Vertex-Minor Universal Graphs for Generating Entangled Quantum Subsystems - Université de Lyon
Conference Papers Year : 2024

Vertex-Minor Universal Graphs for Generating Entangled Quantum Subsystems

Abstract

We study the notion of k-stabilizer universal quantum state, that is, an n-qubit quantum state, such that it is possible to induce any stabilizer state on any k qubits, by using only local operations and classical communications. These states generalize the notion of k-pairable states introduced by Bravyi et al., and can be studied from a combinatorial perspective using graph states and k-vertex-minor universal graphs. First, we demonstrate the existence of k-stabilizer universal graph states that are optimal in size with n = Θ(k2) qubits. We also provide parameters for which a random graph state on Θ(k2) qubits is k-stabilizer universal with high probability. Our second contribution consists of two explicit constructions of k-stabilizer universal graph states on n = O(k 4) qubits. Both rely upon the incidence graph of the projective plane over a finite field Fq. This provides a major improvement over the previously known explicit construction of k-pairable graph states with n = O(23k), bringing forth a new and potentially powerful family of multipartite quantum resources.
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hal-04632835 , version 1 (04-11-2024)

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Maxime Cautrès, Nathan Claudet, Mehdi Mhalla, Simon Perdrix, Valentin Savin, et al.. Vertex-Minor Universal Graphs for Generating Entangled Quantum Subsystems. ICALP 2024 51st EATCS International Colloquium on Automata, Languages and Programming, European Association for Theoretical Computer Science (EATCS), Jul 2024, Tallinn, Estonia. ⟨10.4230/LIPIcs.ICALP.2024.36⟩. ⟨hal-04632835⟩
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