Engineering a Cost Function for Real-world Implementation of a Variational Quantum Algorithm

Hybrid quantum-classical variational algorithm execution typically involve the use of quantum processing for state evolution, and classical processing for cost function evaluation and guiding optimization. This paper proposes a new approach for engineering cost functions for a certain class of quantum- classical hybrid variation algorithms, in order to improve performance of these algorithms on today's small qubit systems. In this work, we apply this approach to a variational algorithm that generates thermofield double states (in the transverse field Ising model), which are relevant for studying thermal phase transitions in condensed matter systems. We discuss the benefits and drawbacks of various cost functions, apply our new engineering approach and show that it yields good agreement across the full temperature range.