Summary

Quantum Bogo Sort is a thought experiment in algorithm design based on the many-worlds interpretation of quantum mechanics. It operates under the assumption that for any random event, all possible outcomes occur in separate, newly created universes. The algorithm uses a quantum source of entropy to generate one random permutation. If that permutation is sorted, the algorithm succeeds. If not, it triggers the destruction of its own universe. Consequently, the only universes that survive are those in which the list was successfully sorted on the first try.

How it Works

• 1. Quantum Permutation: Generate a single, random permutation of the input list using a quantum source of entropy. This happens in a single pass.

• 2. Check Order: Check if the list is sorted. This takes $O(n)$ time.

• 3. Universal Fate: If the list is sorted, the algorithm terminates successfully. If not, the universe is destroyed. From the perspective of an observer in a surviving universe, the sort appears to be instantaneous and always successful.