A time-space tradeoff for element distinctness
SIAM Journal on Computing
A general sequential time-space tradeoff for finding unique elements
SIAM Journal on Computing
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Strengths and Weaknesses of Quantum Computing
SIAM Journal on Computing
Quantum circuits with mixed states
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Quantum lower bounds by quantum arguments
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
Introduction to Algorithms
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Theoretical Computer Science - Complexity and logic
Quantum Lower Bounds for the Collision and the Element Distinctness Problems
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Optimal Time-Space Trade-Offs for Sorting
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Super-linear time-space tradeoff lower bounds for randomized computation
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Quantum Algorithms for Element Distinctness
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Quantum lower bounds for the collision and the element distinctness problems
Journal of the ACM (JACM)
Quantum and classical communication-space tradeoffs from rectangle bounds
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
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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 ≥ S ≥ log3n, one can devise a quantum algorithm that sorts n numbers (using comparisons only) in time T=O(n3/2 log3/2 n/√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(n3/2). Hence for small values of S the upper bound is almost tight. Classically the time-space tradeoff for sorting is TS=Θ(n2).