PIRSA:08050020

Universal quantum walks on graphs

Landahl, A. (2008). Universal quantum walks on graphs . Perimeter Institute. https://pirsa.org/08050020

Landahl, Andrew. Universal quantum walks on graphs . Perimeter Institute, May. 01, 2008, https://pirsa.org/08050020 

          @misc{ pirsa_PIRSA:08050020,
            doi = {10.48660/08050020},
            url = {https://pirsa.org/08050020},
            author = {Landahl, Andrew},
            keywords = {Quantum Information},
            language = {en},
            title = {Universal quantum walks on graphs },
            publisher = {Perimeter Institute},
            year = {2008},
            month = {may},
            note = {PIRSA:08050020 see, \url{https://pirsa.org}}
          }

Andrew Landahl

University of New Mexico

Talk number
PIRSA:08050020
Collection
Talk Type
Subject
Abstract
We construct a family of time-independent nearest-neighbor Hamiltonians coupling eight-state systems on a 1D ring that enables universal quantum computation. Hamiltonians in this family can achieve universality either by driving a continuous-time quantum walk or by terminating an adiabatic algorithm. In either case, the universality property can be understood as arising from an efficient simulation of a programmable quantum circuit. Using gadget perturbation theory, one can demonstrate the same kind of universality for related Hamiltonian families acting on qubits in 2D. Our results demonstrate that simulating 1D chains of spin-7/2 particles is BQP-hard, and indeed BQP-complete because the outputs of decision problems can be encoded in the outputs of such simulations.