Quantum-Circuit-Based Visual Fractal Image Generation in Qiskit and Analytics

Abstract: As nature is ascribed as quantum, the fractals also pose some intriguing appearance which is found in many micro and macro observable entities or phenomena. Fractals show self-similarity across sizes; structures that resemble the entire are revealed when zoomed in. In Quantum systems, the probability density or wavefunction may exhibit recurring interference patterns at various energy or length scales. Fractals are produced by basic iterative rules (such as Mandelbrot or Julia sets), and they provide limitless complexity. Despite its simplicity, the Schr\"odinger equation in quantum mechanics produces incredibly intricate patterns of interference and entanglement, particularly in chaotic quantum systems. Quantum computing, the root where lies to the using the principles of quantum-mechanical phenomenon, when applied in fractal image generation, what outcomes are expected? The paper outlines the generation of a Julia set dataset using an approach coupled with building quantum circuit, highlighting the concepts of superposition, randomness, and entanglement as foundational elements to manipulate the generated dataset patterns. As Quantum computing is finding many application areas, the possibility of using quantum circuits for fractal Julia image generation posits a unique direction of future research where it can be applied to quantum generative arts across various ecosystems with a customised approach, such as producing an exciting landscape based on a quantum art theme.