Control of trapped-ions for quantum error correction
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 which realize elements of error correction using two different approaches. Working with the electronic states of a three-ion chain, we have demonstrated repeated multi-qubit correlation readout which we have used to stabilize entangled states using real-time active feedback. While this contains the basic ingredients for quantum error-correction, realization of the latter requires the control of many more ions. An alternative approach to realizing full quantum codes uses single harmonic oscillators, which we realize in 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. I will describe experiments in which we create, measure and manipulate logical information stored in such a code, including teleportation of non-Clifford rotations onto the code space. Alongside the direct focus on quantum computation, the techniques developed for this work also provide new perspectives for quantum control and measurement.