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PIRSA:22110119

Video URL

https://pirsa.org/22110119

Quantum Constraint Problems can be complete for BQP, QCMA, and BPP

          @misc{ scivideos_PIRSA:22110119,
            doi = {10.48660/22110119},
            url = {https://pirsa.org/22110119},
            author = {Meiburg, Alexander},
            keywords = {Quantum Information},
            language = {en},
            title = {Quantum Constraint Problems can be complete for BQP, QCMA, and BPP},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2022},
            month = {nov},
            note = {PIRSA:22110119 see, \url{https://scivideos.org/index.php/pirsa/22110119}}
          }

Alexander Meiburg University of California System

Talk numberPIRSA:22110119
DOI10.48660/22110119
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

Constraint satisfaction problems are known to always be "easy" or "hard", in the sense of being either solvable in P or being NP-complete, with no intermediate difficulty levels. The quantum analog of constraint problems, frustration-free Hamiltonians, are known to exhibit at least two more levels of complexity: QMA (for arbitrary local Hamiltonians) and MA (for stoquastic Hamiltonians). Wondering if other complexity classes can occur, we answer in the affirmative: there are interactions which can be freely arranged on qubits in any arrangement, such that the resulting frustration problem is BQP-complete, and captures exactly the difficulty of quantum computation. Simple modifications of this construction show that quantum constraint problems can be complete for QCMA and BPP as well. Based on https://arxiv.org/abs/2101.08381