  Despite its simplicity and strong theoretical guarantees, adiabatic state
preparation has received considerably less interest than variational approaches
for the preparation of low-energy electronic structure states. Two major
reasons for this are the large number of gates required for Trotterising
time-dependent electronic structure Hamiltonians, as well as discretisation
errors heating the state. We show that a recently proposed randomized
algorithm, which implements exact adiabatic evolution without heating and with
far fewer gates than Trotterisation, can overcome this problem. We develop
three methods for measuring the energy of the prepared state in an efficient
and noise-resilient manner, yielding chemically accurate results on a 4-qubit
molecule in the presence of realistic gate noise, without the need for error
mitigation. These findings suggest that adiabatic approaches to state
preparation could play a key role in quantum chemistry simulations both in the
era of noisy as well as error-corrected quantum computers.
