NP is as easy as detecting unique solutions
Theoretical Computer Science
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
Rectangular matrix multiplication revisited
Journal of Complexity
Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Quantum computation and quantum information
Quantum computation and quantum information
Quantum lower bounds by quantum arguments
Journal of Computer and System Sciences - Special issue on STOC 2000
Quantum Algorithms for Element Distinctness
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Quantum and Classical Strong Direct Product Theorems and Optimal Time-Space Tradeoffs
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Quantum Walk Algorithm for Element Distinctness
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Quantum Speed-Up of Markov Chain Based Algorithms
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Quantum algorithms for the triangle problem
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Quantum search on bounded-error inputs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
All quantum adversary methods are equivalent
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Quantum complexity of testing group commutativity
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On the hitting times of quantum versus random walks
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
The quantum query complexity of the determinant
Information Processing Letters
Claw finding algorithms using quantum walk
Theoretical Computer Science
Recent progress in quantum algorithms
Communications of the ACM
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 walks with multiple or moving marked locations
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
The quantum complexity of group testing
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
A note on the search for k elements via quantum walk
Information Processing Letters
Finding is as easy as detecting for quantum walks
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
New developments in quantum algorithms
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
SIAM Journal on Computing
Improved output-sensitive quantum algorithms for Boolean matrix multiplication
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Quantum and classical communication-space tradeoffs from rectangle bounds
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Improving quantum query complexity of boolean matrix multiplication using graph collision
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Quantum walks: a comprehensive review
Quantum Information Processing
The quantum query complexity of algebraic properties
FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
An improved claw finding algorithm using quantum walk
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
The quantum query complexity of read-many formulas
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
| Hi-index | 0.02 |
We present a quantum algorithm that verifies a product of two n × n matrices over any integral domain with bounded error in worst-case time O(n5/3) and expected time O(n5/3/ min(w, √n)1/3), where ω is the number of wrong entries. This improves the previous best algorithm [3] that runs in time O(n7/4). We also present a quantum matrix multiplication algorithm that is efficient when the result has few nonzero entries.