An efficient geometric approach to quantum-inspired classifications

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.

Quantum-Inspired Applications for Classification Problems

“…Nevertheless the quantum encoding can be realized in terms of the Bloch vectors saving space resources. The improvement of memory occupation within the Bloch representation is evident when we take multiple tensor products of a density matrix constructing a feature map to enlarge the dimension of the representation space [ 1 ].…”

“…It has revealed how such algorithms have the potential to provide benefits in spite of lacking the computational power of quantum computers with several qubits. Some of these binary classifiers have been analyzed from a geometric perspective [ 1 ]. In this work, we implement some 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.…”

A Quantum LSTM Based Approach to Cyber Threat Detection in Virtual Environment

“…Quantum Information Processing (QIP) is expected to supplement classical computing by bringing efficiencies afforded by quantum phenomena [8]. The Quantum Inspired methods have been successful in many ML areas such as classification [9,10]. And while the progress in the development of quantum computers and associated technology had been relatively slow in the 1990s and 2000s, the last decade has witnessed explosive growth in the field, both in terms of the hardware platforms from IBM [11], D-Wave [12], Rigetti [13], and others, and also from algorithmic and framework development initiatives such as IBM Qiskit [11], Xanadu PennyLane [14], Google Cirq [15] etc.…”

Quantum-Inspired Classification Based on Voronoi Tessellation and Pretty-Good Measurements

“…Classification with quantum computers is a widely investigated topic (e.g., [1][2][3]), but the quantum-inspired paradigm can also be applied. Some quantum-inspired classification algorithms based on a geometric approach have recently been presented in [4] and compared with well-known classical methods.…”

“…More precisely, we consider a Vonoroi-type tessellation of the dataset proposed in [5] to classify an unlabeled instance without considering the entire dataset but, instead, only a neighborhood of the test point. Therefore, the present proposal involves investigation that goes beyond the quantum-inspired classifiers studied in [4]. Here, we integrate the geometric approach to classification based on quantum discrimination with a local strategy that has been successfully applied in [5], but which has also been suggested as a promising path to improve classification in less recent proposals, such as [6].…”