QUANTUM APPLICATIONS, PARALLEL OPERATIONS, AND NOISE CHARACTERIZATION ON A TRAPPED ION QUANTUM COMPUTER

Abstract

Quantum computing holds vast potential for solving classically hard problems ranging from optimization to simulations critical in material science research and drug discovery. While large-scale fault-tolerant quantum computers capable of these tasks are yet to come, small and noisy prototypes have been demonstrated on several candidate platforms. Among these, trapped-ion qubits have been at the forefront of quantum computing hardware because of their long coherence times, high-fidelity quantum gates, and all-to-all connectivity. This dissertation investigates new methods for efficient quantum computing at the interface of quantum information theory and trapped-ion experiments, and advances both the control of physical trapped-ion hardware and the characterization of their decoherence processes. We present a number of proof-of-principle experiments for early quantum applications on a trapped-ion quantum computer (TIQC). First, we experimentally show that the results of the Quantum Approximate Optimization Algorithm (QAOA)---a method to solve graph combinatorial optimization problems by applying multiple rounds of variational circuits---improve with deeper circuits for multiple graph-theoretic problems on several arbitrary graphs. We also demonstrate a modified version of QAOA that allows sampling of all optimal solutions with predetermined weights. Additionally, we implement the real-time evolution of a one-dimensional scattering process and demonstrate a more efficient and accurate method to extract the phase shift, forming a tentative first step toward the goal of lattice quantum chromodynamics (QCD) simulation. Furthermore, we demonstrate two Bell-type nonlocal games that can be used to prove quantum computational advantage as well as offer a set of practical and scalable benchmarks for quantum computers in the pre-fault-tolerant regime. Our experimental results indicate that the performance of quantum strategies for the non-local games exceeds basic classical bounds, and is on the cusp of demonstrating quantum advantage against more complicated classical strategies. We propose and demonstrate a high-fidelity and resource-efficient scheme for driving simultaneous entangling gates on different sets of orthogonal motional modes of a trapped-ion chain. We show the advantage of parallel operation with a simple digital quantum simulation where parallel implementation improves the overall fidelity significantly. We test and improve the performance of an ancilla-assisted protocol for learning Pauli noise in Clifford gates on a TIQC. With N ancilla, Pauli noise in an N-qubit Clifford gate can be learned with a sample size linear to N. We also design and demonstrate a way to improve the protocol's performance by reducing ancilla noise in post-processing.