Isolated zero mode in a quantum computer from a duality twist

• URL: http://arxiv.org/abs/2308.02387v4
• Date: Mon, 25 Nov 2024 18:51:52 GMT
• Title: Isolated zero mode in a quantum computer from a duality twist
• Authors: Sutapa Samanta, Derek S. Wang, Armin Rahmani, Aditi Mitra,
• Abstract summary: We investigate the interplay of dualities, generalized symmetries, and topological defects beyond theoretical models. A simple model exhibiting this physics is the transverse-field Ising model, which can host atopological defect. When acting on one point in space, this duality defect imposes the duality twisted boundary condition and a single zero mode.
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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 atopological 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 $Z_2$ 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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