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In 2009, using the $\textsf{Fourier Checking}$ problem, Aaronson claimed to construct the relativized worlds such that $\textsf{BQP} \not\subset \mathsf{BPP_{path}}$ and $\textsf{BQP} \not\subset \textsf{SZK}$.
Strengths and weaknesses of quantum computing
Charles H Bennett, Ethan Bernstein, Gilles Brassard, and Umesh Vazirani · 1997
Earlier work this paper cites.
Threshold computation and cryptographic security
Yenjo Han, Lane A Hemaspaandra, and Thomas Thierauf · 1997
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On the power of quantum computation
Daniel R Simon · 1997
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An introduction to quantum complexity theory
Richard Cleve · 1999
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Quantum lower bound for the collision problem
Scott Aaronson · 2002
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Complexity measures and decision tree complexity: a survey
Harry Buhrman and Ronald de Wolf · 2002
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Limits on the power of quantum statistical zero-knowledge
John Watrous · 2002
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Exponential algorithmic speedup by a quantum walk
Andrew M Childs, Richard Cleve, Enrico Deotto, Edward Farhi, Sam Gutmann, and Daniel A Spielman · 2003
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A complete problem for statistical zero knowledge
Amit Sahai and Salil Vadhan · 2003
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Quantum lower bounds for the collision and the element distinctness problems
Scott Aaronson and Yaoyun Shi · 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
Later among the works it cites.
BQP and the polynomial hierarchy
Scott Aaronson · 2010
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A strong direct product theorem for quantum query complexity
Troy Lee and Jeremie Roland · 2013
Later among the works it cites.
Forrelation: A problem that optimally separates quantum from classical computing
Scott Aaronson and Andris Ambainis · 2015
Later among the works it cites.
Separations in query complexity using cheat sheets
Scott Aaronson, Shalev Ben-David, and Robin Kothari · 2015
Later among the works it cites.
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