(Disclaimer: I don't know much principles how quantum computers work)
The high-level idea for algorithm:
Select two random vertices in the first graph, call them "source" and "sink".
Create a wave starting from "source" that will propagate through the graph and collect at "sink", reflecting from leaf nodes, creating a unique complex number "fingerprinting" the graph.
For the second graph, iterate through all pairs of "source" and "sink", calculate the resulting fingerprints and check them for equality with the first one.
If an equal fingerprint was found, graphs are isomorphic, otherwise not.
Resolves YES if there is a peer-reviewed paper (referenced in comments) that confirms that algorithm identical to the above one can be implemented and will work OR if in university professor tells me that the above algorithm will work.
Resolves NO if conditions are not met till the close date.
This market can be resolved PROB in borderline cases according to my best judgement.
I will not bet in this market but may subsidize it.
1,000