Abstract
Greenberger-Horne-Zeilinger (GHZ) states play a central role in quantum computing and communication protocols, as a typical multipartite entanglement resource. This work introduces an efficient enumeration and simulation method for circuits that preserve and distill noisy GHZ states, significantly reducing the simulation complexity of a gate on n qubits, from exponential O(2ⁿ) for standard state-vector methods or O(n) for Clifford circuits, to a constant O(1) for the method presented here. This method has profound implications for the design of quantum networks, where preservation and purification of entanglement with minimal resource overhead is critical. In particular, we demonstrate the use of the new method in an optimization procedure enabled by the fast simulation, that discovers GHZ distillation circuits far outperforming the state of the art. Fine-tuning to arbitrary noise models is possible as well. We also show that the method naturally extends to graph states that are local Clifford equivalent to GHZ states.
My contributions
- Classified GHZ-preserving local Clifford operations and derived an affine binary representation of their action on GHZ-basis labels, enabling O(1) online label updates.
- Used this representation for noisy-circuit search and finite-resource distillation optimization, and implemented the framework in GHZPreserving.jl.
Research overview
By restricting attention to operations that preserve the GHZ structure, this work represents gate actions as affine transformations of compact binary labels. Each online label update takes O(1) time in this specialized representation, making noisy-circuit simulation practical for distillation optimization. The construction also applies to graph states related to GHZ states by local Clifford transformations.
Cite this work
Mingyuan Wang, Guus Avis, Stefan Krastanov. GHZ-Preserving Gates and Optimized Distillation Circuits. arXiv:2510.25854 (2025). 10.48550/arXiv.2510.25854.
BibTeX citation
@misc{wang2025ghzpreservinggates,
title = {{GHZ-Preserving Gates and Optimized Distillation Circuits}},
author = {Mingyuan Wang and Guus Avis and Stefan Krastanov},
year = {2025},
eprint = {2510.25854},
archivePrefix = {arXiv},
primaryClass = {quant-ph},
doi = {10.48550/arXiv.2510.25854},
url = {https://doi.org/10.48550/arXiv.2510.25854}
}