State preparation and measurement in a quantum simulation of the O(3) sigma model

TL;DR

This paper demonstrates methods for preparing ground states and measuring key quantities in a quantum simulation of the O(3) sigma model, advancing quantum field theory simulations on near-term quantum devices.

Contribution

It introduces quantum algorithms for ground state preparation and measurement of Noether charge in the O(3) sigma model, including Trotter and shadow tomography techniques.

Findings

Trotter methods quantify adiabatic ground state preparation complexity.

Shadow tomography effectively measures local observable dynamics.

Proposes a non-unitary randomized algorithm suitable for noisy intermediate-scale quantum devices.

Abstract

Recently, Singh and Chandrasekharan showed that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. In a paper by the NuQS collaboration, the proposal is made to simulate such field theories on a quantum computer using the universal properties of a similar model. In this paper, following that direction, we demonstrate how to prepare the ground state of the model from and measure a dynamical quantity of interest, the O(3) Noether charge, on a quantum computer. In particular, we apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes and use shadow tomography to measure the dynamics of local observables. We then present and analyze a quantum algorithm based on non-unitary randomized simulation methods that may yield an approach suitable for intermediate-term noisy quantum devices.