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We show that lattice systems, such as the Bose-Hubbard model, can besimulated on a single nano- or micro-mechanical resonator, by exploiting itsmany modes. The on-site Hamiltonians are engineered by coupling the mechanicalmodes to the modes of a pair of optical or stripline resonators, and theconnections between the lattice sites are engineered in a similar way. Thelattice network structure is encoded in the frequency components of the fieldsdriving the resonators. This three-resonator configuration also allowsuniversal quantum computing on the nano-resonator.

Simulating many-body lattice systems on a single nano-mechanical resonator