We　propose　a　distributed　quantum　architecture　(three　atoms　trapped　in　three　coupled　cavities)　to　construct　an　asymmetric　spin　1/2　Heisenberg　XY　model.　The　effective　atom-atom　coupling　is　obtained　with　the　cavity　modes　and　the　atomic　excited　states　being　virtually　populated.　We　then　demonstrate　that　the　model　can　be　used　for　implementing　a　three-qubit　Toffoli　gate　with　high　fidelity.　The　feasibility　and　effectiveness　of　our　scheme　as　well　as　the　influences　of　decoherence　effects　(the　atomic　spontaneous　emission　and　the　cavity　decay)　on　the　gate　fidelity　are　finally　discussed.　The　scheme　can　be　generalized　for　distributed　quantum　computation　with　the　Heisenberg　XY　model.　©　2015　Taylor　&　Francis.