I want to replace my existing heat pump thermostat, Carrier HH01AT171, with a programmable digital thermostat. Is Honeywell T8011R1006 compatible with the Carrier thermostat? Are the wiring the same?

First you need to read about your new thermostat.

LINK

http://customer.honeywell.com/techlit/pdf/69-0000s/69-1436.pdf

Then you have to compare the new ones wiring with the old because I have no information on the old Carrieer thermostat.