Qubitization strategies for bosonic field theories

Abstract

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 $O(3)$ non-linear $\sigma$-model - one that truncates the Hilbert space for the unit sphere by setting an angular momentum cutoff and a fuzzy sphere truncation inspired by non-commutative 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 $\sigma$-model and that the anti-ferromagnetic fuzzy model agrees with the full theory.

10 pages, 5 figures

References in corpus (4)

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• A Formulation of Lattice Gauge Theories for Quantum Simulations
• The spectrum of qubitized QCD: glueballs in a $S(1080)$ gauge theory
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Cited by in corpus (7)

• Exponential improvements in the simulation of lattice gauge theories using near-optimal techniques
• Fuzzy gauge theory for quantum computers
• Preparation for Quantum Simulation of the 1+1D O(3) Non-linear σ-Model using Cold Atoms
• Towards a Quantum Simulation of Nonlinear Sigma Models with a Topological Term
• Continuous variable quantum computation of the $O(3)$ model in 1+1 dimensions
• Estimating truncation effects of quantum bosonic systems using sampling algorithms
• Toward quantum computations of the $O(3)$ model using qumodes