Quantum Circuits, Feature Maps, and Expanded Pseudo-Entropy: Analysis of Encoding Real-World Data into a Quantum Computer

Andrew Vlasic; Payal Solanki; Anh Pham

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arXiv · 2410.22084

Quantum Circuits, Feature Maps, and Expanded Pseudo-Entropy: Analysis of Encoding Real-World Data into a Quantum Computer

Andrew Vlasic·Payal Solanki·Anh Pham

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Abstract

This manuscript introduces a computationally efficient method to calculate the nonlinearity of a quantum feature map, as well as a method for determining whether a quantum feature map will have a high concentration of quantum states. The technique analyzes quantum operators, through an extension of the functions of von Neumann entropy and state-transition pseudo-entropy, by deriving a method to extract the entropy of an operator. The technique is denoted as operator pseudo-entropy, is rigorously derived, and is generally complex valued; as with state-transition pseudo-entropy, complex values contain a lot of information about entanglement or nonlinearity. The characteristics of a class of quantum feature maps are rigorously shown. The operator pseudo-entropy is illuminated through experiments and compared with von Neumann entropy and state-transition pseudo-entropy. We end the manuscript with open questions and potential directions for further research.

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Andrew Vlasic, Payal Solanki, Anh Pham. 2025-10-29. Quantum Circuits, Feature Maps, and Expanded Pseudo-Entropy: Analysis of Encoding Real-World Data into a Quantum Computer. https://arxiv.org/abs/2410.22084

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