Characterisation and control of trapped-ion qubit

Abstract

Trapped ions are one of the promising platforms that realise a quantum bit, or qubit, in quantum computation. The fundamental quantum operations, such as single- and two-qubit gates, have been demonstrated. However, the fidelity of a quantum gate is easily compromised by inadequate qubit initialisation or incorrect settings of experimental parameters. This thesis aims to address those issues, allowing for the complete coherent control of the trapped ion qubit.

This thesis describes the construction and testing of a new ion trap apparatus for optimal control of a trapped ion qubit, which ideally makes the quantum gates more robust against experimental parameters.

This thesis extends the two-level Ramsey interferometry to higher order in a trapped ion. Creation and certification of the motional superposition require excellent control of the trapped ion qubit. We prepare a motional superposition state with undesired AC Stark shift due to the off-resonant carrier compensated by our compensation scheme. We successfully certify the superposition consists of three motional Fock states, $(\ket{0}+\ket{1}+\ket{2})/\sqrt{3}$, using a robust certifier derived from statistical moments of the interference pattern.

The thesis presents the results of a Bayesian estimator that estimates the Rabi frequency and detuning frequency by processing the measurement records via Bayes' theorem. We compare the estimate from the Bayesian estimator and the standard fitting method, in which Rabi frequency and detuning are estimated by fitting the Rabi oscillation and the frequency spectrum of the ion, and found the Bayesian estimator can estimate those unknown parameters as accurately as the standard fitting method, but only requires less than one-hundredth of measurements necessary for the fitting method.

We also experimentally demonstrate measurement-based cooling, which is an alternative way to cool the ion to its ground state. Contrary to resolved sideband cooling, which is routinely used for the ground state cooling in our experiment, this cooling method probabilistically prepares the ion in its motional ground state. We perform a state-dependent mapping operation that maps the ion's atomic state to either $\ket{g}$ or $\ket{e}$ conditioned on its motional states: the ion's atomic state is mapped to $\ket{e}$ if its motional state is $\ket{0}$; otherwise the ion's atomic state is mapped to $\ket{g}$. The following projective measurement of the atomic state of the ion enables the discrimination between the motional ground state and the motional excited states. Therefore we can prepare the ion in the motional ground state by selecting the instances where the ion is measured to be in $\ket{e}$, which heralds the motional ground state.

In the near future, the group will begin a project to implement and evaluate recent proposals for making quantum gates robust against a mis-set of frequency using a polychromatic light field.