelity. Our method reveals that the classification performance does not improve monotonically with the number of data copies. Instead, it needs to be treated as a hyperparameter subject to optimization, achievable only through the method proposed in this work. We present a Quantum-Inspired Machine Learning binary classifier with excellent performance, providing such empirical evidence by benchmarking on eight datasets and comparing it with 13 hyperparameter optimized standard classifiers.

arXiv:2403.15308Mar 22, 20240 citations