SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Adiabatic quantum state generation and statistical zero knowledge
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Quantum Computation and Lattice Problems
SIAM Journal on Computing
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
On the impossibility of a quantum sieve algorithm for graph isomorphism
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Quantum Algorithms for Hidden Nonlinear Structures
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Superpolynomial Speedups Based on Almost Any Quantum Circuit
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Quantum algorithm for the Boolean hidden shift problem
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Quantum adversary (upper) bound
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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The curvelet transform is a directional wavelet transform over Rn, which is used to analyze functions that have singularities along smooth surfaces (Candes and Donoho, 2002). I demonstrate how this can lead to new quantum algorithms. I give an efficient implementation of a quantum curvelet transform, together with two applications: a single-shot measurement procedure for approximately finding the center of a ball in Rn, given a quantum-sample over the ball; and, a quantum algorithm for finding the center of a radial function over Rn, given oracle access to the function. I conjecture that these algorithms succeed with constant probability, using one quantum-sample and O(1) oracle queries, respectively, independent of the dimension n -- this can be interpreted as a quantum speed-up. To support this conjecture, I prove rigorous bounds on the distribution of probability mass for the continuous curvelet transform. This shows that the above algorithms work in an idealized "continuous" model.