TRAPPED IONS: FROM ERROR CORRECTION TO SIMULATION OF QUANTUM FIELD THEORIES

Abstract

Trapped ions stand out as a leading platform for quantum computing due to their long coherence times, high-fidelity quantum gates, and the ability to precisely control individual qubits, enabling scalable and precise quantum computations. This dissertation reports advances in quantum computing with trapped ions, focusing on robust and high-fidelity entanglement generation, logical qubit encoding, and applications in quantum simulations of high-energy physics.

In particular, we report the implementation of a novel pulse optimization scheme forachieving high-fidelity entangling gates in our setup. The scheme enables a balanced trade- off between robustness to experimental drift, laser power, and gate duration, without the need for expensive optimization. We also demonstrate the implementation of the Shor code with different code distances on our trapped-ion quantum computer, highlighting the fault-tolerant preparation of a logical qubit with high fidelity and showcasing the potential for reliable quantum computing.

Finally, we detail an experimental quantum simulation of the Schwinger model, a quantum electrodynamics theory in 1+1 dimensions, using two, four, and six qubits, demonstrating non-perturbative effects such as pair creation over extended periods of time. We study the gate requirement for two formulations of the model using a quantum simulation algorithm, considering the trade-offs between Hamiltonian term ordering, the number of time steps, and experimental errors. We employ a symmetry-protection protocol with random unitaries and a symmetry based post-selection technique to minimize errors. This work emphasizes the importance of the integrated approach between theory, algorithms, and experiments for efficient simulation of complex physical systems like lattice gauge theories.