Explicit implementation of quantum circuits on a quantum-cellular-automata-like architecture

We present an efficient strategy to translate a normal quantum algorithm into a sequence of operations on the quantum-cellular-automata-like architecture (QCALA) originally proposed by Lloyd. The QCALA assumes arrays of weakly coupled quantum systems where an interaction exists only between neighboring qubits and can only perform the same quantum operation onto all the qubits. The sequence obtained by the strategy proposed by Lloyd needs at most 12n operations, where n is the number of qubits for the original circuit. The sequence obtained by our strategy needs at most 6n operations. We also clarified the relations between the upper bound of the number of translated operations and the period of the QCALA and between the upper bound of the number of qubits and the period of the QCALA.