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The (negative-weighted) quantum adversary bound is a tight characterisation of the quantum query complexity for any partial function.
Quantum measurements and the Abelian stabilizer problem
A. Kitaev · 1995
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Strengths and weaknesses of quantum computing
C. H. Bennett, E. Bernstein, G. Brassard, and U. Vazirani · 1997
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Quantum algorithms revisited
R. Cleve, A. Ekert, C. Macchiavello, and M. Mosca · 1998
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Analog analogue of a digital quantum computation
E. Farhi and S. Gutmann · 1998
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Quantum lower bounds by quantum arguments
A. Ambainis · 2002
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Quantum amplitude amplification and estimation
G. Brassard, P. Høyer, M. Mosca, and A. Tapp · 2002
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Polynomial degree vs. quantum query complexity
A. Ambainis · 2003
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Quantum decision trees and semi-definite programming
H. Barnum, M. Saks, and M. Szegedy · 2003
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Quantum query complexity for some graph problems
A. Berzina, A. Dubrovsky, R. Freivalds, L. Lace, and O. Scegulnaja · 2004
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Convex optimization
S. Boyd and L. Vandenberghe · 2004
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Quantum query complexity of some graph problems
C. Dürr, M. Heiligman, P. Høyer, and M. Mhalla · 2004
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On the power of Ambainis lower bounds
S. Zhang · 2005
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Quantum verification of matrix products
H. Buhrman and R. Špalek · 2006
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All quantum adversary methods are equivalent
R. Špalek and M. Szegedy · 2006
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The quantum query complexity of algebraic properties
S. Dörn and T. Thierauf · 2007
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Negative weights make adversaries stronger
P. Høyer, T. Lee, and R. Špalek · 2007
Cited alongside, same era.
The multiplicative quantum adversary
R. Špalek · 2008
Cited alongside, same era.
Positive definite matrices
R. Bhatia · 2009
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Efficient discrete-time simulations of continuous-time quantum query algorithms
R. Cleve, D. Gottesman, M. Mosca, R. D. Somma, and D. Yonge-Mallo · 2009
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B. W. Reichardt · 2009
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Improved bounds for the randomized decision tree complexity of recursive majority
Super-polynomial quantum speed-ups for Boolean evaluation trees with hidden structure
B. Zhan, S. Kimmel, and A. Hassidim · 2012
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Quantum walks and electric networks
A. Belovs · 2013
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Time-efficient quantum walks for 3-distinctness
A. Belovs, A. M. Childs, S. Jeffery, R. Kothari, and F. Magniez · 2013
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Adversary lower bounds for the collision and the set equality problems
A. Belovs and A. Rosmanis · 2013
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Adversary lower bound for the k k -sum problem
A. Belovs and R. Špalek · 2013
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F. Magniez, A. Nayak, M. Santha, and D. Xiao · 2010
Cited alongside, same era.
Symmetry-assisted adversaries for quantum state generation
A. Ambainis, L. Magnin, M. Rötteler, and J. Roland · 2011
Cited alongside, same era.
Quantum query complexity of state conversion
T. Lee, R. Mittal, B. W. Reichardt, R. Špalek, and M. Szegedy · 2011
Cited alongside, same era.
Reflections for quantum query algorithms
B. W. Reichardt · 2011
Cited alongside, same era.
Adversary lower bounds in the Hamiltonian oracle model
D. Yonge-Mallo · 2011
Cited alongside, same era.
Learning-graph-based quantum algorithm for k k -distinctness
A. Belovs · 2012
Cited alongside, same era.
Span programs for functions with constant-sized 1-certificates
A. Belovs · 2012
Cited alongside, same era.
Nested quantum walks with quantum data structures
S. Jeffery, R. Kothari, and F. Magniez · 2013
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Improved quantum query algorithms for triangle finding and associativity testing
T. Lee, F. Magniez, and M. Santha · 2013
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Quantum algorithms for learning symmetric juntas via the adversary bound
A. Belovs · 2014
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On the power of non-adaptive learning graphs
A. Belovs and A. Rosmanis · 2014
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Exponential improvement in precision for simulating sparse Hamiltonians
D. W. Berry, A. M. Childs, R. Cleve, R. Kothari, and R. D. Somma · 2014
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A quantum algorithm for computing the unit group of an arbitrary degree number field
K. Eisenträger, S. Hallgren, A. Kitaev, and F. Song · 2014
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Quantum algorithms for finding constant-sized sub-hypergraphs
F. Le Gall, H. Nishimura, and S. Tani · 2014
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Span-program-based quantum algorithm for evaluating unbalanced formulas
B. W. Reichardt · 2014
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Quantum algorithm for monotonicity testing on the hypercube
A. Belovs and E. Blais · 2015
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