Efficient discrete-time simulations of continuous-time quantum query algorithms
Proceedings of the forty-first annual ACM symposium on Theory of computing
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
Optimal bounds for sign-representing the intersection of two halfspaces by polynomials
Proceedings of the forty-second ACM symposium on Theory of computing
New developments in quantum algorithms
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Depth-independent lower bounds on the communication complexity of read-once Boolean formulas
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Any AND-OR Formula of Size $N$ Can Be Evaluated in Time $N^{1/2+o(1)}$ on a Quantum Computer
SIAM Journal on Computing
The quantum query complexity of certification
Quantum Information & Computation
Efficient circuits for quantum walks
Quantum Information & Computation
Quantum Information & Computation
Making polynomials robust to noise
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Limit theorems for the discrete-time quantum walk on a graph with joined half lines
Quantum Information & Computation
The quantum query complexity of AC0
Quantum Information & Computation
Intricacies of quantum computational paths
Quantum Information Processing
Average-case lower bounds for formula size
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Gate-efficient discrete simulations of continuous-time quantum query algorithms
Quantum Information & Computation
| Hi-index | 0.00 |
For any AND-OR formula of size N, there exists a bounded-error N^{1/2 + o(1)} -time quantum algorithm, based on a discrete-time quantum walk, that evaluates this formula on a black-box input. Balanced, or "approximately balanced," formulas can be evaluated in {\rm O}(\sqrt N ) {\rm O}(\sqrt N ) (2 - o(1))th power of the quantum query complexity is a lower bound on the formula size, almost solving in the positive an open problem posed by Laplante, Lee and Szegedy.