Size-depth tradeoffs for Boolean formulae
Information Processing Letters
Size-Depth Tradeoffs for Algebraic Formulas
SIAM Journal on Computing
Quantum vs. classical communication and computation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Quantum lower bounds by polynomials
Journal of the ACM (JACM)
New degree bounds for polynomial threshold functions
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Two applications of information complexity
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Classical and Quantum Computation
Classical and Quantum Computation
Journal of Computer and System Sciences - STOC 2001
Learning intersections and thresholds of halfspaces
Journal of Computer and System Sciences - Special issue on FOCS 2002
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
Polynomial degree vs. quantum query complexity
Journal of Computer and System Sciences - Special issue on FOCS 2003
THE QUANTUM ADVERSARY METHOD AND CLASSICAL FORMULA SIZE LOWER BOUNDS
Computational Complexity
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Any AND-OR Formula of Size N can be Evaluated in time N^{1/2 + o(1)} on a Quantum Computer
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Span-program-based quantum algorithm for evaluating formulas
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Probabilistic Boolean decision trees and the complexity of evaluating game trees
SFCS '86 Proceedings of the 27th Annual 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
On the Monte carlo boolean decision tree complexity of read‐once formulae
Random Structures & Algorithms
The quantum query complexity of certification
Quantum Information & Computation
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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.