Universality of a truncated sigma-model

Abstract

Bosonic quantum field theories, even when regularized using a finite lattice, possess an infinite dimensional Hilbert space and, therefore, cannot be simulated in quantum computers with a finite number of qubits. A truncation of the Hilbert space is then needed and the physical results are obtained after a double limit: one to remove the truncation and another to remove the regulator (the continuum limit). A simpler alternative is to find a model with a finite dimensional Hilbert space belonging to the same universality class as the continuum model (a "qubitization"), so only the space continuum limit is required. A qubitization of the $1+1$ dimensional asymptotically free $O(3)$ nonlinear $\sigma$-model based on ideas of non-commutative geometry was previously proposed arXiv:1903.06577 and, in this paper, we provide evidence that it reproduces the physics of the $\sigma$-model both in the infrared and the ultraviolet regimes.

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Cited by in corpus (6)

• How many quantum gates do gauge theories require?
• Qubitization strategies for bosonic field theories
• Fuzzy gauge theory for quantum computers
• Continuous variable quantum computation of the $O(3)$ model in 1+1 dimensions
• Space-time symmetric qubit regularization of the asymptotically free two-dimensional O(4) model
• Lattice regularizations of $\theta$ vacua: Anomalies and qubit models