Encoding and controlling a GKP logical qubit in a trapped-ion oscillator*

Useful large-scale quantum computers are expected to spend a vast majority of their resources on error correction. Quantum error correction requires storing qubits in systems with enlarged Hilbert spaces, on which measurements can be made to extract error information without disturbing the stored information. I will describe trapped-ion experiments in which we encode a logical qubit using the motion of a single trapped ion. One powerful code of this type is constructed from a set of logical and error-check operators which are displacements in the oscillator phase space [1,2]. We create, measure and manipulate logical information stored in such a code, including teleportation of non-Clifford rotations onto the code space [3]. Alongside the direct focus on quantum computation, the techniques developed for this work also provide new perspectives for quantum control and measurement.

[2] Gottesman et al. PRA 64, 012310 (2001)
[3] Noh et al. arXiv:1801.07271 (2018)
[4] Flühmann et al. arXiv:1807.01033 (2018)