Measuring higher-order bulk topology in a programmable quantum simulator
Abstract
Topological insulators lie outside the standard Landau paradigm: Instead of being characterized by local order parameters and spontaneous symmetry breaking, their defining properties are encoded in the global structure of their quantum states and manifested as robust boundary states. Crystalline higher-order topological insulators can extend this principle by hosting localized corner modes in two and higher dimensions. Although these boundary modes can be detected spectroscopically through the local density of states, determining the underlying bulk topology, for example through nested Wilson loops, remains an outstanding experimental challenge. Here we use up to 728 qubits in a superconducting analogue-digital quantum simulator to realize and probe a hierarchy of one-, two-, and three-dimensional topological insulators governed by effective tight-binding Hamiltonians. By reconstructing complex propagators from real-space measurements, we obtain complementary boundary and bulk characterizations: local densities of states reveal localized boundary modes, whereas experimentally reconstructed band projectors yield bulk topological invariants, culminating in a three-dimensional octupole moment extracted through third nested Wilson loops. These results establish a route to realizing, characterizing, and manipulating topologically protected states in programmable three-dimensional quantum matter.
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BibTeX
@misc{sathe2026measuring,
title = {{Measuring higher-order bulk topology in a programmable quantum simulator}},
author = {Pratik Sathe and Niclas Heinsdorf and Majid Kheirkhah and Rahul Deshpande and Fabio Altomare and Andrew J. Berkley and Martin Dehn and Richard Harris and Emile Hoskinson and Stefan Paul and Gabriel Poulin-Lamarre and Jack Raymond and Chris Rich and Mohammad H. Amin and Marcel Franz and Andrew D. King},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16046},
eprint = {2610.16046},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16046},
}
RIS
TY - UNPB
TI - Measuring higher-order bulk topology in a programmable quantum simulator
AU - Pratik Sathe
AU - Niclas Heinsdorf
AU - Majid Kheirkhah
AU - Rahul Deshpande
AU - Fabio Altomare
AU - Andrew J. Berkley
AU - Martin Dehn
AU - Richard Harris
AU - Emile Hoskinson
AU - Stefan Paul
AU - Gabriel Poulin-Lamarre
AU - Jack Raymond
AU - Chris Rich
AU - Mohammad H. Amin
AU - Marcel Franz
AU - Andrew D. King
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16046
UR - https://arxiv.org/abs/2610.16046
AB - Topological insulators lie outside the standard Landau paradigm: Instead of being characterized by local order parameters and spontaneous symmetry breaking, their defining properties are encoded in the global structure of their quantum states and manifested as robust boundary states. Crystalline higher-order topological insulators can extend this principle by hosting localized corner modes in two and higher dimensions. Although these boundary modes can be detected spectroscopically through the local density of states, determining the underlying bulk topology, for example through nested Wilson loops, remains an outstanding experimental challenge. Here we use up to 728 qubits in a superconducting analogue-digital quantum simulator to realize and probe a hierarchy of one-, two-, and three-dimensional topological insulators governed by effective tight-binding Hamiltonians. By reconstructing complex propagators from real-space measurements, we obtain complementary boundary and bulk characterizations: local densities of states reveal localized boundary modes, whereas experimentally reconstructed band projectors yield bulk topological invariants, culminating in a three-dimensional octupole moment extracted through third nested Wilson loops. These results establish a route to realizing, characterizing, and manipulating topologically protected states in programmable three-dimensional quantum matter.
ER -