Von Neumann entropy vs AlgoBubbles

This app represents von Neumann entropy for density matrix. The density matrix represents the mixed states of two states.

Algorithms become easier when you can see every step. AlgoBubbles turns 33 computer-science algorithms into clear, interactive animations. Move forward or backward one step at a time, play the full sequence, and understand what each comparison, swap, or graph visit means. LEARN WITH CONTEXT • Compare best, average, and worst-case time complexity • See space complexity and practical use cases • Read clear explanations for every animation step • View implementation code in Swift, Python, and JavaScript BUILD REAL PROGRESS • Search the full algorithm catalog • Track completion by category and across the app • Learn through Arabic or English with full RTL support • Start with a short, value-first onboarding guide • Continue learning offline without creating an account EXPLORE 33 ALGORITHMS Sorting, searching, graph traversal and shortest paths, data structures, string matching, dynamic programming, cryptography, and divide-and-conquer techniques. Four algorithms are free. A single optional premium purchase unlocks the remaining 29 algorithms and removes ads—no subscription. Download AlgoBubbles and turn abstract algorithms into visible, understandable steps.