Abstract: Fully controlled coherent coupling of arbitrary harmonic oscillators is an important tool for processing quantum information. Coupling between quantum harmonic oscillators has previously been demonstrated in several physical systems using a two-level system as a mediating element. Direct interaction at the quantum level has only recently been realized by means of resonant coupling between trapped ions. Here we implement a tunable direct coupling between the microwave harmonics of a superconducting resonator by means of parametric frequency conversion. We accomplish this by coupling the mode currents of two harmonics through a superconducting quantum interference device (SQUID) and modulating its flux at the difference (~7GHz) of the harmonic frequencies. We deterministically prepare a single-photon Fock state and coherently manipulate it between multiple modes, effectively controlling it in a superposition of two different 'colours'. This parametric interaction can be described as a beamsplitter-like operation that couples different frequency modes. As such, it could be used to implement linear optical quantum computing protocols on-chip.

Abstract: The universal quantum computer is a device capable of simulating any physical system and represents a major goal for the field of quantum information science. In the context of quantum information, `universal' refers to the ability to carry out arbitrary unitary transformations in the system's computational space. Combining arbitrary single-quantum-bit (qubit) gates with an entangling two-qubit gate provides a set of gates capable of achieving universal control of any number of qubits, provided that these gates can be carried out repeatedly and between arbitrary pairs of qubits. Although gate sets have been demonstrated in several technologies, they have so far been tailored towards specific tasks, forming a small subset of all unitary operators. Here we demonstrate a quantum processor that can be programmed with 15 classical inputs to realize arbitrary unitary transformations on two qubits, which are stored in trapped atomic ions. Using quantum state and process tomography, we characterize the fidelity of our implementation for 160 randomly chosen operations. This universal control is equivalent to simulating any pairwise interaction between spin-1/2 systems. A programmable multiqubit register could form a core component of a large-scale quantum processor, and the methods used here are suitable for such a device.

Abstract: A single microwave photon in a superposition of two states of different frequency is now demonstrated using a superconducting quantum interference device to mediate the coupling between two harmonics of a resonator. Such quantum circuits bring closer the possibility of controlling photon-photon interactions at the single-photon level.