# Quantum sort

A quantum sort is any sorting algorithm that runs on a quantum computer. Any comparison-based quantum sorting algorithm would take at least ${\displaystyle \Omega (n\log n)}$ steps,[1] which is already achievable by classical algorithms. Thus, for this task, quantum computers are no better than classical ones. However, in space-bounded sorts, quantum algorithms outperform their classical counterparts.[2]

## References

1. ^ P. Høyer; J. Neerbek; Y. Shi (2001). "Quantum complexities of ordered searching, sorting, and element distinctness". 28th International Colloquium on Automata, Languages, and Programming. pp. 62–73. Also in quant-ph/0102078
2. ^ Klauck, Hartmut (2003). "Quantum Time-Space Tradeoffs for Sorting". Proceedings of the thirty-fifth annual ACM symposium on Theory of computing.