Higher energy levels of a quantum processor are usually considered an annoyance. It leaves room for leakage and coherent errors that can be hard to diagnose and mitigate. But they can also be seen as a quantum resource. One can use the larger Hilbert space to implement algorithms more compactly. Another advantage of introducing these levels is the possibility to reduce the number of entanglement gates to perform complex gates like the Toffoli gate
In our group, we are trying to take advantage of the multi-level structure of our transmon 8-qubits chip to construct a qutrit quantum processor rather than a qubit-based one. There are several aspects to this work: First, we have implemented qutrit singles gates and entanglement gates, overcoming the difficulties coming from crosstalk and controlling a larger control space. Using this architecture, we have showcased a multi-qutrit algorithm using 5 qutrits to simulate the Scrambling of information of a Black Hole [2]. Finally, the last aspect of this project is to develop a useful metric to assess the performance of qutrit-based processors and how to compare it to a qubit-based processor. For this last question, we have generalized several randomized benchmarking protocols to qutrits and performed characterization with these techniques.
