It appears that a springer book has been released on the topic : https://link.springer.com/book/10.1007/978-981-32-9796-8.
It covers both theory and applications of quantum computing to finance. Without having read all of it, it seems to be a serious (but expensive) source on the matter.
You should replace the differential of the correlated process dBt with its value in the volatility equation, then replace dW~t in the same equation with:
you will get an formula with Vt,W1t and W2t.
You can then simulate the volatility.