Quantum gate optimisation in stoichiometric rare-earth ensembles

This thesis is an investigation into implementing quantum computing in stoichiometric rare-earth systems, with the crystal EuCl3 6D2O used as an example system. In a stoichiometric satellite system, a crystal stoichiometric in one rare-earth species is doped with a second rare-earth. The ions around a dopant experience shifts in their optical and hyperfine transition frequencies uniquely determined by their location relative to the dopant. This creates an ensemble of identical spin clusters with strong and consistent local interactions between ions in spin clusters. Ensembles of ions in the unique positions around the dopant can be used as qubits, enabling the creation of small quantum systems of 5-10 high-quality qubits for use in a small quantum processor. This thesis investigates the conditions necessary for implementation of a quantum processor in EuCl3 6D2O and other stoichiometric rare-earth systems. The primary factors explored in this thesis are the manipulation of system parameters and the implementation and optimisation of quantum gates in EuCl3 6D2O to minimise gate error. The quantum gate error of EuCl3 6D2O with Gaussian pulse shapes was first explored. It was determined that the oscillator strengths of EuCl3 6D2O are too unequal to be able to perform low error quantum operations at zero-field. The use of applied magnetic fields to manipulate the oscillator strengths and hyperfine splittings of EuCl3 6D2O was explored. It was found that broad magnetic field regions exist in which the parameters of EuCl3 6D2O can be manipulated to be closer to an ideal L system. Through the application of an 8T field, it was found that a three-qubit bit-flip error correction sequence could potentially be implemented with an error as low as 0.022. The optimisation of the optical pulses used to perform quantum gates in EuCl3 6D2O was investigated. It was determined that standard Gaussian pulses were sufficient to perform gates of a sufficiently low error for quantum error correction. Simulations of a NOT gate on an inhomogeneously broadened ensemble were performed with both a compensated pulse sequence and direct rotations. It was determined that compensated pulses do not reduce gate error over direct pulses in EuCl3 6D2O. The use of arbitrary pulse shapes was investigated and it was determined that a reduction of approximately 37% in gate error could be achieved by using optimised pulses of arbitrary shape. It was determined that the quantum gate error in europium systems is fundamentally limited by the size of the europium hyperfine splittings relative to the optical coherence time. The rare-earth species erbium and holmium were proposed for computing due to their large hyperfine structure, and it was established that there is potential for up to a 100-fold reduction in quantum gate error by moving to these host ions