https://github.com/syedt1/qsvm_t4

https://github.com/syedt1/qsvm_t4

Last synced: 8 months ago
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• Host: GitHub
• URL: https://github.com/syedt1/qsvm_t4
• Owner: SyedT1
• Created: 2025-10-11T15:22:57.000Z (8 months ago)
• Default Branch: main
• Last Pushed: 2025-10-19T06:12:43.000Z (8 months ago)
• Last Synced: 2025-10-19T18:12:07.351Z (8 months ago)
• Language: Jupyter Notebook
• Size: 90.8 KB
• Stars: 0
• Watchers: 0
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

          
# QSVM_T4

## 1. Alternating Entanglement Feature Map (AEFM)

### Circuit Structure (2 layers):

- **Initial encoding:**

  $$R_{y}(x_1) \otimes R_{y}(x_2)$$

- **Layer 1:**

  - $$R_{y}(x_1) \otimes R_{y}(x_2)$$

  - $$\mathrm{CNOT}_{0\to1}$$

  - $$R_{z}(x_1) \otimes R_{z}(x_2)$$

  - $$\mathrm{CNOT}_{1\to0}$$

- **Layer 2:**

  - $$R_{y}(x_1) \otimes R_{y}(x_2)$$

  - $$\mathrm{CNOT}_{0\to1}$$

  - $$R_{z}(x_1) \otimes R_{z}(x_2)$$

  - $$\mathrm{CNOT}_{1\to0}$$

### Quantum Feature State:

$$|\phi_\text{AEFM}(x)\rangle = U_\text{AEFM}(x)|00\rangle$$

### Kernel Function:

$$k_\text{AEFM}(\mathbf{x}, \mathbf{x'}) = |\langle\phi_\text{AEFM}(\mathbf{x})|\phi_\text{AEFM}(\mathbf{x'})\rangle|^2$$

## 2. Strongly Entangling Feature Map with Hadamard (SEFM-H)

### Circuit Structure (3 identical layers):

- **Initial encoding:**

  $$R_{y}(x_1) \otimes R_{y}(x_2)$$

- **Each layer ℓ = 1,2,3:**

  - $$H \otimes H$$

  - $$R_{y}(x_1) \otimes R_{y}(x_2)$$

  - $$\mathrm{CNOT}_{0\to1}$$

  - $$R_{z}(x_1) \otimes R_{z}(x_2)$$

### Quantum Feature State:

$$|\phi_\text{SEFM-H}(x)\rangle = U_\text{SEFM-H}(x)|00\rangle$$

### Kernel Function:

$$k_\text{SEFM-H}(\mathbf{x}, \mathbf{x'}) = |\langle\phi_\text{SEFM-H}(\mathbf{x})|\phi_\text{SEFM-H}(\mathbf{x'})\rangle|^2$$