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University of Colorado

1. Tan, Ting Rei. High-Fidelity Entangling Gates with Trapped-Ions.

Degree: PhD, Physics, 2016, University of Colorado

Quantum entangling logic gates are key ingredients for the implementation of a quantum information processing device. In this thesis, we focus on experimental implementations of three types of entangling geometric-phase gates with trapped ions, which rely on the effective spin-spin interactions generated with state-dependent forces. First, a mixed-species entangling gate is demonstrated using a beryllium and a magnesium ion to create a Bell state with a fidelity of 0.979(1). Combined with single-qubit gates, we use this mixed-species gate to implement controlled-NOT and SWAP gates. Second, we implement a high-fidelity universal gate set with beryllium ions. Single-qubit gates with error per gate of 3.8(1)x10-5 are achieved. By creating a Bell state with a deterministic two-qubit entangling gate, we deduce a gate error as low as 8(4)x10-4. Third, a novel two-qubit entangling gate with dynamical decoupling built-in is demonstrated with a fidelity of 0.974(4). This gate is robust against qubit dephasing errors and offers simplifications in experimental implementation compared to some other gates with trapped ions. Errors in the above implementations are evaluated and methods to further reduce imperfections are discussed. In a separate experiment, correlated measurements made on pairs of ions violate a "chained" Bell inequality obeyed by any local-realistic theory. The lowest chained Bell inequality parameter determined from our measurements is 0.296(12), this value is significantly lower than 0.586, the minimum value derived from a perfect Clauser-Horne-Shimony-Horne (CHSH) Bell inequality experiment. Furthermore, our CHSH Bell inequality results provide a device-independent certification of the deterministically created Bell states. Advisors/Committee Members: David J. Wineland, Emanuel Knill, Ana Maria Rey, Jun Ye, Eric Cornell.

Subjects/Keywords: Atomic; molecular; and optical physics; Chained Bell inequality; Mixed-species entangling gate; Quantum entanglement; Quantum information; Trapped ions; Atomic, Molecular and Optical Physics; Physics; Quantum Physics

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APA (6th Edition):

Tan, T. R. (2016). High-Fidelity Entangling Gates with Trapped-Ions. (Doctoral Dissertation). University of Colorado. Retrieved from

Chicago Manual of Style (16th Edition):

Tan, Ting Rei. “High-Fidelity Entangling Gates with Trapped-Ions.” 2016. Doctoral Dissertation, University of Colorado. Accessed March 02, 2021.

MLA Handbook (7th Edition):

Tan, Ting Rei. “High-Fidelity Entangling Gates with Trapped-Ions.” 2016. Web. 02 Mar 2021.


Tan TR. High-Fidelity Entangling Gates with Trapped-Ions. [Internet] [Doctoral dissertation]. University of Colorado; 2016. [cited 2021 Mar 02]. Available from:

Council of Science Editors:

Tan TR. High-Fidelity Entangling Gates with Trapped-Ions. [Doctoral Dissertation]. University of Colorado; 2016. Available from: