Number theory in science and communication
Number theory in science and communication
Quantum computation of Fourier transforms over symmetric groups
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
On the Power of Quantum Computation
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Normal subgroup reconstruction and quantum computation using group representations
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Simulation of entanglement generation and variation in quantum computation
Journal of Computational Physics
The hidden subgroup problem and permutation group theory
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Interconnection Networks for Scalable Quantum Computers
Proceedings of the 33rd annual international symposium on Computer Architecture
Graph Edit Distance without Correspondence from Continuous-Time Quantum Walks
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Graph matching using the interference of continuous-time quantum walks
Pattern Recognition
Quantum random walks - new method for designing quantum algorithms
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
New developments in quantum algorithms
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Quantum computation from a quantum logical perspective
Quantum Information & Computation
Quantum algorithms for shifted subset problems
Quantum Information & Computation
Super-polynomial quantum speed-ups for boolean evaluation trees with hidden structure
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Quantum algorithms for a set of group theoretic problems
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
Finding hidden Borel subgroups of the general linear group
Quantum Information & Computation
Quantum Information & Computation
Quantum algorithms for one-dimensional infrastructures
Quantum Information & Computation
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Among the most remarkable successes of quantum computation are Shor's efficient quantum algorithms for the computational tasks of integer factorization and the evaluation of discrete logarithms. In this article, we review the essential ingredients of these algorithms and draw out the unifying generalization of the so-called abelian hidden subgroup problem. This involves an unexpectedly harmonious alignment of the formalism of quantum physics with the elegant mathematical theory of group representations and Fourier transforms on finite groups. Finally we consider the nonabelian hidden subgroup problem mentioning some open questions where future quantum algorithms may be expected to have a substantial impact.