Quantum algorithms for algebraic problems

Childs, Andrew M., van Dam, Wim·2010·Reviews of Modern Physics
DOI 10.1103/revmodphys.82.1

Cites (266)

Items 201–264 of 264

  1. Approximate Counting and Quantum Computation
    Magnus Bordewich, Michael Hartley Freedman, László Lovász, Dominic J. A. Welsh · 2005 · Combinatorics Probability Computing
  2. Elementary Algebraic Geometry
    Klaus Hulek · 2003 · Student mathematical library
  3. The Power of Strong Fourier Sampling: Quantum Algorithms for Affine Groups and Hidden Shifts
    Cristopher Moore, Daniel N. Rockmore, Alexander C. Russell, Leonard J. Schulman · 2007 · SIAM Journal on Computing
  4. Fast Quantum Fourier Transforms for a Class of Non-abelian Groups
    Markus Püschel, Martin Rötteler, Thomas Beth · 1999 · Lecture notes in computer science
  5. Computational Indistinguishability Between Quantum States and Its Cryptographic Application
    Akinori Kawachi, Takeshi Koshiba, Harumichi Nishimura, Tomoyuki Yamakami · 2005 · Lecture notes in computer science
  6. Quantum algorithm for a generalized hidden shift problem
    Andrew M. Childs, Wim van Dam · 2007 · CaltechAUTHORS (California Institute of Technology)
  7. Polynomial time quantum algorithm for the computation of the unit group of a number field
    Arthur Schmidt, Ulrich Vollmer · 2005 · ACM Symposium on Theory of Computing (STOC)
  8. On the computational complexity of the general discrete fourier transform
    Thomas Beth · 1987 · Theoretical Computer Science
  9. Frobenius Maps of Abelian Varieties and Finding Roots of Unity in Finite Fields
    J. Pila · 1990 · Mathematics of Computation
  10. Discrete Algorithms and Complexity
    1987 · Elsevier eBooks
  11. A 2 rebit gate universal for quantum computing
    Terry Rudolph, Lov K. Grover · 2002 · arXiv (Cornell University)
  12. Counting curves and their projections
    Joachim von zur Gathen, Marek Karpiński, Igor E. Shparlinski · 1996 · Computational Complexity
  13. Efficient Quantum Algorithms for Estimating Gauss Sums
    Wim van Dam, G. Seroussi · 2002 · arXiv (Cornell University)
  14. Counting points on varieties over finite fields of small characteristic
    Alan G. B. Lauder, Daqing Wan · 2006 · arXiv (Cornell University)
  15. Algorithmic Number Theory
    Richard P. Brent, Pierrick Gaudry, Emmanuel Thomé, Paul Zimmermann · 2008 · Lecture notes in computer science
  16. An Efficient Quantum Algorithm for the Hidden Subgroup Problem in Nil-2 Groups
    Gábor Ivanyos, Luc Sanselme, Miklós Sántha · 2008 · Lecture notes in computer science
  17. Fast Monte Carlo Algorithms for Permutation Groups
    László Babai, Gene D. Cooperman, L. Finkelstein, Eugene M. Luks, Ákos Seress · 1995 · Journal of Computer and System Sciences
  18. Solving Medium-Density Subset Sum Problems in Expected Polynomial Time
    Abraham D. Flaxman, Bartosz Przydatek · 2005 · Lecture notes in computer science
  19. A Key Exchange System Based on Real Quadratic Fields
    Johannes A Buchmann, Hugh C. Williams · 1989 · International Cryptology Conference
  20. Fast Fourier analysis for abelian group extensions
    Daniel N. Rockmore · 1990 · Advances in Applied Mathematics
  21. Sharp Quantum versus Classical Query Complexity Separations
    Niel de Beaudrap, Not Available Not Available, Not Available Not Available · 2002 · Algorithmica
  22. Quantum Algorithms for Weighing Matrices and Quadratic Residues
    Dam van · 2002 · Algorithmica
  23. Quantum solution to the hidden subgroup problem for Poly-Near-Hamiltonian groups
    Dmitry Gavinsky · 2004 · Quantum Information and Computation
  24. Quantum measurements for hidden subgroup problems with optimal sample complexity
    Masahito Hayashi, A. Kawachi, H. Kobayashi · 2008 · Quantum Information and Computation
  25. A nearly optimal discrete query quantum algorithm for evaluating NAND formulas
    Andris Ambainis · 2007 · arXiv (Cornell University)
  26. Random Measurement Bases, Quantum State Distinction and Applications to the Hidden Subgroup Problem
    Jaikumar Radhakrishnan, Martin Rötteler, Pranab Kumar Sen · 2008 · Algorithmica
  27. Quantum computation of zeta functions of curves
    Kiran S. Kedlaya · 2006 · Computational Complexity
  28. Counting Points on Curves and Abelian Varieties Over Finite Fields
    Leonard M. Adleman, Ming-Deh A. Huang · 2001 · Journal of Symbolic Computation
  29. The Symmetric Group Defies Strong Fourier Sampling
    Cristopher Moore, Alexander C. Russell, Leonard J. Schulman · 2008 · SIAM Journal on Computing
  30. Classical and quantum function reconstruction via character evaluation
    Alexander C. Russell, Igor E. Shparlinski · 2004 · Journal of Complexity
  31. Random Measurement Bases, Quantum State Distinction and Applications to the Hidden Subgroup Problem
    Pranab Kumar Sen · 2006 · Proceedings - IEEE Conference on Computational Complexity/Proceedings
  32. On the complexity of some problems in algorithmic algebraic number theory
    Christoph Thiel · 1995 · TUbilio (Technical University of Darmstadt)
  33. Asymptotically Fast Discrete Logarithms in Quadratic Number Fields
    Ulrich Vollmer · 2000 · Lecture notes in computer science
  34. The Quantum Fourier Transform and Extensions of the Abelian Hidden Subgroup Problem
    Lisa Hales · 2002 · arXiv (Cornell University)
  35. On the Power of Random Bases in Fourier Sampling: Hidden Subgroup Problem in the Heisenberg Group
    Jaikumar Radhakrishnan, Martin Roetteler, Pranab Sen · 2005 · Lecture notes in computer science
  36. Optimized quantum implementation of elliptic curve arithmetic over binary fields
    Phillip Kaye · 2005 · Quantum Information and Computation
  37. Every NAND formula of size N can be evaluated in time N^{1/2+o(1)} on a quantum computer
    Andrew M. Childs, Ben W. Reichardt, Robert Špalek, Shengyu Zhang · 2007 · arXiv (Cornell University)
  38. Efficient Computation of the Fourier Transform on Finite Groups
    Persi W. Diaconis, Daniel N. Rockmore · 1990 · Journal of the American Mathematical Society
  39. Verification of Identities
    Sridhar Rajagopalan, Leonard J. Schulman · 2000 · SIAM Journal on Computing
  40. The quantum query complexity of the abelian hidden subgroup problem
    Pascal Koiran, Vincent Nesme, Natacha Portier · 2007 · Theoretical Computer Science
  41. An Efficient Quantum Algorithm for the Hidden Subgroup Problem in Extraspecial Groups
    Gábor Ivanyos, Luc Sanselme, Miklós Sántha · 2007 · Lecture notes in computer science
  42. The query complexity of order-finding
    Richard Cleve · 2004 · Information and Computation
  43. The Quantum Query Complexity of Algebraic Properties
    Sebastian Dörn, Thomas Thierauf · 2007 · Lecture notes in computer science
  44. On the quantum hardness of solving isomorphism problems as nonabelian hidden shift problems
    Andrew M. Childs, Paweł Wocjan · 2007 · Quantum Information and Computation
  45. Quantum Algorithms for Matching and Network Flows
    Andris Ambainis, Robert Špalek · 2005 · UvA-DARE (University of Amsterdam)
  46. On the Power of Random Bases in Fourier Sampling: Hidden Subgroup Problem in the Heisenberg Group
    Jaikumar Radhakrishnan, Martin Roetteler, Pranab Kumar Sen · 2005 · arXiv (Cornell University)
  47. A Quantum Lower Bound for the Query Complexity of Simon’s Problem
    Pascal Koiran, Vincent Nesme, Natacha Portier · 2005 · Lecture notes in computer science
  48. Quantum algorithms for Simon's problem over general groups
    Gorjan Alagic, Cristopher Moore, Alexander C. Russell · 2007
  49. How a Clebsch-Gordan transform helps to solve the Heisenberg hidden subgroup problem
    Dave Bacon · 2008 · Quantum Information and Computation
  50. Quantum computation in algebraic number theory: Hallgren’s efficient quantum algorithm for solving Pell’s equation
    Richard Jozsa · 2003 · Annals of Physics
  51. Optimal phase estimation in quantum networks
    Wim van Dam, Giacomo Mauro D’Ariano, ARTUR K. EKERT, Chiara Macchiavello, Michele Mosca · 2007 · Journal of Physics A Mathematical and Theoretical
  52. Séminaire de Théorie des Nombres, Paris, 1990–91
    1993 · Birkhäuser Boston eBooks
  53. Sharp Quantum vs. Classical Query Complexity Separations
    Niel de Beaudrap, Richard Cleve, John Watrous · 2000 · arXiv (Cornell University)
  54. Efficient quantum algorithm for identifying hidden polynomials
    Thomas Decker, Jan Draisma, Paweł Wocjan · 2009 · Quantum Information and Computation
  55. On solving systems of random linear disequations
    Gábor Ivanyos · 2008 · Quantum Information and Computation
  56. Introduction to Cryptography (Undergraduate Texts in Mathematics)
    Johannes A Buchmann · 2004 · Springer eBooks
  57. The Quantum Complexity of Group Testing
    Sebastian Dörn, Thomas Thierauf · 2008 · Springer eBooks
  58. Trading Inverses for an Irrep in the Solovay-Kitaev Theorem
    Adam Bouland, Māris Ozols · 2017 · arXiv (Cornell University)
  59. Adapted diameters and the efficient computation of Fourier transforms on finite groups
    David K. Maslen, Daniel N. Rockmore · 1995 · Symposium on Discrete Algorithms
  60. Quantum Complexity Bounds of Independent Set Problems.
    Sebastian Dörn · 2007 · Conference on Current Trends in Theory and Practice of Informatics
  61. Quantum computation and the evaluation of tensor networks
    Itai Arad, Zeph A. Landau · 2008 · arXiv (Cornell University)
  62. Estimating Jones and HOMFLY polynomials with one clean qubit
    Stephen P. Jordan, Paweł Wocjan · 2009 · Quantum Information and Computation
  63. Isomorphism and Factorization – Classical and Quantum Algorithms
    Sebastian Dörn, Daniel Haase, Jacobo Torán, Fabian Wagner · 2009
  64. On the Complexity of the Hidden Subgroup Problem
    Stephen Fenner, Yong Zhang · 2008 · Springer eBooks