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arXiv · 2308.02387

Isolated zero mode in a quantum computer from a duality twist

Sutapa Samanta·Derek S. Wang·Armin Rahmani·Aditi Mitra
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Abstract

Investigating the interplay of dualities, generalized symmetries, and topological defects beyond theoretical models is an important challenge in condensed matter physics and quantum materials. A simple model exhibiting this physics is the transverse-field Ising model, which can host a topological defect that performs the Kramers-Wannier duality transformation. When acting on one point in space, this duality defect imposes the duality twisted boundary condition and binds a single zero mode. This zero mode is unusual as it lacks a localized partner in the same $\mathbb{Z}_2$ sector and has an infinite lifetime, even in finite systems. Using Floquet driving of a closed Ising chain with a duality defect, we generate this zero mode in a digital quantum computer. We detect the mode by measuring its associated persistent autocorrelation function using an efficient sampling protocol and a compound strategy for error mitigation. We also show that the zero mode resides at the domain wall between two regions related by a Kramers-Wannier duality transformation. Finally, we highlight the robustness of the isolated zero mode to integrability- and symmetry-breaking perturbations. Our findings provide a method for exploring exotic topological defects, associated with noninvertible generalized symmetries, in digitized quantum devices.

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Sutapa Samanta, Derek S. Wang, Armin Rahmani, Aditi Mitra. 2023-08-04. Isolated zero mode in a quantum computer from a duality twist. https://doi.org/10.22331/q-2025-12-30-1957

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