Two-Qubit Operations for Finite-Energy Gottesman-Kitaev-Preskill Encodings.

We present techniques for performing two-qubit gates on Gottesman-Kitaev-Preskill (GKP) codes with finite energy, and find that operations designed for ideal infinite-energy codes create undesired entanglement when applied to physically realistic states. We demonstrate that this can be mitigated using recently developed local error-correction protocols, and evaluate the resulting performance. We also propose energy-conserving finite-energy gate implementations which largely avoid the need for further correction.

Penning micro-trap for quantum computing.

Trapped ions in radio-frequency traps are among the leading approaches for realizing quantum computers, because of high-fidelity quantum gates and long coherence times. However, the use of radio-frequencies presents several challenges to scaling, including requiring compatibility of chips with high voltages, managing power dissipation and restricting transport and placement of ions. Here we realize a micro-fabricated Penning ion trap that removes these restrictions by replacing the radio-frequency field with a 3 T magnetic field.

Integration of a high finesse cryogenic build-up cavity with an ion trap.

We report on the realization of a hemispherical optical cavity with a finesse of F = 13 000 and sustaining inter-cavity powers of 10 kW, which we operate in a closed-cycle cryostat vacuum system close to 4 K. This was designed and built with an integrated radio-frequency Paul trap in order to combine optical and radio-frequency trapping. The cavity provides a power build-up factor of 2300.

Trapping and Ground-State Cooling of a Single H_{2}^{+}.

We demonstrate co-trapping and sideband cooling of a H_{2}^{+}-^{9}Be^{+} ion pair in a cryogenic Paul trap. We study the chemical lifetime of H_{2}^{+} and its dependence on the apparatus temperature, achieving lifetimes of up to 11_{-3}^{+6}  h at 10 K. We demonstrate cooling of two of the modes of translational motion to an average phonon number of 0.

Phonon Laser in the Quantum Regime.

We demonstrate a trapped-ion system with two competing dissipation channels, implemented independently on two ion species cotrapped in a Paul trap. By controlling coherent spin-oscillator couplings and optical pumping rates we explore the phase diagram of this system, which exhibits a regime analogous to that of a (phonon) laser but operates close to the quantum ground state with an average phonon number of n[over ¯]<10. We demonstrate phase locking of the oscillator to an additional resonant drive, and also observe the phase diffusion of the resulting state under dissipation by reconstructing the quantum state from a measurement of the characteristic function.