Scalable quantum computer with optical lattices

Quantum computer that is composed of Mott insulator atoms trapped in an optical lattice and a control atom(s) that moves with an independent optical lattice is discussed. A three-dimensional array of Mott insulator atoms functions as memory qubits. The control atom that moves with the second lattice mediates one and two qubit operations among memory qubits with the help of resonant optical beams. Explicit examples of general quantum computational operations are described. In this system all memory qubits are equivalent, and the system is scalable. It is also not necessary to address individual memory qubits by optical means.