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We prove a generalization of the parallel adversary method to multi-valued functions, and apply it to prove that there is no parallel quantum advantage for approximate counting.
Grover’s quantum searching algorithm is optimal
Christof Zalka · 1910
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The spectral norm of a nonnegative matrix
Roy Mathias · 1990
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Quantum counting
Gilles Brassard, Peter Høyer, and Alain Tapp · 1998
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The quantum query complexity of approximating the median and related statistics
Ashwin Nayak and Felix Wu · 1999
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Quantum lower bounds by polynomials
Robert Beals, Harry Buhrman, Richard Cleve, Michele Mosca, and Ronald de Wolf · 2001
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Quantum lower bounds by quantum arguments
Andris Ambainis · 2002
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Lower bounds on quantum query complexity
P. Høyer and R. Špalek · 2005
Cited alongside, same era.
All quantum adversary methods are equivalent
Robert Špalek and Mario Szegedy · 2006
Cited alongside, same era.
Quantum speedup of monte carlo methods
Ashley Montanaro · 2015
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Optimal parallel quantum query algorithms
Stacey Jeffery, Frédéric Magniez, and Ronald de Wolf · 2017
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Quantum Computing in the NISQ era and beyond
John Preskill · 2018
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