BQP and the Polynomial Hierarchy

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Hamzei, Fahid | 2023

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 56423 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Ebrahimi Broojeni, Javad; Abolfath Beigi, Salman
Abstract:
The relation between BQP and PH has been one of the most fundamental open questions since the beginning of the field of quantum computational complexity. Despite the common belief that BQP contains problems outside the polynomial hierarchy, no real progress had been made in solving the problem even in relativized world. In 2009, Aaronson took the first serious step by proposing an oracle problem to separate the relation version of these two complexity classes. Finally, based on Aaronson’s works, in 2018 Raz and Tal separated BQP and PH relative to an oracle in a breakthrough work. This thesis studies the tools and techniques used to solve this challenging problem
Keywords:
Quantum Computation ; Computational Complexity ; Black Box Model ; Bounded-Error Quantum Polynomial Time (BQP)Problem ; Polynomial Hierarchy