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THU: Thursday Contributed Sessions
THU 6: Quantum Computing and Communication: Contributed Session II (Concepts)
THU 6.4: Vortrag
Donnerstag, 11. September 2025, 15:00–15:15, ZHG007
Local Complementation Orbit Scaling and Universal Resources for MBQC — •Frederik Hahn — Electrical Engineering and Computer Science Department, Technische Universität Berlin, 10587 Berlin, Germany
In Measurement-Based Quantum Computing (MBQC), quantum computation is performed through adaptive measurements on entangled resource states, with graph states serving as the canonical example. The computational power and efficiency of MBQC is fundamentally connected to the properties of these underlying graph states. Here, we focus on how classes of quantum graph states transform under local Clifford operations and how these transformations scale in the number of qubits. It is well known that local Clifford transformations can be represented by local complementations of the underlying graphs. All graphs that can be reached via local complementation from a given starting graph form that graph’s local complementation orbit. We can now investigate how the size of these local complementation orbits scales with the number of qubits n of the underlying graph states. For simple classes, such as GHZ states, this scaling is known to be linear in n and an upper bound is given by 3n. However, for general graph states, counting the orbit sizes is a problem that is known to be #P-complete. Can we still calculate the orbit scaling for classes of graph states that are known to be universal quantum computing resources?
Keywords: Local Complementation; Local Complementation Orbits; Measurement-Based Quantum Computing; Universal Resources; Scaling