Quantum Interference project submission for #unitaryDesign

QuantumInterference.md

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+![Quantum Interference Logo](https://quantuminterference.netlify.app/interfence_logo_128.png)
+
+# Quantum Interference ⚛️ — Project Submission
+### Author
+Luis J Camargo
+### Live Demo  
+[https://quantuminterference.netlify.app/](https://quantuminterference.netlify.app/)
+### Repository  
+[https://github.com/ljcamargo/quantum_interference](https://github.com/ljcamargo/quantum_interference)
+
+**Quantum Interference** is a generative art experiment that artistically portrays the interference patterns of quantum mechanics from a quantum computing perspective. Built for the **#UnitaryDESIGN** hackathon for project **"QuantumBrush"**.
+
+## 🚀 Overview
+The application simulates a quantum system with $n$ qubits. Users can manipulate the state of the system by injecting quantum gates (H, X, S, T, CNOT, CCNOT) and observe the resulting probability amplitude field as a beautiful, evolving interference pattern.
+
+## 📡 The Algorithm: StateVector to Image
+The visualizer maps purely mathematical quantum states into a physical wave interference field:
+
+1. **Source Mapping**: Each of the $2^n$ computational basis states ($|00...0\rangle$ to $|11...1\rangle$) is mapped to a spatial coordinate $\mathbf{r}_i$ arranged in a circular formation.
+2. **Wave Emission**: Each state acts as a point source emitting a wave. The "strength" of the source is determined by its **Probability Amplitude** $c_i$:
+   - **Amplitude magnitude ($|c_i|$)**: Controls the wave's peak intensity.
+   - **Amplitude phase ($\phi_i$)**: Controls the wave's phase shift.
+3. **Interference Calculation**: For every pixel $\mathbf{r}$ on the canvas, the total wave function $\Psi$ is the complex sum of all contributions:
+   $$\Psi(\mathbf{r}, t) = \sum_{i} |c_i| e^{j(k|\mathbf{r} - \mathbf{r}_i| - \omega t - \phi_i)}$$
+4. **Rendering**: The final pixel intensity is calculated as $I = |\Psi|^2$. This intensity is mapped to a matrix-inspired color gradient (Deep Dark to Neon Green) and rendered in real-time.
+
+## 🎨 Controls
+- **Qubits**: Scale the complexity of the Hilbert space.
+- **Wave Dynamics**: Adjust the Wave Number ($k$) for spatial frequency and Frequency ($\omega$) for temporal speed.
+- **Inject Gate**: Apply unitary transformations to perturb the field and create entanglement.
+- **Download**: Capture the current interference pattern as a high-resolution PNG.
+
+## 📚 References
+This project takes ideas on how to render the interference pattern from the work of:
+
+- Ruimy, R., Tziperman, O., Gorlach, A., Mølmer, K., & Kaminer, I. (2024). Many-body entanglement via ‘which-path’ information. *npj Quantum Information*, 10(1), 121. [https://doi.org/10.1038/s41534-024-00899-6](https://doi.org/10.1038/s41534-024-00899-6)
+- SSS Quantum. (n.d.). *What is Quantum Interference?* Medium. [https://medium.com/sss-quantum/what-is-quantum-interference-52d1d7fa0517](https://medium.com/sss-quantum/what-is-quantum-interference-52d1d7fa0517)
+
+## 📜 License
+MIT
+
+## ✒️​ Authorship
+Created by **Luis J Camargo** for the **#UnitaryDESIGN** hackathon.
+Copyleft 2026.
+
+---