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arXiv:1907.08569 · Physical Review Research

Practical trapped-ion protocols for universal qudit-based quantum computing

Pei Jiang Low, Brendan White, Andrew A. Cox, Matthew L. Day, Crystal Senko

Published Jul 23, 2020• 133 citations
arXivHTMLPDF

Abstract

This work uses multi-level qudit systems for quantum computation in the context of trapped ions and show all of the necessary operations for qudit quantum computation with trapped ions along with realistic error estimates.
DOI
10.1103/physrevresearch.2.033128

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Abstract Scaling up the computational space of a quantum system is necessary to demonstrate quantum algorithmic advantage. Currently, including more information carriers is still a physical challenge in general. A less explored avenue for scaling up the computational space involves utilizing the rich energy level structure of a trapped ion to encode multi-level qudits rather than two-level qubits. Here we show control and single-shot readout of qudits with 13 computational states in our chosen information host, 137 Ba + . Utilizing the additional energy states found in 137 Ba + comes with non-trivial complexities which obscure the practical choices of energy states for qudit encoding. We report on tools we have developed for predicting energy states that are practical for qudit encoding, validated with good agreement with our experimental data. We also identify the major error sources for qudit control with 137 Ba + as avenues for improvement to achieve high fidelity operations.
Quantum information has typically focused on using 2-level qubits to perform simulation and computation. We propose to expand the number of levels for computation using qudits, where \\(d>2\\). Doing so could be a viable option for making trapped ion systems scalable for quantum computation. Our group in particular will use Barium ions because of some energy features and convenient laser wavelengths. This thesis presents much of the necessary background needed to work with Barium as a qudit for quantum computation. Energy structure, branching ratios, and saturation intensities are derived and presented. In addition, a method for selecting different isotopes of Barium for trapping is discussed. A method for measuring out the state of a Barium qudit is presented, with error rates estimated to be under \11\\%\1 for up to 5-level qudits. Finally, various optics projects which were necessary for building up our first ion trap are outlined.
The accurate estimation of observables is a crucial task in quantum computing. Recent advances have highlighted the need for (a) specialized protocols for qudit-based devices, that include (b) error-aware strategies. Here, we present AQUIRE, the first protocol that can (a) accurately estimate both the mean and the error of an observable on qudit-based quantum computers. AQUIRE achieves this by constructing a Bayesian model to accommodate generalized Pauli operators. It is designed to continuously monitor the estimated average and the associated error of the observable, adjusting the subsequent measurements in real-time. Additionally, AQUIRE is (b) device- and experiment-specific error-aware, and accounts for hardware imperfections and experimental noise during the estimation process. We demonstrate AQUIRE's advantage via numerical simulations and showcase its ability to quantify the noise affecting the estimation by implementing it on a trapped-ion qudit quantum processor. By exploiting general commutation relations and overlap grouping measurements, our protocol is state-of-the-art when restricted to qubit-based quantum computers and extends this advantage to the qudit case.