Phonon-mediated entanglement for trapped ion quantum computing

Trapped ions are a near ideal system to study quantum information processing due to the high degree of control over the ion's external confinement and internal degrees of freedom. We demonstrate the key steps necessary for trapped ion quantum computing and focus on phonon-mediated entangling gates. We highlight several key algorithms implemented over the last decade with these gates and give a detailed description of Grover's quantum database search implemented with two trapped ion qubits.