Quantum Time-Space Tradeoffs for Sorting
| dc.creator | Klauck, Hartmut | |
| dc.date | 2002-11-26 | |
| dc.date | 2003-05-22 | |
| dc.date.accessioned | 2026-07-07T06:05:36Z | |
| dc.date.available | 2026-07-07T06:05:36Z | |
| dc.description | We investigate the complexity of sorting in the model of sequential quantum circuits. While it is known that in general a quantum algorithm based on comparisons alone cannot outperform classical sorting algorithms by more than a constant factor in time complexity, this is wrong in a space bounded setting. We observe that for all storage bounds n/\log n\ge S\ge \log^3 n, one can devise a quantum algorithm that sorts n numbers (using comparisons only) in time T=O(n^{3/2}\log^{3/2} n/\sqrt S). We then show the following lower bound on the time-space tradeoff for sorting $n$ numbers from a polynomial size range in a general sorting algorithm (not necessarily based on comparisons): TS=Ω(n^{3/2}). Hence for small values of S the upper bound is almost tight. Classically the time-space tradeoff for sorting is TS=Θ(n^2). | |
| dc.description | 17 pages, appears in STOC '03 | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0211174 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0211174 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/90690 | |
| dc.subject | Quantum Physics | |
| dc.subject | Computational Complexity | |
| dc.title | Quantum Time-Space Tradeoffs for Sorting | |
| dc.type | text |