Year: 2008
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Chase, Bradley A., Landahl, Andrew J.
Institution: University of New Mexico
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1549293441