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
Exact Quantum Algorithms for the Leader Election Problem
ACM Transactions on Computation Theory (TOCT)
A stronger LP bound for formula size lower bounds via clique constraints
Theoretical Computer Science
Span programs and quantum algorithms for st-connectivity and claw detection
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
The quantum query complexity of read-many formulas
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Quipper: a scalable quantum programming language
Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation
An introduction to quantum programming in quipper
RC'13 Proceedings of the 5th international conference on Reversible Computation
Time-Efficient quantum walks for 3-distinctness
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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Consider the problem of evaluating an AND-OR formula on an $N$-bit black-box input. We present a bounded-error quantum algorithm that solves this problem in time $N^{1/2+o(1)}$. In particular, approximately balanced formulas can be evaluated in $O(\sqrt{N})$ queries, which is optimal. The idea of the algorithm is to apply phase estimation to a discrete-time quantum walk on a weighted tree whose spectrum encodes the value of the formula.