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arXiv · 2607.04227

Genuine Multipartite Entanglement between Logical Qubits via Cross-Code Lattice Surgery

Alex Steiner·Tomasz Andrzejewski·Phila Rembold·Hendrik Poulsen Nautrup·Christian D. Marciniak·Robert Freund·Ivan Pogorelov·Thomas Monz·Philipp Schindler·Marcel Meyer·Nicolai Friis
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Abstract

Universal quantum computers are expected to generate arbitrary complex quantum states of logical qubits encoded in many physical qubits. This capability hinges on a fault-tolerantly implemented universal gate set, which no single quantum error-correction code admits transversally but which becomes accessible by joining complementary codes via lattice surgery. Here we report on the experimental generation and certification of logical genuine multipartite entanglement in a trapped-ion quantum processor using a transversally implemented universal logical gate set. The gate set is accessed via lattice surgery across two different codes and comprises a Hadamard gate on a four-qubit surface code and a doubly controlled Pauli-$Z$ ($\overline{\mathrm{CCZ}}$) gate on an eight-qubit 3D colour code. To showcase this lattice-surgery toolbox, we generate both stabiliser (Greenberger-Horne-Zeilinger) and non-stabiliser ($|\overline{\mathrm{CCZ}}\rangle$) states of three logical qubits and verify their genuine multipartite entanglement--a form of correlation beyond statistical mixtures of bipartite entanglement across any bipartition. We further use these cross-code primitives to demonstrate arbitrary rotations of single logical qubits via a $\overline{\mathrm{CCZ}}$-based resource gadget accessing the full universal gate set through lattice surgery. Together, these demonstrations showcase the core building blocks of an architecture for fault-tolerant quantum computation and its ability to generate complex logical quantum states.

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Alex Steiner, Tomasz Andrzejewski, Phila Rembold, Hendrik Poulsen Nautrup, Christian D. Marciniak, Robert Freund, Ivan Pogorelov, Thomas Monz, Philipp Schindler, Marcel Meyer, Nicolai Friis. 2026-07-05. Genuine Multipartite Entanglement between Logical Qubits via Cross-Code Lattice Surgery. https://arxiv.org/abs/2607.04227

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