Synthetic high angular momentum spin dynamics in a microwave oscillator

Spins and oscillators are foundational to physics and applied sciences. For quantum information, a spin 1/2 exemplifies the most basic unit, a qubit. High angular momentum spins (HAMSs) and harmonic oscillators provide multi-level manifolds (e.g., qudits) which have the potential for hardware-efficient protected encodings of quantum information and simulation of many-body quantum systems. In this talk, I will explain a new quantum control protocol that conceptually merges these disparate hardware platforms. We show how to modify a harmonic oscillator on-demand to implement a continuous range of generators associated with resonant driving of a harmonic qudit. We can interpret these dynamics as accomplishing linear and nonlinear control over a harmonic HAMS degree of freedom. The spin-like dynamics are verified by demonstration of linear spin coherent (SU(2)) rotations, nonlinear spin control, and comparison to other manifolds like simply-truncated oscillators. Our scheme allows the first universal control of such a harmonic qudit encoding: we use linear operations to accomplish four logical gates, and further show that nonlinear harmonicity-preserving operations complete the logical gate set. Our results show how motion on a closed Hilbert space can be useful for quantum information processing and opens the door to superconducting circuit simulations of higher angular momentum quantum magnetism. This talk is based on our work in doi.org/10.48550/arXiv.2405.15695.