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This research challenges the assumption that non-invertible symmetry protected topological phases lack symmetric entanglers by proving their existence in 1+1d systems via topological holography. The authors provide an explicit construction of such an entangler as a matrix product unitary for specific $\mathrm{Rep}(A_4)$-symmetry phases, offering a concrete counterexample to previous theoretical limitations. This advancement refines the understanding of quantum circuit structures connecting topological states, which is relevant for foundational work in quantum simulation and error correction.

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Symmetric entanglers for non-invertible SPT phases

arXivJune 3, 20261 min read

arXiv:2509.04581v3 Announce Type: replace-cross Abstract: It has been suggested that non-invertible symmetry protected topological phases (SPT), due to the lack of a stacking structure, do not have symmetric entanglers (globally symmetric finite-depth quantum circuits) connecting them. Using topological holography, we argue that a symmetric entangler should in fact exist for $1+1$d systems whenever the non-invertible symmetry has SPT phases connected by fixed-charge dualities (FCD). Moreover, we construct an explicit example of a symmetric entangler for the two SPT phases with $\mathrm{Rep}(A_4)$-symmetry, as a matrix product unitary (MPU).

Abstract:It has been suggested that non-invertible symmetry protected topological phases (SPT), due to the lack of a stacking structure, do not have symmetric entanglers (globally symmetric finite-depth quantum circuits) connecting them. Using topological holography, we argue that a symmetric entangler should in fact exist for $1+1$d systems whenever the non-invertible symmetry has SPT phases connected by fixed-charge dualities (FCD). Moreover, we construct an explicit example of a symmetric entangler for the two SPT phases with $\mathrm{Rep}(A_4)$-symmetry, as a matrix product unitary (MPU).

Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)

arXiv:2509.04581 [cond-mat.str-el]

(or arXiv:2509.04581v3 [cond-mat.str-el] for this version)

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