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projects:quantum:hawking-projector [2025/03/31 09:06] – created kymkiprojects:quantum:hawking-projector [2025/04/30 09:28] (current) – kymki
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-# Black Hole Mechanics in Quantum Image Compression+<html> 
 +<head> 
 +  <meta charset="UTF-8"> 
 +  <meta name="viewport" content="width=device-width, initial-scale=1.0"> 
 +  <title>Ramble Meter</title> 
 +  <style> 
 +    /* Container for the entire Ramble Meter */ 
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 +      display: flex; 
 +      align-items: center; 
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-## Hawking Radiation and Information Theory +    /* Ramble Meter */ 
-The `HawkingProjector` class uses black hole physics as inspiration for quantum data compression. The fundamental concept relates to how information behaves near a black hole's event horizon, particularly drawing from Hawking radiation theory.+    .ramble-meter { 
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 +      const needle = document.querySelector(".needle"); 
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 +      const level = rambleMeter.getAttribute("data-level"); // Read the level from the attribute (0-100) 
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 +<body> 
 +  <!-- Ramble Meter --> 
 +  <div class="ramble-meter-container"> 
 +    <div class="ramble-wrapper"> 
 +      <div class="ramble-meter" data-level="90"> <!-- Adjust level here (0-100) --> 
 +        <div class="meter-label">Ramble Meter</div> 
 +        <div class="needle"></div> 
 +      </div> 
 +      <div class="tooltip">Warning: this post is under construction and is very speculative </div> 
 +    </div> 
 +  </div> 
 +</body> 
 +</html> 
 + 
 + 
 + 
 +==== Black Hole Mechanics in Quantum Image Compression ==== 
 + 
 +=== Hawking Radiation and Information Theory === 
 +The Hawking Projector uses black hole physics as inspiration for quantum data compression. The fundamental concept relates to how information behaves near a black hole's event horizon, particularly drawing from Hawking radiation theory.
  
 $$ $$
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 Where $\mathcal{H}(\rho)$ represents the von Neumann entropy of a quantum state $\rho$, analogous to the entropy of a black hole. Where $\mathcal{H}(\rho)$ represents the von Neumann entropy of a quantum state $\rho$, analogous to the entropy of a black hole.
  
-## Black Hole Information Paradox +=== Black Hole Information Paradox === 
-The compression algorithm draws inspiration from the black hole information paradox, where information that falls into a black hole appears to be lost but is theoretically preserved in a scrambled form. In the code, this is implemented as:+The compression algorithm addresses concepts from the black hole information paradox, which presents a fundamental conflict between quantum mechanics and general relativity. According to quantum mechanics, information cannot be destroyed (quantum unitarity), while general relativity suggests that information crossing the event horizon becomes permanently inaccessible to outside observers.
  
-$$ +Stephen Hawking proposed that information is preserved through quantum entanglement between the radiation emitted from black holes and the interior matter. This quantum information scrambling transforms but conserves the information in a highly complex encoded form rather than destroying it.
-\text{entropy} = -\sum_{i} p_i \log_2(p_i) +
-$$+
  
-This is calculated in the `analyze_entropy` method, which computes the Shannon entropy as an approximation of von Neumann entropy.+The algorithm implements this principle by computing quantum state entropy:
  
-## Quantum Circuit Encoding+$ 
 +S  = -\sum_{i} p_i \log_2(p_i) 
 +$ 
 + 
 +Where $p_i$ represents the probability of measuring the quantum system in state $i$. 
 + 
 +The Shannon entropy is then calculated as a mathematical approximation of the von Neumann entropy ($S(\rho) = -\text{Tr}(\rho\log\rho)$), which quantifies quantum information content. This entropy calculation measures how distributed the information becomes across different quantum states after applying the compression transformations, analogous to how black holes distribute information across radiation and interior degrees of freedom. 
 + 
 +=== Quantum Circuit Encoding ===
 The encoding process uses quantum circuits that preserve structural information, similar to how information might be encoded on a black hole's event horizon: The encoding process uses quantum circuits that preserve structural information, similar to how information might be encoded on a black hole's event horizon:
  
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 Where $|\psi\rangle$ is the quantum state representing encoded image data, and $\alpha_i$ are complex amplitudes. Where $|\psi\rangle$ is the quantum state representing encoded image data, and $\alpha_i$ are complex amplitudes.
  
-## Holographic Principle +=== Holographic Principle === 
-The `create_quantum_circuit` method implements a form of the holographic principle, where the information content of a region is encoded on its boundary:+A form of the holographic principle is implemented, where the information content of a region is encoded on its boundary:
  
 $$ $$
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 $$ $$
  
-This equation from black hole thermodynamics relates entropy ($S$) to the area ($A$) of the event horizon. In the code, this manifests as spatial locality preservation in the quantum encoding:+This equation from black hole thermodynamics relates entropy ($S$) to the area ($A$) of the event horizon. In the code, this is implemented as spatial locality preservation in the quantum encoding:
  
-``` +''sqrt_n = int(np.sqrt(self.num_qubits))''
-# Custom entanglement pattern that preserves locality +
-sqrt_n = int(np.sqrt(self.num_qubits)) +
-```+
  
-## Information Scrambling with Controlled Rotation+=== Information Scrambling with Controlled Rotation ===
 The quantum circuits use controlled rotation gates to simulate the scrambling of information that occurs near a black hole: The quantum circuits use controlled rotation gates to simulate the scrambling of information that occurs near a black hole:
  
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 ``` ```
  
-## Weighted Reconstruction Model+=== Weighted Reconstruction Model ===
 The reconstruction algorithm uses a weighted combination of quantum states, inspired by how information might be retrieved from Hawking radiation: The reconstruction algorithm uses a weighted combination of quantum states, inspired by how information might be retrieved from Hawking radiation:
  
 $$ $$
-\text{reconstructed\_bit}_i = \begin{cases} +\text{reconstructed\_bit}_i = \begin{cases}
 1 & \text{if } \sum_{j} p_j \cdot \text{bit}_j^i \geq \text{threshold} \\ 1 & \text{if } \sum_{j} p_j \cdot \text{bit}_j^i \geq \text{threshold} \\
 0 & \text{otherwise} 0 & \text{otherwise}
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 Where $p_j$ are the probabilities of different quantum states, and $\text{bit}_j^i$ is the $i$-th bit of the $j$-th state. Where $p_j$ are the probabilities of different quantum states, and $\text{bit}_j^i$ is the $i$-th bit of the $j$-th state.
  
-## Entropy Ratio Analysis+=== Entropy Ratio Analysis ===
 The code calculates an entropy ratio that measures how close the system is to maximum entropy: The code calculates an entropy ratio that measures how close the system is to maximum entropy:
  
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 Where $n$ is the number of qubits. This relates to the idea that black holes represent maximum entropy configurations. Where $n$ is the number of qubits. This relates to the idea that black holes represent maximum entropy configurations.
  
-## Context-Aware Reconstruction+=== Context-Aware Reconstruction ===
 The spatial relationships in the image are preserved using a context-aware reconstruction method that treats adjacent blocks as entangled systems: The spatial relationships in the image are preserved using a context-aware reconstruction method that treats adjacent blocks as entangled systems:
  
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 This is implemented in the `reconstruct_with_context` method. This is implemented in the `reconstruct_with_context` method.
  
-## Performance Metrics Inspired by Black Hole Physics+=== Performance Metrics Inspired by Black Hole Physics ===
 The reinforcement learning environment uses a reward function that incorporates metrics inspired by black hole information theory: The reinforcement learning environment uses a reward function that incorporates metrics inspired by black hole information theory:
  
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 These metrics measure how well the information is preserved through the compression and reconstruction process, similar to how information might theoretically be preserved despite passing through a black hole. These metrics measure how well the information is preserved through the compression and reconstruction process, similar to how information might theoretically be preserved despite passing through a black hole.
 +