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

• URL: http://arxiv.org/abs/2410.22084v3
• Date: Wed, 29 Oct 2025 19:15:37 GMT
• Title: Quantum Circuits, Feature Maps, and Expanded Pseudo-Entropy: Analysis of Encoding Real-World Data into a Quantum Computer
• Authors: Andrew Vlasic, Payal Solanki, Anh Pham,
• Abstract summary: The technique analyzes quantum operators, through an extension of the functions of von Neumann entropy and state-transition pseudo-entropy.<n>The characteristics of a class of quantum feature maps are rigorously shown.
• Score: 0.8493762124830675
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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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