  We introduce an adiabatic state preparation protocol which implements quantum
imaginary time evolution under the Hamiltonian of the system. Unlike the
original quantum imaginary time evolution algorithm, adiabatic quantum
imaginary time evolution does not require quantum state tomography during its
runtime, and unlike standard adiabatic state preparation, the final Hamiltonian
is not the system Hamiltonian. Instead, the algorithm obtains the adiabatic
Hamiltonian by integrating a classical differential equation that ensures that
one follows the imaginary time evolution state trajectory. We introduce some
heuristics that allow this protocol to be implemented on quantum architectures
with limited resources. We explore the performance of this algorithm via
classical simulations in a one-dimensional spin model and highlight essential
features that determine its cost, performance, and implementability for longer
times, and compare to the original quantum imaginary time evolution for
ground-state preparation. More generally, our algorithm expands the range of
states accessible to adiabatic state preparation methods beyond those that are
expressed as ground-states of simple explicit Hamiltonians.
