Synthetic high angular momentum spin dynamics for bosonic control in a microwave oscillator

Multilevel quantum systems exemplified by high angular momentum spins (HAMS) and harmonic oscillators, are foundational for hardware-efficient multi-level quantum information encodings and simulation of many-body quantum systems. In our work [1], we have demonstrated a new quantum control protocol that conceptually merges the HAMS and harmonic oscillator platforms. We show how to modify a harmonic oscillator on demand to implement a continuous range of generators to accomplish linear and nonlinear HAMS dynamics. Our scheme allows universal control of a spin cat logical qubit encoding with interpretable drive pulses: we use linear spin operations to accomplish four logical gates and further show that nonlinear spin rotations can complete the logical gate set. However, these gate operations are not protected from errors during the operation – which remain as a significant challenge for bosonic encodings in harmonic oscillators. We propose how to theoretically construct error-transparent amplitude-mixing gates for the binomial encoding in harmonic oscillators and how we can leverage our new scheme to implement them [2]. We plan to numerically optimize this gate construction to realize error transparent gates in experiment.

[1] S. Roy et al, Synthetic high angular momentum spin dynamics in a microwave oscillator, Phys. Rev. X 15, 021009 (2025)

[2] O. C. Wetherbee et al, A Mathematical structure for amplitude-mixing error-transparent gates for binomial codes, Quantum 9, 1890 (2025)