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

TL;DR

This paper proposes a method to simulate the 1+1-dimensional $O(3)$ non-linear sigma model using qumodes in quantum computing, aiming to observe asymptotic freedom on near-term photonic devices.

Contribution

It reformulates the $O(3)$ model for continuous variable quantum computing using qumodes, enabling potential near-term quantum simulations of its properties.

Findings

Formulation suitable for photonic quantum devices

Potential to observe asymptotic freedom experimentally

Scalability prospects for quantum simulation of the model

Abstract

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.