Engineering the Cost Function of a Variational Quantum Algorithm for Implementation on Near-Term Devices

Abstract: Variational hybrid quantum-classical algorithms are some of the most promising workloads for near-term quantum computers without error correction. The aim of these variational algorithms is to guide the quantum system to a target state that minimizes a cost function, by varying certain parameters in a quantum circuit. This paper proposes a new approach for engineering cost functions to improve the performance of a certain class of these variational algorithms on today's small qubit systems. We apply this approach to a variational algorithm that generates thermofield double states of the transverse field Ising model, which are relevant when studying 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.