title: Universal adiabatic quantum computation via the space-time circuit-to-Hamiltonian construction.
abstract: We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic XXZ chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its q-deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice.
authors.affiliation: Institute for Quantum Computing and Dept. of Combinatorics and Optimization, University of Waterloo, Ontario N2L 3G1, Canada.
authors.forename: David
authors.initials: D
authors.lastname: Gosset
authors.affiliation: JARA Institute for Quantum Information, RWTH Aachen University, 52056 Aachen, North Rhine-Westphalia, Germany.
authors.forename: Barbara M
authors.initials: BM
authors.lastname: Terhal
authors.affiliation: JARA Institute for Quantum Information, RWTH Aachen University, 52056 Aachen, North Rhine-Westphalia, Germany.
authors.forename: Anna
authors.initials: A
authors.lastname: Vershynina