Quantum logic gates for superconducting resonator qudits

We study quantum information processing using superpositions of Fock states in superconducting resonators, as quantum $d$-level systems (qudits). A universal set of single and coupled logic gates is theoretically proposed for resonators coupled by superconducting circuits of Josephson juctions. These gates use experimentally demonstrated interactions, and provide an attractive route to quantum information processing using harmonic oscillator modes.