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The quantum query complexity of evaluating any read-once formula with n black-box input bits is Theta(sqrt(n)).
A Boolean function
E. I. Nechiporuk · 1966
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Complexity of the realization of a linear function in the class of Π \Pi -circuits
V. M. Khrapchenko · 1971
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Quantum mechanics helps in searching for a needle in a haystack
Lov K. Grover · 1996
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Strengths and weaknesses of quantum computing
Charles H. Bennett, Ethan Bernstein, Gilles Brassard, and Umesh Vazirani · 1997
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Quantum lower bounds by polynomials
Robert Beals, Harry Buhrman, Richard Cleve, Michele Mosca, and Ronald de Wolf · 1998
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Tight bounds on quantum searching
Michel Boyer, Gilles Brassard, Peter Høyer, and Alain Tapp · 1998
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Quantum vs. classical communication and computation
Harry Buhrman, Richard Cleve, and Avi Wigderson · 1998
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Limit on the speed of quantum computation in determining parity
Edward Farhi, Jeffrey Goldstone, Sam Gutmann, and Michael Sipser · 1998
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Quantum search on bounded-error inputs
Peter Høyer, Michele Mosca, and Ronald de Wolf · 2003
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Quantum lower bounds for the collision and the element distinctness problems
Scott Aaronson and Yaoyun Shi · 2004
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A lower bound on the quantum query complexity of read-once functions
Howard Barnum and Michael Saks · 2004
Cited alongside, same era.
Quantum query complexity for some graph problems
Aija Berzina, Andrej Dubrovsky, Rusins Freivalds, Lelde Lace, and Oksana Scegulnaja · 2004
Cited alongside, same era.
Quantum query complexity of some graph problems
Christoph Dürr, Mark Heiligman, Peter Høyer, and Mehdi Mhalla · 2004
Cited alongside, same era.
On the power of Ambainis lower bounds
S. Zhang · 2004
Cited alongside, same era.
Polynomial degree and lower bounds in quantum complexity: Collision and element distinctness with small range
Andris Ambainis · 2005
Cited alongside, same era.
Quantum lower bound for the collision problem with small range
Samuel Kutin · 2005
Cited alongside, same era.
Any AND-OR formula of size N N can be evaluated in time N 1 / 2 + o ( 1 ) N^{1/2+o(1)} on a quantum computer
Andris Ambainis, Andrew M. Childs, Ben W. Reichardt, Robert Špalek, and Shengyu Zhang · 2007
Later among the works it cites.
Quantum query complexity of boolean functions with small on-sets
Andris Ambainis, Kazuo Iwama, Masaki Nakanishi, Harumichi Nishimura, Rudy Raymond, Seiichiro Tani, and Shigeru Yamashita · 2008
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Unitals in Projective Planes
Susan Barwick and Gary Ebert · 2008
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A quantum algorithm for the Hamiltonian NAND tree
Edward Farhi, Jeffrey Goldstone, and Sam Gutmann · 2008
Later among the works it cites.
Discrete-query quantum algorithm for NAND trees
Andrew M. Childs, Richard Cleve, Stephen P. Jordan, and David Yonge-Mallo · 2009
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Span programs and quantum query complexity: The general adversary bound is nearly tight for every boolean function
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Quantum algorithms for the triangle problem
Frédéric Magniez, Miklos Santha, and Mario Szegedy · 2005
Cited alongside, same era.
All quantum adversary methods are equivalent
R. Špalek and M. Szegedy · 2005
Cited alongside, same era.
Quantum verification of matrix products
Harry Buhrman and Robert Špalek · 2006
Cited alongside, same era.
The quantum query complexity of AC 0
Paul Beame and Widad Machmouchi
Cited in the paper.
Ben Reichardt · 2009
Later among the works it cites.
Formula size lower bounds for AC 0 \text{AC}^{0} functions
Robin Kothari (cstheory.stackexchange.com/users/206) · 2011
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Reflections for quantum query algorithms
Ben Reichardt · 2011
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Boolean Function Complexity
Stasys Jukna · 2012
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