Cache the target of AerSimulator

[wshanks]

What is the expected behavior?

Currently, generating a backend with AerSimulator() does not cache the .target property. The target is only cached if AerSimulator._from_backend is set by passing a target to AerSimulator's constructor. The target generation is somewhat expensive, about 0.7 seconds on my machine. When looping over circuits, this time can add up. Looking at the code, I think the target could be cached safely as long as the cache was invalidated by calling set_option since that is the only supported way of changing configuration() and properties() which are the only things AerSimulator.target references.

I noticed this when finally tracking down why some code that looped over circuits calling transpile had gotten slow (it had been slow for a while, probably since support for BackendV2 was added to Aer). I can address it locally by changing the code to call transpile on the lists of circuits but it would still be worth considering doing this caching if it seems reasonable to the maintainers.