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

TL;DR

This paper introduces a novel method for engineering cost functions in variational quantum algorithms, enhancing their performance on current small-scale quantum devices, demonstrated on thermofield double states of the transverse field Ising model.

Contribution

It presents a new approach for designing cost functions to improve variational quantum algorithms on near-term quantum hardware, specifically applied to thermofield double state generation.

Findings

The engineered cost function improves algorithm performance across temperature ranges.

The approach yields better state fidelity compared to traditional cost functions.

Demonstrates applicability to condensed matter physics simulations.

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.