A quantum sort is any sorting algorithm that runs on a

quantum computer Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...

. Any comparison-based quantum sorting algorithm would take at least

\Omega(n \log n)

steps, which is already achievable by classical algorithms. Thus, for this task, quantum computers are no better than classical ones, and should be disregarded when it comes to time complexity. However, in space-bounded sorts, quantum algorithms outperform their classical counterparts.

References

Sorting algorithms Quantum algorithms {{comp-sci-theory-stub