Normally the owner of the vehicle, at least if the driver was using it with their permission. Think about this before you let someone borrow your car.

How can you old the owner responsible for the AI's errors?

It's their car, they are operating it on the public roads.

The thing that gets me about this autonomous car thing is that it shouldn't really happen. When a car has to swerve to avoid an accident it is typically because the driver was speeding and/or not paying attention.

Autonomous cars wouldn't speed and they are always paying attention. Maybe you could argue that it happened because the other driver was drunk or for some other reason swerved into your lane but this is still an incredibly niche situation and if it does happen just sue that guy. The vast majority of car-to-car accidents happen when both drivers are irresponsible. Autonomous cars will significantly reduce accident rates just by following the rules of traffic and being constantly aware.

The whole who should be sued thing is asinine, just have a national insurance fund for it or whatever. Cheaper than all the accidents it prevents.

I’ve read that self driving cars almost always try to slow down /brake opposed to swerving for the simple reason of removing energy from any potential collision.

There was an article here serveral weeks ago about how in some self driving cars the brakes can be pre-loaded and can be used much quicker than a human could, reaction times aside.