Actualizing High-Dimensional Qudits on a Trapped-Ion Quantum Computer

Abstract

Trapped-ion processors offer unrivalled qubit fidelities but encounter heating and spectral-crowding limits as chain lengths increase. This thesis mitigates those bottlenecks by encoding high-dimensional qudits in the 25 hyperfine–Zeeman sublevels of a single ¹³⁷Ba⁺ ion, thereby expanding the Hilbert space without adding additional ions. The work presented spans the key challenges of preparing arbitrary qudit basis states, efficiently maintaining calibration of the 80 transitions used to manipulate the ion, and benchmarking coherent control, culminating in performing a full quantum algorithm on a qudit. A narrow-band optical-pumping sequence was devised to prepare any of the five 6S₁/₂ (F = 2) sublevels and then selectively shelve population into the long-lived 5D₅/₂ manifold, achieving an average state-preparation-and-measurement (SPAM) fidelity of 99.51% across 25 levels. Two-point Ramsey interferometry, supported by analytic calculations of magnetic-field sensitivities and laser-polarisation geometries, allows for sub-100 Hz transition-frequency calibration and Rabi-frequency normalization. Coherence was benchmarked with multilevel Ramsey interferometry on registers of dimension d = 2–24. Star-topology encodings retained high contrast up to d = 17; beyond this, the bus-state architecture required for larger d was limited chiefly by 60 Hz and 180 Hz line noise, as confirmed by a noise-resolved Monte Carlo model that predicted measured contrasts to within ±3% with no free parameters. Using the same physical toolbox, qudit registers were mapped onto virtual-qubit subspaces and algorithmic primitives executed: the Bernstein–Vazirani algorithm succeeded with probabilities of 95% (two virtual qubits) and 84% (three virtual qubits), while a four-virtual-qubit controlled-Toffoli gate reached 99.5% success—currently limited by SPAM error—using a single Givens rotation. Collectively, these results establish ¹³⁷Ba⁺ as a versatile 25-level qudit platform and demonstrate that high-fidelity, noise-aware control of large qudit Hilbert spaces is already practical, opening a path toward resource-efficient, fault-tolerant quantum computing with far fewer ions than traditional qubit-based architectures require.