Universal set of gates for microwave dressed-state quantum computing

Abstract

We propose a set of techniques that enable universal quantum computing to be carried out using dressed states. This applies in particular to the effort of realizing quantum computation in trapped ions using long-wavelength radiation, where coupling enhancement is achieved by means of static magnetic-field gradient. We show how the presence of dressing fields enables the construction of robust single and multi-qubit gates despite the unavoidable presence of magnetic noise, an approach that can be generalized to provide shielding in any analogous quantum system that relies on the coupling of electronic degrees of freedom via bosonic modes.

Quantum dynamics of trapped ions in a dynamic field gradient using dressed states

“…Single-qubit gates using the dressed states ñ | as a qubit can be carried out by employing a resonant RF-field [35][36][37]. In order to implement conditional quantum gates, for example 2-qubit gates, the application of an RF-field tuned (close) to resonance with a motional sideband transition between dressed states can be used [1,17,22,38,39]. In this case, the effective Lamb-Dicke parameter j n , e allows for the necessary coupling between qubit states and motional states [10].…”

“…In this case, the effective Lamb-Dicke parameter j n , e allows for the necessary coupling between qubit states and motional states [10]. Gates with dressed states in a static field gradient have been proposed and successfully implemented with high fidelity [17,35,[37][38][39].…”

“…In existing implementations of dynamic MAGIC, a static bias magnetic field having a well defined magnitude is applied to a qubit resonance in order to make it to first order field insensitive and therefore only weakly sensitive to ambient magnetic fields, and thus enhance its coherence time [13,24,29,40]. An additional benefit from using dressed states that exist in a non-zero dynamic gradient field would be that dressed qubits are already resistant against dephasing by ambient noise fields [17,[35][36][37][38][39] without application of an accurately controlled, strong bias field. The dressed state qubit's coherence time would be sensitive to fluctuations in the amplitude of the dressing field.…”

“…In the main text of this article, we concentrate on conditional multi-qubit gates described by H J equation (10), which is directly induced by a single static or resonant dynamic gradient field. However, also Mølmer-Sørensen like gates [22] can be performed with MAGIC [11,17,25,38,39] with and without dressed states. In this section, we discuss some possibilities of carrying out Mølmer-Sørensen-type gates in the dressed-state picture of dynamic MAGIC.…”

“…In this section, we discuss a new idea to create a Mølmer-Sørensen gate where the gate itself is performed with two fields without gradient and the coupling between the internal and motional degrees of freedom is created by a resonant dynamic gradient field. This approach is based on methods used in [14,38,39]. In these cases, a static gradient field was used to create the coupling between internal and motional degrees of freedom.…”