Implementation and Applications of Two Qutrit Gates in Superconducting Transmon Qubits*

With recent improvements in state-selective quantum control and the coherent lifetimes of superconducting circuits, it has become feasible to encode quantum information in the higher excited states of a transmon qubit. A three-level quantum system (qutrit) has an exponentially larger Hilbert space for a given number of elements and is the minimal system required to observe non-contextuality and the physics of scrambling. Here we describe the implementation of a gate between two transmon qutrits in a 2D planar architecture. The gate is constructed by incorporating the well-established cross-resonance interaction into a multi-level decoupling sequence. In combination with single qutrit control, this gate allows for the implementation of a maximally scrambling operation which is a key component in a recently proposed proof-of-principle experiment to simulate the decoding of Hawking radiation to reconstruct a quantum state.