Information Processing Letters
On the rigidity of Vandermonde matrices
Theoretical Computer Science
Quantum computation and quantum information
Quantum computation and quantum information
Quantum Entanglement and the Communication Complexity of the Inner Product Function
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
Exponential lower bound for 2-query locally decodable codes via a quantum argument
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Optimal Lower Bounds for Quantum Automata and Random Access Codes
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A Lattice Problem in Quantum NP
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Lower bounds for local search by quantum arguments
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
The Quantum Adversary Method and Classical Formula Size Lower Bounds
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Algebraic Complexity Theory
Improved lower bounds for locally decodable codes and private information retrieval
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Quantum multiparty communication complexity and circuit lower bounds
Mathematical Structures in Computer Science
Complexity Lower Bounds using Linear Algebra
Foundations and Trends® in Theoretical Computer Science
Quantum multiparty communication complexity and circuit lower bounds
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
A note on quantum algorithms and the minimal degree of ε-error polynomials for symmetric functions
Quantum Information & Computation
Min-rank conjecture for log-depth circuits
Journal of Computer and System Sciences
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
| Hi-index | 0.00 |
The rigidity of a matrix measures how many of its entries need to be changed in order to reduce its rank to some value. Good lower bounds on the rigidity of an explicit matrix would imply good lower bounds for arithmetic circuits as well as for communication complexity. Here we reprove the best known bounds on the rigidity of Hadamard matrices, due to Kashin and Razborov, using tools from quantum computing. Our proofs are somewhat simpler than earlier ones (at least for those familiar with quantum) and give slightly better constants. More importantly, they give a new approach to attack this longstanding open problem.