Benchmarking memory and logic gates for trapped-ion quantum computing

Thesis

Trapped ions are a promising platform for experimental quantum computing, possessing the longest decoherence times and the highest fidelity logic gates of any candidate technology. The challenge remains to scale up ion-trap systems to larger numbers of qubits. This thesis benchmarks two fundamental operations for scalable trapped-ion quantum computing: the memory performance of a ⁴³Ca⁺ hyperfine qubit, and mixed-element entangling gates between ⁴³Ca⁺ and ⁸⁸Sr⁺.

Decoherence is usually measured over long timescales, where the memory errors ε are large compared to state-preparation and measurement errors. Information about the small-error regime relevant for quantum computing is inferred by extrapolation. In this work we use randomised benchmarking to directly measure errors as small as 1.2(7) × 10⁻⁶ after a storage time of 1 ms, which is around an order of magnitude smaller than would be expected based on the usual model of exponential decay. We find ε_m < 10⁻⁴ for up to 50 ms with no additional dynamical decoupling, and ε_m < 10⁻³ for up to 2 seconds using a simple CPMG sequence. These timescales exceed previously-demonstrated gate or measurement times in trapped-ion systems by several orders of magnitude — a requirement for quantum error correction, and a highly desirable feature for near-term processors. The qubit is robust to offsets of the external magnetic-field strength, with ε_m < 10^-4 for 1 ms even at a 50 mG offset, and we identify phase noise on the reference oscillator as the limiting factor on the memory performance.

We provide a comparison of different implementations of mixed-element geometric phase gates in the same experimental system. This includes a light-shift gate which can be implemented on both ion species using a single laser, with a fidelity of 99.8(1)% or 99.7(1)%, measured using partial state tomography or interleaved randomised benchmarking respectively. We also demonstrate several Mølmer–Sørensen gates with measured fidelities of up to 99.6(2)% (by partial state tomography); this mechanism is more susceptible to errors arising from instability of the external magnetic field. For the first time, this pushes mixed-element entangling gate fidelities over the fault-tolerant threshold level (above which error correction is possible), and puts them on par with state-of-the-art single-species gates.

Authors: Hughes, AC

• DOI: 10.5287/ora-zbdobnmdx
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English