Quantum sort

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

References

^ H?yer, P.; Neerbek, J.; Shi, Y. (2001). "Quantum complexities of ordered searching, sorting, and element distinctness". 28th International Colloquium on Automata, Languages, and Programming. Lecture Notes in Computer Science. Vol. 2076. pp. 62–73. arXiv:quant-ph/0102078. doi:10.1007/3-540-48224-5_29. ISBN 978-3-540-42287-7.
^ Klauck, Hartmut (2003). "Quantum Time-Space Tradeoffs for Sorting". Proceedings of the thirty-fifth annual ACM symposium on Theory of computing. p. 69. arXiv:quant-ph/0211174. doi:10.1145/780542.780553. ISBN 1581136749.

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[1] H?yer, P.; Neerbek, J.; Shi, Y. (2001). "Quantum complexities of ordered searching, sorting, and element distinctness". 28th International Colloquium on Automata, Languages, and Programming. Lecture Notes in Computer Science. Vol. 2076. pp. 62–73. arXiv:quant-ph/0102078. doi:10.1007/3-540-48224-5_29. ISBN 978-3-540-42287-7.

[2] Klauck, Hartmut (2003). "Quantum Time-Space Tradeoffs for Sorting". Proceedings of the thirty-fifth annual ACM symposium on Theory of computing. p. 69. arXiv:quant-ph/0211174. doi:10.1145/780542.780553. ISBN 1581136749.

[1]

[2]

v t e Sorting algorithms
Theory	Computational complexity theory Big O notation Total order Lists Inplacement Stability Comparison sort Adaptive sort Sorting network Integer sorting X + Y sorting Transdichotomous model Quantum sort
Exchange sorts	Bubble sort Cocktail shaker sort Odd–even sort Comb sort Gnome sort Proportion extend sort Quicksort
Selection sorts	Selection sort Heapsort Smoothsort Cartesian tree sort Tournament sort Cycle sort Weak-heap sort
Insertion sorts	Insertion sort Shellsort Splaysort Tree sort Library sort Patience sorting
Merge sorts	Merge sort Cascade merge sort Oscillating merge sort Polyphase merge sort
Distribution sorts	American flag sort Bead sort Bucket sort Burstsort Counting sort Interpolation sort Pigeonhole sort Proxmap sort Radix sort Flashsort
Concurrent sorts	Bitonic sorter Batcher odd–even mergesort Pairwise sorting network Samplesort
Hybrid sorts	Block merge sort Introsort Kirkpatrick–Reisch sort Merge-insertion sort Powersort Timsort Spreadsort
Other	Topological sorting Pre-topological order Pancake sorting Spaghetti sort
Impractical sorts	Stooge sort Slowsort Bogosort Stalin sort

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