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

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Vlasic, Andrew, Solanki, Payal, Pham, Anh
Format: Preprint
Published: 2024
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866917049619447808
author Vlasic, Andrew
Solanki, Payal
Pham, Anh
author_facet Vlasic, Andrew
Solanki, Payal
Pham, Anh
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2410_22084
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Quantum Circuits, Feature Maps, and Expanded Pseudo-Entropy: Analysis of Encoding Real-World Data into a Quantum Computer
Vlasic, Andrew
Solanki, Payal
Pham, Anh
Quantum Physics
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.
title Quantum Circuits, Feature Maps, and Expanded Pseudo-Entropy: Analysis of Encoding Real-World Data into a Quantum Computer
topic Quantum Physics
url https://arxiv.org/abs/2410.22084