One- and two-dimensional cluster states for topological phase simulation and measurement-based quantum computation

Abstract:Quantum entanglement is a fundamental resource for quantum information processing and serves as a critical benchmark for quantum hardware performance. Cluster states are a special class of entangled states that serve as universal resources for measurement-based quantum computation and possess an intrinsic symmetry-protected topological order, which confers robustness against symmetry-respecting noise. Here we report the scalable preparation and verification of genuine multipartite cluster states on the 105-qubit Zuchongzhi 3.1 superconducting processor. We achieve one-dimensional cluster states of up to 95 qubits and two-dimensional cluster states of up to 72 qubits. The symmetry-protected topological cluster states exhibit input-state-dependent robustness under symmetry-breaking perturbations due to an operational parity structure that enhances the performance of measurement-based quantum computation. Furthermore, we use our two-dimensional cluster states to implement the Deutsch-Jozsa algorithm within the measurement-based quantum computation framework, achieving higher output-state fidelity compared with traditional circuit-based models and a query efficiency advantage over classical approaches. Our work establishes a scalable platform that combines large-scale entanglement generation, symmetry-protected topological order and practical quantum algorithms to enable robust, fault-tolerant measurement-based quantum computation.

Main text: 24 pages, 5 figures; supplementary materials: 64 pages, 25 figures. Total: 88 pages, 30 figures

arXiv:2505.01978 [quant-ph]

(or arXiv:2505.01978v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2505.01978 Focus to learn more arXiv-issued DOI via DataCite

https://doi.org/10.1038/s41567-026-03179-6 Focus to learn more DOI(s) linking to related resources

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