Quantum-Inspired Linear Regression

This repository implements a quantum-inspired linear regression algorithm, blending ideas from quantum mechanics with gradient descent to overcome optimization challenges like local minima.

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🚀 Features

• Superposition of States: Explores multiple parameter vectors in parallel.
• Quantum Tunneling: Adds controlled random noise to escape stagnation.
• Memory Bank: Stores and reuses high-performing models based on cost.
• Java Implementation: Pure Java with no external libraries required.
• Human-Readable Documentation: Includes both code and theory in a structured way.

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🧪 How It Works

The core idea is to simulate two key quantum concepts:

1. Superposition

Instead of training just one parameter vector θ, we train N of them simultaneously. Each evolves separately using gradient descent.

2. Quantum Tunneling

If a state stagnates (its cost doesn't improve), we inject a small amount of random noise:

double noise = (Math.random() * 2 - 1) * scale;

This lets the model escape bad local minima, just like a quantum particle can tunnel through a potential barrier.

3. Memory Bank

We save the best parameter states so far, with their amplitude (probability of reuse) proportional to 1 / cost.

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🧠 Core Components

File	Role
gradientdescent.java	Main optimization logic + one-step update method
QuantumEnhancedTrainer.java	Quantum-inspired training loop w/ noise + memory
MemoryBank.java	Stores best parameter vectors with their cost
prediction.java	Predicts y = w·x + b
costcalculator.java	Computes cost using MSE formula
Main.java	Uses hardcoded training data to run both optimizers

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🏁 How to Run

1. Open the project

   Make sure you are in the root folder of the project.

2. Compile and run

javac src/*.java
java -cp src Main

This will output weights and bias found by:

• Traditional Gradient Descent
• Quantum-Enhanced Optimization

⚠️ Note: The training data is already provided inside Main.java as an array. You don't need to load from a CSV.

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🔬 Quantum Enhancements in Simple Terms

• Superposition: Keeps N parameter vectors {θ₁, θ₂, ..., θₙ} and trains them in parallel.
• Amplitude-Based Selection: Best-performing vectors are reused more often: P(θᵢ) ∝ 1 / J(θᵢ)
• Tunneling: If a state gets stuck, we let it jump randomly by adding noise:

double noise = (Math.random() * 2 - 1) * scale;

This keeps the model exploring new possibilities even when some solutions are trapped.

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📘 Learn More

Check out QuantumInspiredLinearRegression.pdf for:

• Core quantum mechanics principles (superposition, tunneling)
• Why traditional gradient descent can get stuck
• How this project uses physics ideas to improve ML training

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🤝 Contribute

Suggestions, issues, or pull requests are always welcome!