Quantum Circuits, Feature Maps, and Expanded Pseudo-Entropy: Analysis of Encoding Real-World Data into a Quantum Computer
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| 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 |