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What is the simplest Hamiltonian which can implement quantum computationwithout requiring any control operations during the computation process? In aprevious paper we have constructed a 10-local finite-range interaction amongqubits on a 2D lattice having this property. Here we show thatpair-interactions among qutrits on a 2D lattice are sufficient, too, and canalso implement an ergodic computer where the result can be read out from thetime average state after some post-selection with high success probability.  Two of the 3 qutrit states are given by the two levels of a spin-1/2 particlelocated at a specific lattice site, the third state is its absence. Usualhopping terms together with an attractive force among adjacent particles inducea coupled quantum walk where the particle spins are subjected to spatiallyinhomogeneous interactions implementing holonomic quantum computing. Theholonomic method ensures that the implemented circuit does not depend on thetime needed for the walk.  Even though the implementation of the required type of spin-spin interactionsis currently unclear, the model shows that quite simple Hamiltonians arepowerful enough to allow for universal quantum computing in a closed physicalsystem.Comment: More detailed explanations including description of a programmable  version. 44 pages, 12 figures, latex. To appear in PR

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>∕</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math>particles moving on a two-dimensional lattice with nearest-neighbor interactions can realize an autonomous quantum computer

Spin-1∕2particles moving on a two-dimensional lattice with nearest-neighbor interactions can realize an autonomous quantum computer