Dr Joseph Goodwin

Abstract:

The technical demands to perform quantum error correction are considerable. The task requires the preparation of a many-body entangled state, together with the ability to make parity measurements over subsets of the physical qubits of the system to detect errors. Here we propose two trapped-ion experiments to realise error-correcting codes of variable size to protect a single encoded qubit from dephasing errors. Novel to our schemes is the use of a global entangling phase gate, which could be implemented in both Penning traps and Paul traps. We make use of this entangling operation to significantly reduce the experimental complexity of state preparation and syndrome measurements. We also show, in our second scheme, that storage times can be increased further by repeatedly teleporting the logical information between two codes supported by the same ion Coulomb crystal to learn information about the locations of errors. We estimate that a logical qubit encoded in such a crystal will maintain high coherence for times more than an order of magnitude longer than each physical qubit would.

Abstract:

Quantum error-correcting codes are many-body entangled states used to robustly store coherent quantum states over long periods of time in the presence of noise. Practical implementations will require efficient entangling protocols that minimize the introduction of noise during encoding or readout. We propose an experiment that uses only global operations to encode information to either the five-qubit repetition code or the five-qubit code on a two-dimensional ion Coulomb crystal architecture. We show we can prepare, read out, and acquire syndrome information for these two codes by using only six and ten global entangling pulses, respectively. We provide an error analysis, estimating we can achieve a sixfold improvement in coherence time with as much as 1% noise in the control parameters for each entangling operation.

Abstract:

Ion Coulomb crystals containing small numbers of ions have been created and manipulated in a wide range of configurations in a Penning trap, from a linear string, through various three-dimensional conformations, to a planar crystal. We show that the dynamics of the system simplifies enormously in a frame which rotates at half the cyclotron frequency and we discuss the effect of the radial cooling laser beam in this frame. Simulations show that the crystal conformations can be reproduced by finding the minimum energy configuration in a frame whose radial potential is modified by the rotation of the ion crystal. The rotation frequency of the crystal deduced from the simulations is consistent with the known laser parameters. We also show that even though the number of ions in our system is small (typically less than 20), the system still behaves like a plasma and its static properties can be calculated using the standard model for a single-component plasma in a trap

Abstract:

We perform resolved optical sideband spectroscopy on a single 40Ca+ ion in a Penning trap. We probe the electric quadrupole allowed S1/2 ↔ D5/2 transition at 729 nm and observe equally spaced sidebands for the three motional modes. The axial mode, parallel to the trap axis, is a one-dimensional harmonic oscillator, whereas the radial cyclotron and magnetron modes are circular motions perpendicular to the magnetic field. The total energy associated with the magnetron motion is negative, but here we probe only the (positive) kinetic energy. From the equivalent Doppler widths of the sideband spectra corresponding to the three motions we find effective temperatures of 1.1 ± 0.2 mK, 7 ± 3 mK, and 42 ± 8 μK for the axial, modified cyclotron, and magnetron modes, respectively. These should be compared to the cooling limits, estimated using optimal laser parameters, of 0.38 mK, 0.8 mK, and ∼10 μK. In future work we aim to perform resolved-sideband cooling of the ion on the 729-nm transition