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THU: Thursday Contributed Sessions
THU 1: Fault-Tolerant Quantum Computing: Contributed Session (Quantum Error Correction)
THU 1.7: Talk
Thursday, September 11, 2025, 15:45–16:00, ZHG001
Graph Representations and Circuit-Based Codes from GHZ States — •Zahra Raissi1, Hrachya Zakaryan1, Konstantinos-Rafail Revis1, Yinzi Xiao1, Stanislaw Soltan1, Mario Flory2, and Johannes Blömer1 — 1Department of Computer Science and Institute for Photonic Quantum Systems (PhoQS), Paderborn University, Paderborn, Germany — 2Jagiellonian University, Cracow, Poland
GHZ states are key resources for quantum communication and error correction. While symmetric GHZ states (defined as equal superpositions of basis states) are known to be locally unitary (LU) equivalent to both star-shaped and fully connected graph states, their non-symmetric counterparts lack a comparable framework. Non-symmetric GHZ states, defined as unequal superpositions of basis states, naturally arise in experiments due to decoherence and imperfections in state preparation.
We establish that these non-symmetric GHZ states are LU-equivalent to two graphical formalisms: (i) fully connected weighted hypergraph states, and (ii) controlled-unitary star-shaped graphs. Although weighted hypergraph states typically lack a stabilizer description, we construct a complete stabilizer set using only a single ancilla qubit, independent of system size.
Building on this, we consider a qutrit quantum error-correcting code with parameters [[n=3, k=1, d=2]]3, whose codewords take the form of GHZ states. We inject these codewords into quantum circuits arranged in brickwall architectures and construct new quantum codes. Using this method, we obtain both optimal and good codes.
Keywords: Non-symmetric GHZ states; Weighted graph states; Quantum error correction; Brickwall circuits; Ancilla-assisted stabilizers