Toward quantum computations of the $O(3)$ model using qumodes

We express the discrete 1+1-dimensional $O(3)$ non-linear sigma model (NL$\sigma$M) in a form well-suited for the continuous variable approach to quantum computing. Within the Schwinger boson formulation, we need two qumodes (quantum-mechanical oscillators) at each lattice site. We envision that it might be possible to reach the scaling regime of this model and observe asymptotic freedom on near-term photonic quantum devices in the coming decade.