Optimizing Quantum Annealing for Trapped Ions: Performance, Resources, and Noise Mitigation

Quantum annealing is a promising method for solving combinatorial optimization problems with quantum computers, but its practical performance on near-term devices is constrained by the architecture of the underlying platform, the presence of noise, and the design of the annealing protocol itself. This thesis addresses these challenges along two complementary directions, using trapped-ion hardware based on the Magnetic Gradient Induced Coupling (MAGIC) scheme as a reference architecture. On the hardware side, we analyze the MAGIC setup beyond its standard leading-order description, computing higher-order corrections arising from anharmonicities of the Coulomb repulsion and the trapping potential, as well as from magnetic-field curvature. Most resulting terms are negligible in realistic situations, with the notable exceptions of a phonon-occupation-dependent longitudinal field that grows with chain length and a two-to-one phonon conversion process. To address fluctuations of external magnetic fields, the dominant error channel for magnetically sensitive qubits, we discuss an active noise mitigation protocol for quantum annealing in which the optimization problem is encoded exclusively in two-body interactions through a single ancilla qubit, allowing periodic global spin-flip pulses to average out the longitudinal noise without disturbing the encoded ground state. Analytical arguments and numerical simulations on industrially motivated benchmarks demonstrate that modest pulse rates achievable on current hardware suffice to recover noise-free fidelity, and reveal a universal scaling of the final fidelity in terms of a generalized parameter combining noise amplitude and pulse interval. On the algorithmic side, we investigate how the structure of the annealing Hamiltonian affects the minimum spectral gap that controls the annealing runtime. On the cost side, we show that retaining the native polynomial unconstrained binary optimization (PUBO) structure of combinatorial problems, rather than reducing them to the standard quadratic (QUBO) form, can significantly enlarge the minimum gap and reduce qubit requirements, with numerical studies on the paradigmatic 3-SAT problem revealing an exponential improvement in the gap-scaling exponent for certain problem instances. Finally, we study non-stoquastic annealing protocols with the ferromagnetic p-spin model and a geometrically local Ising model as benchmarks, and find that the regimes in which non-stoquasticity enlarges the spectral gap coincide with those of enhanced bipartite entanglement and non-stabilizerness of the instantaneous ground state, providing a link between annealing performance and the difficulty of classical simulation. Taken together, these results support a clear path toward practical quantum annealing on near-term quantum hardware, combining a careful characterization of the physical platform, an active mitigation of the dominant noise channel, and a suitable design of the algorithm.