Matrix analysis
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Matrix computations (3rd ed.)
The quantum query complexity of approximating the median and related statistics
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Complexity measures and decision tree complexity: a survey
Theoretical Computer Science - Complexity and logic
Quantum Factoring, Discrete Logarithms, and the Hidden Subgroup Problem
Computing in Science and Engineering
The Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum Computer
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Quantum Cryptanalysis of Hash and Claw-Free Functions
LATIN '98 Proceedings of the Third Latin American Symposium on Theoretical Informatics
Quantum Cryptanalysis of Hidden Linear Functions (Extended Abstract)
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Quantum lower bounds by quantum arguments
Journal of Computer and System Sciences - Special issue on STOC 2000
Exponential algorithmic speedup by a quantum walk
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
How Powerful is Adiabatic Quantum Computation?
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
ACM SIGACT News
A lower bound on the quantum query complexity of read-once functions
Journal of Computer and System Sciences
Quantum Speed-Up of Markov Chain Based Algorithms
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Coins make quantum walks faster
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum verification of matrix products
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Polynomial degree vs. quantum query complexity
Journal of Computer and System Sciences - Special issue on FOCS 2003
Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem
Journal of the ACM (JACM)
Negative weights make adversaries stronger
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Quantum Walk Algorithm for Element Distinctness
SIAM Journal on Computing
Quantum Algorithms for the Triangle Problem
SIAM Journal on Computing
Any AND-OR Formula of Size N can be Evaluated in time N^{1/2 + o(1)} on a Quantum Computer
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Span-program-based quantum algorithm for evaluating formulas
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Probabilistic Boolean decision trees and the complexity of evaluating game trees
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Lower Bounds for Randomized and Quantum Query Complexity Using Kolmogorov Arguments
SIAM Journal on Computing
Quantum Walks for Computer Scientists
Quantum Walks for Computer Scientists
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
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
Quantum walk based search algorithms
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Finding is as easy as detecting for quantum walks
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Faster quantum algorithm for evaluating game trees
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Reflections for quantum query algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Quantum walks: a comprehensive review
Quantum Information Processing
| Hi-index | 0.00 |
In this talk, we describe two recent developments in quantum algorithms. The first new development is a quantum algorithm for evaluating a Boolean formula consisting of AND and OR gates of size N in time O(√N). This provides quantum speedups for any problem that can be expressed via Boolean formulas. This result can be also extended to span problems, a generalization of Boolean formulas. This provides an optimal quantum algorithm for any Boolean function in the black-box query model. The second new development is a quantum algorithm for solving systems of linear equations. In contrast with traditional algorithms that run in time O(N2.37...) where N is the size of the system, the quantum algorithm runs in time O(logc N). It outputs a quantum state describing the solution of the system.