Nuclear spin interactions and coherent control in rare-earth-ion-doped crystals for quantum computing

This thesis work concerns studies of two rare-earth-ions, praseodymium (Pr3+) and europium (Eu3+), doped into a yttrium orthosilicate (Y2SiO5) crystal for applications in quantum computing. The nuclear spin levels of these ions can have very long coherence times, up to several hours. Coherence can also be effectively transferred between the optical and hyperfine levels. These systems, therefore, have been extensively used for storing quantum information e.g. quantum memories and quantum computing. With the goal of working towards building a rare-earth quantum computer, the aim of this thesis work is to understand the processes affecting the lifetime of the hyperfine states used as qubits and design ways to achieve high-fidelity gate operations.

One of the mechanisms of relaxation between hyperfine levels is flip-flop processes due to magnetic dipole-dipole interaction between neighboring ions. Modeling of this mechanism has generally been macroscopic, characterized
by an average rate describing the relaxation of all ions. One part of this thesis presents a microscopic model of flip-flop interactions between individual nuclear spins of dopant ions. Every ion is situated in a unique local environment in the crystal, where each ion has different distances and a unique orientation relative to its nearest neighbors, as determined by the lattice structure and the random doping. Thus, each ion has a unique flip-flop rate and the collective relaxation dynamics of all ions in a bulk crystal is a sum of many exponential decays, giving
rise to a distribution of rates rather than a single average decay rate. The model can serve as a general tool to calculate other kinds of interactions at the microscopic level and it could also be used to study the dynamics of
other rare-earth ions in different materials.

Another part of this thesis identifies several limitations in the rare-earth system that must be overcome in order to successfully perform gate operations with high fidelities. This is presented in the context of ensemble qubits in rare-earth-ions. Although single-ion qubits are essential for scalability, an approach to building small computing nodes using ensemble qubits exists. There is also reason to explore fundamental limitations using the available technology. Two methods to tackle these limitations are presented. One is an adiabatic approach, which is slow
but resilient against several imperfections in the system. The second method is ‘Shortcut to Adiabaticity’, which is a faster approach and can be advantageous to perform operations with high fidelity when the initial and final
quantum states are known.