State preparation and measurement in a quantum simulation of the $$O(\mathrm{3})$$ sigma model
Recently, Singh and Chandrasekharan [Phys. Rev. D 100, 054505 (2019)] showed that fixed points of the nonlinear 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 [Phys. Rev. Lett. 123, 090501 (2019)], 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 Singh and Chandrasekharan 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. Finally, we then present and analyze a quantum algorithm based on nonunitary randomized simulation methods that may yield an approach suitable for intermediate-term noisy quantum devices.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- Grant/Contract Number:
- 89233218CNA000001
- OSTI ID:
- 1774448
- Report Number(s):
- LA-UR--20-24538
- Journal Information:
- Physical Review D, Journal Name: Physical Review D Journal Issue: 11 Vol. 102; ISSN 2470-0010
- Publisher:
- American Physical Society (APS)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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