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Collective spins of large atomic samples trapped inside optical resonatorscan carry quantum information that can be processed in a way similar to quantumcomputation with continuous variables. It is shown here that by combining theresonators in multi-path interferometers one can realize coupling betweendifferent samples, and that polynomial Hamiltonians can be constructed byrepeated spin rotations and twisting induced by dispersive interaction of theatoms with light. Application can be expected in efficient simulation ofquantum systems.

Quasi-continuous variable quantum computation with collective spins in multi-path interferometers