aiqbench takeQuantum Computing

This research establishes a fundamental limitation in quantum simulation by proving that stabilizer states cannot approximate the vacuum or short-distance physics of local Quantum Field Theories. Consequently, simulating physically relevant QFTs necessitates resources beyond standard Clifford operations and stabilizer circuits, highlighting an intrinsic complexity gap for near-term quantum hardware. The findings also offer new insights into holography through the lens of entanglement spectrum properties in type III$_1$ von Neumann algebras.

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Universality of Magic in Local Quantum Field Theory

arXivJuly 21, 20261 min read

arXiv:2607.16403v1 Announce Type: cross Abstract: We show that no stabilizer state in a discrete realization of a local quantum field theory can flow in the continuum to the vacuum or to any state that resembles the vacuum at short distances. The argument rests on the fact that the entanglement spectrum is flat for stabilizer states but non-flat for cyclic and separating states in a local QFT as a consequence of the type III$_1$ nature of the von Neumann algebras associated with arbitrary subregions. Our result implies that simulating physically relevant QFT states necessarily requires quantum resources beyond stabilizer states and Clifford operations. We comment on the implications for holography.

Abstract:We show that no stabilizer state in a discrete realization of a local quantum field theory can flow in the continuum to the vacuum or to any state that resembles the vacuum at short distances. The argument rests on the fact that the entanglement spectrum is flat for stabilizer states but non-flat for cyclic and separating states in a local QFT as a consequence of the type III$_1$ nature of the von Neumann algebras associated with arbitrary subregions. Our result implies that simulating physically relevant QFT states necessarily requires quantum resources beyond stabilizer states and Clifford operations. We comment on the implications for holography.

High Energy Physics - Theory (hep-th); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Lattice (hep-lat); Quantum Physics (quant-ph)

arXiv:2607.16403 [hep-th]

(or arXiv:2607.16403v1 [hep-th] for this version)

https://doi.org/10.48550/arXiv.2607.16403 arXiv-issued DOI via DataCite (pending registration)

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