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We explore the space "just above" BQP by defining a complexity class PDQP (Product Dynamical Quantum Polynomial time) which is larger than BQP but does not contain NP relative to an oracle.
Relativizations of the 𝒫 = ? 𝒩 𝒫 \mathcal{P}=?\mathcal{NP} question
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Two simple proofs of the Kochen-Specker theorem
A Peres · 1991
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Quantum complexity theory
Ethan Bernstein and Umesh Vazirani · 1993
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A fast quantum mechanical algorithm for database search
Lov K. Grover · 1996
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Quantum computability
Leonard M. Adleman, Jonathan Demarrais, Ming-deh, and A. Huang · 1997
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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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A complete promise problem for statistical zero-knowledge
A. Sahai and S.P. Vadhan · 1997
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Daniel S. Abrams and Seth Lloyd. Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems. Phys. Rev. Lett., 81, 3992–3995, 1998
1998
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Quantum lower bound for the collision problem
Scott Aaronson · 2002
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Both Toffoli and controlled-NOT need little help to do universal quantum computing
Y. Shi · 2003
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The quantum query complexity of the hidden subgroup problem is polynomial
Mark Ettinger, Peter Høyer, and Emanuel Knill · 2004
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Quantum Computation and Quantum Information (Cambridge Series on Information and the Natural Sciences)
Michael A. Nielsen and Isaac L. Chuang · 2004
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Quantum computing and hidden variables
Scott Aaronson · 2005
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Quantum computing, postselection, and probabilistic polynomial-time
Scott Aaronson · 2005
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The Solovay-Kitaev algorithm
Christopher M. Dawson and Michael A. Nielsen · 2006
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Computational Complexity: A Modern Approach
Sanjeev Arora and Boaz Barak · 2009
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