Tunneling qubit operation on a protected Josephson junction array

We propose a complete quantum computation process on a topologically protected Josephson junction array system, originally proposed by Ioffe and Feigel'man [Phys. Rev. B 66, 224503 (2002)]. Logical qubits for computation are encoded in the punctured array. The number of qubits is determined by the number of holes. The topological degeneracy is lightly shifted by tuning the flux along specific paths. We show how to perform both single-qubit and basic quantum-gate operations in this system, especially the controlled-NOT (CNOT) gate. ©2010 The American Physical Society