Universal SU(N) gates on an error-detected qudit embedded within a multimode superconducting device: Part 1

A qudit-based quantum computer can offer advantages in algorithm depth and hardware efficiency compared to qubit-based machines. This has motivated researchers to look beyond engineering two-level systems, and recent results have shown that many well-explored platforms can be straightforwardly adapted to qudits. However, the larger computational space adds to the complexity of performing control and measurement, and makes it more difficult to build operations that are resilient to hardware noise. In this two-part talk, we show that a two-mode (“dual-rail”) superconducting device not only offers straightforward methods for implementing the higher-order gates needed for universal control of a protected logical qudit, but does so in a way that still allows errors during the gates to be detected.

The first part will explore the mechanisms behind error-detectable qudits which can be adapted from standard circuit QED techniques. We will also introduce the beamsplitter interaction, which acts as a displacement operation within the qudit defined on the photon-number-conserving manifold of the dual-rail cavities. Lastly, we will examine why the beamsplitter interaction is essential for achieving qudit control with built-in error detectability.