Qubitization strategies for bosonic field theories

Quantum simulations of bosonic field theories require a truncation in field space to map the theory onto finite quantum registers. Ideally, the truncated theory preserves the symmetries of the original model and has a critical point in the same universality class. In this paper, we explore two diffe...

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Bibliographic Details
Published in:Physical review. D 2023-02, Vol.107 (3), Article 034503
Main Authors: Alexandru, Andrei, Bedaque, Paulo F., Carosso, Andrea, Cervia, Michael J., Sheng, Andy
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
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Summary:Quantum simulations of bosonic field theories require a truncation in field space to map the theory onto finite quantum registers. Ideally, the truncated theory preserves the symmetries of the original model and has a critical point in the same universality class. In this paper, we explore two different truncations that preserve the symmetries of the 1+1-dimensional Ο⁡(3) nonlinear σ model—one that truncates the Hilbert space for the unit sphere by setting an angular momentum cutoff and a fuzzy sphere truncation inspired by noncommutative geometry. We compare the spectrum of the truncated theories in a finite box with the full theory. We use open boundary conditions, a novel method that improves on the correlation lengths accessible in our calculations. We provide evidence that the angular-momentum truncation fails to reproduce the σ model and that the antiferromagnetic fuzzy model agrees with the full theory.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.107.034503