Qudit Quantum Computation on Trapped Barium-137 Ions

Abstract

Quantum processors promise to revolutionise humanity’s computational prowess. Today’s leading quantum processors are built on trapped atomic ions, using one particular isotope of barium. In this thesis, we explore a less pursued avenue toward using this promising ion, 137Ba+, as the quantum system for fully scaled and fault-tolerant quantum computing. We explore the advantages and trade-offs inherent in using this atomic playground to encode not just the typical two level systems that make the canonical qubits of today’s quantum computers, but instead pushing this boundary out to encoding dozens of levels (qudits) in individual ions.

Starting from precision spectroscopy of the stable and meta-stable manifolds within the ion that make this high-dimensional control possible, we first design protocols for high-fidelity state preparation and measurement (SPAM) over 25 distinct levels which we implement with an average fidelity of 99.51%. Using an extension of the classic Ramsey interferometric techniques for probing the noise and coherence of quantum systems, we study the coherence properties of multi-level superpositions in this ion. We develop a no-free-parameters model of the behaviour of this system in which noise sources such as laser frequency fluctuations, magnetic field drifts, calibration errors, and coherent errors are independently characterised in order to fully capture system performance.

We use this demonstrated coherent control to execute small quantum algorithms by encoding multiple virtual qubits within a single trapped 137Ba+ ion. We implement the well-known Bernstein-Vazirani key-finding algorithms on 2- and 3-virtual qubit encodings and demonstrate secret key guessing success probabilities of 98% and 84% respectively. We also implement Grover’s database search algorithm on 2-virtual qubits, showing a 96% success rate.

We then demonstrate a simple and scalable “all-software” approach to compensating for one of the largest sources of noise in our system: AC power-line synchronous magnetic field fluctuations. By characterising this source precisely, and compensating the attendant frequency and phase shifts associated with this coherent noise source, we are able to push the implementation of the Bernstein-Vazirani algorithm up to a 16-level qudit, with a 70% algorithm success rate. This is a record high dimension on which to implement a full algorithm for any qudit, across any quantum computing platform.

Finally, we demonstrate fully Haar-random unitary gate set benchmarking on qudits of varying dimension in this platform and comment on the future feasibility of high-dimensional encoding in trapped ion processors. Taken together, these results present a strong case for quantum processors with primitives that encode more than the typical two states in any given single ion.