Google+ Banner Size [Cover Photo]
Google Plus cover photo should have a minimum size of 480 x 270 pixels. The ideal size should be 1080 x 608 pixels. The largest image you can use on Google+ would be upto 2120 x 1192 pixels.
Profile Photo Size
The profile photo size for Google+ should be a 250 x 250 pixel square image. If you need better quality, you can upload an image more than 500 x 500 pixel in size though it would not be required in most cases if the small image itself has good clarity.