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arXiv:2505.08396 · New Journal of Physics

Graph state extraction from two-dimensional cluster states

Julia Freund, Alexander Pirker, Lina Vandré, Wolfgang Dür

Published Sep 1, 2025• 2 citations
arXivHTMLPDF

Abstract

Abstract We propose schemes to extract arbitrary graph states from two-dimensional cluster states by locally manipulating the qubits solely via single-qubit measurements. We introduce graph state manipulation tools that allow one to increase the local vertex degree and to merge subgraphs. We utilize these tools together with the previously introduced zipper scheme that generates multiple edges between distant vertices to extract the desired graph state from a two-dimensional cluster state. We show how to minimize overheads by avoiding multiple edges, and compare with a local manipulation strategy based on measurement-based quantum computation together with transport. These schemes have direct applications in entanglement-based quantum networks, sensor networks, and distributed quantum computing in general.

DOI
10.1088/1367-2630/ae02bd

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Abstract We propose schemes to extract arbitrary graph states from two-dimensional cluster states by locally manipulating the qubits solely via single-qubit measurements. We introduce graph state manipulation tools that allow one to increase the local vertex degree and to merge subgraphs. We utilize these tools together with the previously introduced zipper scheme that generates multiple edges between distant vertices to extract the desired graph state from a two-dimensional cluster state. We show how to minimize overheads by avoiding multiple edges, and compare with a local manipulation strategy based on measurement-based quantum computation together with transport. These schemes have direct applications in entanglement-based quantum networks, sensor networks, and distributed quantum computing in general.
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Abstract We present protocols to generate arbitrary photonic graph states from quantum emitters that are in principle deterministic. We focus primarily on two-dimensional cluster states of arbitrary size due to their importance for measurement-based quantum computing. Our protocols for these and many other types of two-dimensional graph states require a linear array of emitters in which each emitter can be controllably pumped, rotated about certain axes, and entangled with its nearest neighbors. We show that an error on one emitter produces a localized region of errors in the resulting graph state, where the size of the region is determined by the coordination number of the graph. We describe how these protocols can be implemented for different types of emitters, including trapped ions, quantum dots, and nitrogen-vacancy centers in diamond.
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We consider multipath generation of Bell states in quantum networks, where a preprepared multipartite entangled two-dimensional cluster state serves as a resource to perform different tasks on demand. We show how to achieve parallel connections between multiple, freely chosen groups of parties by performing appropriate local measurements along a diagonal, staircase-shaped path on a two-dimensional cluster state. Remarkably, our measurement scheme preserves the entanglement structure of the cluster state such that the remaining state is again a two-dimensional cluster state. We demonstrate strategies for generating crossing, turning, and merging of multiple measurement lines along the two-dimensional cluster state. The results apply to local area as well as to long-distance networks. Published by the American Physical Society 2024
We present protocols to generate arbitrary photonic graph states from quantum emitters that are in principle deterministic. We focus primarily on two-dimensional cluster states of arbitrary size due to their importance for measurement-based quantum computing. Our protocols for these and many other types of two-dimensional graph states require a linear array of emitters in which each emitter can be controllably pumped, rotated about certain axes, and entangled with its nearest neighbors. We show that an error on one emitter produces a localized region of errors in the resulting graph state, where the size of the region is determined by the coordination number of the graph. We describe how these protocols can be implemented for different types of emitters, including trapped ions, quantum dots, and nitrogen-vacancy centers in diamond.
Graph states are a large class of multipartite entangled quantum states that form the basis of schemes for quantum computation, communication, error correction, metrology, and more. In this work, we consider verification of graph states generated by an untrusted source and shared between a network of possibly dishonest parties. This has implications in certifying the application of graph states for various distributed tasks. We present a protocol which is globally efficient for a large family of useful graph states, including cluster states, GHZ states, cycle graph states, and more. For general graph states, efficiency with respect to the security parameter is maintained, though there is a cost increase with the size of the graph state. The protocols are practical, requiring only multiple copies of the graph state, local measurements, and classical communication.