Qutrit Clifford+T gates by two-body angular momentum couplings, rotations and one-axis-twistings

TL;DR

This paper presents a method to implement the qutrit Clifford+T gate set using two-body angular momentum couplings, rotations, and one-axis-twisting, which are experimentally feasible in various quantum systems.

Contribution

It introduces a new angular momentum-based approach for realizing qutrit Clifford+T gates with minimal interaction complexity and extends the implementation to bosonic modes using the Jordan-Schwinger map.

Findings

Local gates can be realized with rotations and one-axis-twisting operations.

Full qutrit Clifford+T set expressed via two-body angular momentum couplings.

Implementation in bosonic modes using Jordan-Schwinger map and cross-Kerr interaction.

Abstract

We develop an angular momentum representation and implementation of the Clifford+T set of unitaries for qutrits. We show that local gates from this set can be realized by the sole use of suitable rotations and one-axis-twisting operations, which are at most quadratic in the angular momentum operators and thus can be experimentally realized in many quantum systems. Controlled rotations are shown to only require linear angular momentum couplings and, as a consequence, the full qutrit Clifford+T set is shown to be expressed solely in terms of two-body angular momentum couplings, rotations and one-axis-twisting operations. By employing the Jordan-Schwinger map, we show an analogous implementation in terms of bosonic modes, improving on the number of modes with regard to a previous scheme. Moreover, we employ the cross-Kerr interaction in order to obtain any qutrit Clifford+T gate for bosonic modes. We illustrate our findings with simple schemes for preparing entangled states of interest.