My work on multipartite entanglement distillation asks which parts of a quantum-state description are needed to simulate and optimize a purification protocol. Restricting attention to preserving operations can make the relevant dynamics much simpler to represent.
What role do GHZ-preserving gates play?
For GHZ states, I characterized local Clifford operations that preserve the GHZ basis and developed an affine binary description of their action on basis labels. A preserving gate can then update a compact label directly, avoiding repeated updates to a full stabilizer description.
In this representation, each online label update takes O(1) time, supporting noisy-circuit search and finite-resource distillation optimization. The details are in GHZ-Preserving Gates and Optimized Distillation Circuits.
How does graph topology enter the problem?
General graph states need not have the same symmetry as GHZ states. In the graph-state work, I characterized factorized graph-preserving Clifford operations using structural features such as bipartiteness and leaf configurations. These constraints yield compact homogeneous and bilocal gate families for graph-basis simulation.
Why organize operations across local Clifford orbits?
Locally Clifford-equivalent graph states belong to the same entanglement class, but their graph representations can expose different operational structure. Using minimum-edge representatives, I organized the preserving gate families across local-complementation orbits so that purification circuits can be transferred between equivalent states.
The graph-state purification preprint describes this framework and its numerical evaluation under gate and measurement noise.
Where can I find the implementations?
- GHZPreserving.jl: GHZ-preserving simulation and circuit optimization.
- GraphPreserving: representations and simulation of graph-preserving operations.
Next questions
My current work extends this approach to sequence control under correlated noise and resource-constrained graph-state synthesis. These projects ask how protocol history and resource construction affect the error structure available to later operations.
References
- Mingyuan Wang, Guus Avis, and Stefan Krastanov. GHZ-Preserving Gates and Optimized Distillation Circuits. arXiv:2510.25854 (2025). Preprint; submitted to Quantum.
- Mingyuan Wang, Guus Avis, Kenneth Goodenough, and Stefan Krastanov. Efficient Graph State Purification with Factorized Graph-Preserving Operations across Local Clifford Orbits. arXiv:2606.23809 (2026). Preprint; submitted to npj Quantum Information.