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

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.

arXiv comment14 pages, 11 figures. Rev. 3: Corrected typos, updated title, revised abstract and introduction

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• Quantum Algorithms for Quantum Field Theories
• Hamiltonian simulation with nearly optimal dependence on all parameters
• Quantum-assisted quantum compiling
• A random compiler for fast Hamiltonian simulation
• Simulating lattice gauge theories on a quantum computer
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• Faster quantum simulation by randomization
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