We demonstrate how to prepare the ground state of the O(3)-sigma model and measure the O(3) Noether charge, on a quantum computer. We present and analyze a quantum simulation algorithm that is suitable for near-term noisy quantum devices.
We consider a crucial step in simulating field theories, which is a method of truncating the Hilbert space and representing a states of the truncated model using qubits. We use a method that preserves the symmetries of the desired continuum QFT but acts on a smaller space.
For details see "Quantum simulation of the qubit-regularized O(3)-sigma model" by Alexander J. Buser, Tanmoy Bhattacharya, Lukasz Cincio, Rajan Gupta. arXiv:2006.15746.