Quantum algorithm to solve function inversion with time–space trade-off

Quantum algorithm to solve function inversion with time–space trade-off In general, it is a difficult problem to solve the inverse of any function. With the inverse implication operation, we present a quantum algorithm for solving the inversion of function via using time–space trade-off in this paper. The details are as follows. Let function $$f(x)=y$$ f ( x ) = y have k solutions, where $$x\in \{0, 1\}^{n}, y\in \{0, 1\}^{m}$$ x ∈ { 0 , 1 } n , y ∈ { 0 , 1 } m for any integers n, m. We show that an iterative algorithm can be used to solve the inverse of function f(x) with successful probability $$1-\left( 1-\frac{k}{2^{n}}\right) ^{L}$$ 1 - 1 - k 2 n L for $$L\in Z^{+}$$ L ∈ Z + . The space complexity of proposed quantum iterative algorithm is O(Ln), where L is the number of iterations. The paper concludes that, via using time–space trade-off strategy, we improve the successful probability of algorithm. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Quantum algorithm to solve function inversion with time–space trade-off

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Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-017-1622-y
Publisher site
See Article on Publisher Site

Abstract

In general, it is a difficult problem to solve the inverse of any function. With the inverse implication operation, we present a quantum algorithm for solving the inversion of function via using time–space trade-off in this paper. The details are as follows. Let function $$f(x)=y$$ f ( x ) = y have k solutions, where $$x\in \{0, 1\}^{n}, y\in \{0, 1\}^{m}$$ x ∈ { 0 , 1 } n , y ∈ { 0 , 1 } m for any integers n, m. We show that an iterative algorithm can be used to solve the inverse of function f(x) with successful probability $$1-\left( 1-\frac{k}{2^{n}}\right) ^{L}$$ 1 - 1 - k 2 n L for $$L\in Z^{+}$$ L ∈ Z + . The space complexity of proposed quantum iterative algorithm is O(Ln), where L is the number of iterations. The paper concludes that, via using time–space trade-off strategy, we improve the successful probability of algorithm.

Journal

Quantum Information ProcessingSpringer Journals

Published: May 24, 2017

References

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