Abstract
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.
Highlights
Support vector machines are becoming popular in a wide variety of applications [1]
The logic behind the kernel function of an SVM and the kernel methods in general turns out to be rather similar to what is seen in quantum computing when one performs an encoding of classical data into quantum states
After an introduction on the Bloch representation of quantum states in an arbitrary dimension, we considered the Helstrom quantum state discrimination applied to binary classification, observing that its execution is similar to an SVM with linear kernel
Summary
Support vector machines are becoming popular in a wide variety of applications [1]. They are supervised learning models with associated algorithms (such as sub-gradient descent and coordinate descent) that analyze data for classification [2]. To handle multi-class with this binary classifier, there are different techniques: one against one, which constructs a classifier for each pair of classes, one against all, which builds one per class, hierarchical classification, which creates a tree, where the leaves correspond with the classes Another quantum-inspired supervised machine learning algorithm for multi-class classification based on so-called pretty good measurement has been proposed in [17], generalizing the Helstrom quantum state discrimination [18] that can be used for binary classification. Classification accuracy of this quantum-inspired multi-class classifier can be improved by increasing the number of copies of the quantum state that encodes the feature vector, at the cost of increasing the computational space and time.
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