Universal SU(N) gates on an error-detected qudit embedded within a multimode superconducting device: Part 2

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.

In the second part, we demonstrate SU(N) operations on a logical qudit by adapting photon-number-resolved control methods developed for linear oscillators. We highlight that the ability to detect errors can improve the qudit’s performance beyond the usual limits imposed by photon loss.