Towards Quantum Advantage with Trapped Ions

Abstract

Physical systems that use the quantum laws of Nature may potentially achieve quantum advantage—the ability to solve problems intractable for conventional computers. Although quantum information is fragile, quantum error correction may enable the construction of fault-tolerant quantum computers capable of executing deep computations. Also, for the problem of simulating model quantum systems, quantum hardware can utilize its native interactions to perform analog quantum simulation. Fault-tolerant quantum computation and analog quantum simulation are viable paths towards quantum advantage, both requiring precise control of the quantum computing system. This thesis explores theoretical efforts in quantum control, quantum error correction, and analog quantum simulation in the trapped-ion platform. I introduce methods for finding entangling-gate pulses that are robust to noise, leading to their experimental realization, and present an efficient approach for characterizing the motional-mode parameters. Then, I propose using metastable states of trapped ions to enable erasure conversion, which potentially improves the performance of quantum error correction. Moving to analog quantum simulation, I evaluate the prospect of achieving quantum advantage in simulating condensed-phase chemical dynamics, leading to the experimental quantum simulation of spin-boson models. Finally, I study phase transitions in the non-Gaussian extension of the open quantum Rabi model, which offers an interesting target for analog quantum simulation.