Size-depth tradeoffs for algebraic formulae
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Size-depth tradeoffs for Boolean formulae
Information Processing Letters
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Quantum vs. classical communication and computation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
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
Negative weights make adversaries stronger
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Span-program-based quantum algorithm for evaluating formulas
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Quantum search on bounded-error inputs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
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
Reflections for quantum query algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
New developments in quantum algorithms
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Reflections for quantum query algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Span programs and quantum algorithms for st-connectivity and claw detection
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
| Hi-index | 0.00 |
We give an O(√n log n)-query quantum algorithm for evaluating size-n AND-OR formulas. Its running time is poly-logarithmically greater after efficient preprocessing. Unlike previous approaches, the algorithm is based on a quantum walk on a graph that is not a tree. Instead, the algorithm is based on a hybrid of direct-sum span program composition, which generates tree-like graphs, and a novel tensor-product span program composition method, which generates graphs with vertices corresponding to minimal zero-certificates.