Quantum algorithms for some hidden shift problems
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Using HDLs for describing quantum circuits: a framework for efficient quantum algorithm simulation
Proceedings of the 1st conference on Computing frontiers
Generic quantum Fourier transforms
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The power of basis selection in fourier sampling: hidden subgroup problems in affine groups
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
The Symmetric Group Defies Strong Fourier Sampling
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Architectural implications of quantum computing technologies
ACM Journal on Emerging Technologies in Computing Systems (JETC)
Uniformity of quantum circuit families for error-free algorithms
Theoretical Computer Science
Generic quantum Fourier transforms
ACM Transactions on Algorithms (TALG)
Quantum period reconstruction of approximate sequences
Information Processing Letters
An Efficient Quantum Algorithm for the Hidden Subgroup Problem over Weyl-Heisenberg Groups
Mathematical Methods in Computer Science
Quantum Testers for Hidden Group Properties
Fundamenta Informaticae - Machines, Computations and Universality, Part II
Weak Fourier-Schur sampling, the hidden subgroup problem, and the quantum collision problem
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Shor's discrete logarithm quantum algorithm for elliptic curves
Quantum Information & Computation
The quantum fourier transform on a linear nearest neighbor architecture
Quantum Information & Computation
On the quantum hardness of solving isomorphism problems as nonabelian hidden shift problems
Quantum Information & Computation
Quantum Information Processing
Quantum period reconstruction of binary sequences
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Quantum noisy rational function reconstruction
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Quantum Testers for Hidden Group Properties
Fundamenta Informaticae - Machines, Computations and Universality, Part II
Explicit error syndrome calculation for quantum graph codes
Quantum Information Processing
Quantum fourier transform over symmetric groups
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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We give an algorithm for approximating the quantum Fourier transform over an arbitrary Z/sub p/ which requires only O(n log n) steps where n=log p to achieve an approximation to within an arbitrary inverse polynomial in n. This improves the method of A.Y. Kitaev (1995) which requires time quadratic in n. This algorithm also leads to a general and efficient Fourier sampling technique which improves upon the quantum Fourier sampling lemma of L. Hales and S. Hallgren (1997). As an application of this technique, we give a quantum algorithm which finds the period of an arbitrary periodic function, i.e. a function which may be many-to-one within each period. We show that this algorithm is efficient (polylogarithmic in the period of the function) for a large class of periodic functions. Moreover, using standard quantum lower-bound techniques, we show that this characterization is right. That is, this is the maximal class of periodic functions with an efficient quantum period-finding algorithm.